Superradiant Thz Wave Emission from Arrays of Josephson Junctions

Ievgenii Borodianskyi Superradiant THz wave emission from arrays of Josephson junctions

Superradiant THz wave emission from arrays of Josephson junctions Ievgenii Borodianskyi

Ievgenii Borodianskyi

"Never memorize something that you can look up." - Albert Einstein

ISBN 978-91-7911-178-6

Department of Physics

Doctoral Thesis in Physics at Stockholm University, Sweden 2020

Superradiant THz wave emission from arrays of Josephson junctions Ievgenii Borodianskyi Academic dissertation for the Degree of Doctor of Philosophy in Physics at Stockholm University to be publicly defended on Wednesday 9 September 2020 at 13.00 in sal FR4, AlbaNova universitetscentrum, Roslagstullsbacken 21.

Abstract High-power, continuous-wave, compact and tunable THz sources are needed for a large variety of applications. Development of power-efficient sources of electromagnetic radiation in the 0.1-10 THz range is a difficult technological problem, known as the “THz gap.” Josephson junctions allow creation of monochromatic THz sources with an inherently broad range of tunability. However, emission power from a single junction is too small. It can be amplified in a coherent superradiant manner by phase-locking of many junctions. In this case, the emission power should increase as a square of the number of phase-locked junctions.The aim of this thesis is to study a possibility of achieving coherent superradiant emission with significant power and frequency tunability from Joseph-son junction arrays. Two types of devices are studied, based either on stacks (one-dimensional arrays) of intrinsic Josephson junctions naturally formed in single crystals of high-temperature cuprate superconductor Bi2Sr2CaCu2O8+x, or two-dimensional arrays of artificial low-temperature superconducting Nb/NbSi/Nb junctions. Micron-size junctions are fabricated using micro- and nanofabrication tools.The first chapter of this thesis describes the theory of Josephson junctions and how mutual coupling between Josephson junctions can lead to self-syn-chronization, facilitating the superradiant emission of electromagnetic radia-tion. The second chapter is focused on the technical aspects of this work, with detailed descriptions of sample fabrication and experimental techniques. The third chapter presents main results and discussion. It is demonstrated that de-vices based on high-Tc cuprates allow tunable emission in a very broad fre-quency range 1-11 THz. For low- Tc junction arrays synchronization of up to 9000 junctions is successfully achieved. It is argued that an unconventional traveling-waves mechanism facilitates the phase-locking of such huge arrays. The obtained results confirm a possibility of creation of high-power, continu-ous- wave, compact and tunable THz sources, based on arrays of Josephson junctions.

Keywords: Josephson junction, Superconductor, ThZ emission, high-Tc.

Stockholm 2020 http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-181234

ISBN 978-91-7911-178-6 ISBN 978-91-7911-179-3

Department of Physics

Stockholm University, 106 91 Stockholm

SUPERRADIANT THZ WAVE EMISSION FROM ARRAYS OF JOSEPHSON JUNCTIONS

Ievgenii Borodianskyi

Superradiant THz wave emission from arrays of Josephson junctions

Ievgenii Borodianskyi ©Ievgenii Borodianskyi, Stockholm University 2020

ISBN print 978-91-7911-178-6 ISBN PDF 978-91-7911-179-3

Printed in Sweden by Universitetsservice US-AB, Stockholm 2020 "If we knew what it was we were doing, it would not be called research, would it?” Albert Einstein

Abstract

High-power, continuous-wave, compact and tunable THz sources are needed for a large variety of applications. Development of power-efficient sources of electromagnetic radiation in the 0.1-10 THz range is a difficult technological problem, known as the “THz gap.” Josephson junctions allow creation of monochromatic THz sources with an inherently broad range of tunability. However, emission power from a single junction is too small. It can be amplified in a coherent superradiant manner by phase-locking of many junctions. In this case, the emission power should increase as a square of the number of phase-locked junctions. The aim of this thesis is to study a possibility of achieving coherent superradiant emission with significant power and frequency tunability from Joseph- son junction arrays. Two types of devices are studied, based either on stacks (one-dimensional arrays) of intrinsic Josephson junctions naturally formed in single crystals of high-temperature cuprate superconductor Bi2Sr2CaCu2O8+x, or two-dimensional arrays of artificial low-temperature superconducting Nb/NbSi/Nb junctions. Micron-size junctions are fabricated using micro- and nanofabrication tools. The first chapter of this thesis describes the theory of Josephson junctions and how mutual coupling between Josephson junctions can lead to self-synchronization, facilitating the superradiant emission of electromagnetic radiation. The second chapter is focused on the technical aspects of this work, with detailed descriptions of sample fabrication and experimental techniques. The third chapter presents main results and discussion. It is demonstrated that devices based on high-Tc cuprates allow tunable emission in a very broad frequency range 1-11 THz. For low- Tc junction arrays synchronization of up to 9000 junctions is successfully achieved. It is argued that an unconventional traveling-waves mechanism facilitates the phase-locking of such huge arrays. The obtained results confirm a possibility of creation of high-power, continuous-wave, compact and tunable THz sources, based on arrays of Josephson junctions.

Sammanfattning

Högeffekts, kontinuerliga våg, kompakta och inställbara THz-källor behövs för en mängd olika applikationer. Utveckling av energieffektiva källor för elektromagnetisk strålning i området 0,1-10 THz är ett svårt teknologiskt problem, känt som "THz-gap". Josephson-korsningar möjliggör skapandet av monokromatiska THz-källor med ett i sig brett spektrum av inställbarhet. Emissionskraften från en enda korsning är dock för liten. Det kan förstärkas på ett sammanhängande superradiant sätt genom faslåsning av många korsningar. I detta fall bör utsläppseffekten öka som en kvadrat av antalet faslåsta korsningar. Syftet med denna avhandling är att studera en möjlighet att uppnå koherent superradiantemission med betydande effekt och frekvensjusterbarhet från Josephson-korsningsgrupper. Två typer av anordningar studeras, baserade antingen på staplar (endimensionella matriser) av inneboende Josephson- korsningar som är naturligt bildade i enstaka kristaller av högtemperatursuprat-superledare Bi2Sr2CaCu2O8 + x, eller tvådimensionella matriser av konstgjorda låg temperatur superledande Nb / NbSi / Nb- korsningar. Korsningar i mikronstorlek tillverkas med hjälp av mikro- och nanofabriceringsverktyg. Det första kapitlet i denna avhandling beskriver teorin om Josephson- korsningar och hur ömsesidig koppling mellan Josephson-korsningar: er kan leda till självsynkronisering, vilket underlättar överstrålningsutsläpp av elektromagnetisk strålning. Det andra kapitlet är inriktat på de tekniska aspekterna av detta arbete, med detaljerade beskrivningar av provtillverkning och experimentella tekniker. Det tredje kapitlet presenterar huvudresultat och diskussion. Det demonstreras att enheter baserade på hög-Tc-koppar tillåter inställbar utsläpp i ett varierande brett frekvensområde 1-11 THz. För sammankopplingsmatriser med låg Tc uppnås synkronisering av upp till 9000 korsningar med framgång. Det hävdas att faslåsning av så mycket stora matriser underlättas av en okonventionell rörelsevågsmekanism. De uppnådda resultaten bekräftar möjligheten att skapa högeffekta, kontinuerliga våg, kompakta och inställbara THz-källor, baserade på matriser av Josephson- korsningar.

List of appended papers

This thesis is based on the following papers.

I. Borodianskyi, E.A., Krasnov, V.M. “Josephson emission with frequency span 1–11 THz from small Bi2Sr2CaCu2O8+δ mesa structures.” Nat.Commun 8, 1742 (2017).

Author’s contribution: I fabricated the sample, performed the measurements, contributed in data analysis and writhing of the manuscript.

II. M. A. Galin, E. A. Borodianskyi, V. V. Kurin, I. A. Shereshevskiy, N. K. Vdovicheva, V. M. Krasnov, and A. M. Klushin “Synchroni- zation of Large Josephson-Junction Arrays by Traveling Electro- magnetic Waves” Phys. Rev. Applied 9, 054032 (2018)

Author’s contribution: I have been taking active part in measurements and sample characterization and participated in writing the paper.

III. A. A. Kalenyuk, A. Pagliero, E. A. Borodianskyi, S. Aswartham, S. Wurmehl, B. Büchner, D. A. Chareev, A. A. Kordyuk, and V. M. Krasnov “Unusual two-dimensional behavior of iron-based superconductors with low anisotropy” Phys. Rev. B 96, 134512 (2017)

Author’s contribution: I helped with sample fabrication and low temperature electrical measurements.

IV. A. A. Kalenyuk, A. Pagliero, E. A. Borodianskyi, A. A. Kordyuk, and V. M. Krasnov “Phase-Sensitive Evidence for the Sign- Reversal s± Symmetry of the Order Parameter in an Iron-Pnictide Superconductor Using Nb/Ba1-xNaxFe2As2 Josephson Junctions” Phys. Rev. Lett. 120, 067001 (2018)

Author’s contribution: I helped with sample fabrication and low temperature electrical measurements

V. M.A. Galin, F. Rudau. E.A. Borodianskyi, V.V. Kurin, D. Koelle, R. Kleiner, V.M. Krasnov, A.M. Klushin, “Direct visualization of

iii

phase-locking of large Josephson junction arrays by surface elec- tromagenetic waves”. To be pubished…ArXiv:2004.06623

Author’s contribution: I have been taking active part in measurements and sample characterization and participated in writing the paper.

Papers not included in this thesis

VI. R. de Andrés Prada, T. Golod, O. M. Kapran, E. A. Borodianskyi, Ch. Bernhard, and V. M. Krasnov “Memory-functionality superconductor/ferromagnet/superconductor junctions based on the high-Tc cuprate superconductors YBa2Cu3O7−x and the colossal magnetoresistive manganite ferromagnets La2/3X1/3MnO3+δ(X=Ca,Sr)” Phys. Rev. B 99, 214510

Author’s contribution: I took part in measurements and assist with fabrication.

VII. M.A. Galin , E. A. Borodianskyi , V. V. Kurin , I. A. Shereshev- skiy, N. K. Vdovicheva , V. M. Krasnov , and A.M. Klushin,” Ev- idence of synchronization of large Josephson-junction arrays by traveling electromagnetic waves” EPJ Web of Conferences 195,02004 (2018)

Author’s contribution: I have been taking active part in measurements and sample characterization and participated in writing the paper.

List of abbreviations

AC alternative current Bi-2212 Bi2Sr2CaCu2O8+δ BSCCO Bi2Sr2CaCu2O8+δ BWO Backward-wave Oscillator DC direct current FFO flux-flow oscillator FIB focused-ion beam FPGA field-programmable gate array GHz gigahertz HTS high temperature superconductor IV current-voltage ICP inductively coupled plasma JJs Josephson junctions NIN normal metal-insulator-normal metal NIS normal metal-insulator-superconductor PCB printed circuit board RCSJ resistively and capacitively shunted junction RF radio frequency RIE reactive ion etching SEM scanning electron microscope SIS superconductor-insulator-superconductor THz terahertz UV ultraviolet YBCO yttrium barium copper oxide

Contents

Abstract i

Sammmanfatning ii

List of appended papers iii

Abbreviations v

Contents vii

I Introduction 1 1.1 Motivation 1 1.1.1 Overview of Terahertz sources 2 1.2 Josephson Effect in BSCCO 4 1.2.1 Tunnel junction 4 1.2.2 High-Tc BSCCO crystals 6 1.2.3 DC Josephson effect 8 1.2.4 AC Josephson effect 8 1.2.5 Current voltage characteristics,RCSJ model,sine-Gordon equation 9 1.2.6 Intrinsic Josephson junctions 11 1.2.7 Washboard potential 12 1.2.8 Switch current detector of electromagnetic radiation 13 1.3 Coherent supperradiant emission 14 1.3.1 Flux-flow emission from a single junction 15 1.3.2 The Coupled sine-Gordon equation for inductively coupled stacked Josephson junctions 16 1.3.3 Geometrical resonances in stacked junctions 18 1.3.4 Synchronization of large Josephson junction arrays 20

II Experimental 21 2.1 Sample fabrication and equipment 21 2.2 Low-temperature setup 37

III Results and discussion 41 3.1 Small-but-high Bi-2212 mesa structures characterization 41 3.2 THz generation 45 3.3 Switch current detector 47 3.4 THz radiation detection 49 3.5 Power efficiency 52 3.6 Radiation from large Josephson arrays 53

Summary 58 Acknowledgments 59 References 60

Appended papers 67

vii

I Introduction

1.1 Motivation

Thirty-five years ago, two researchers from IBM, Georg Bednorz and Alex Muller, discovered a novel class of superconductors that had significantly higher critical temperatures compared with previously known low-temperature superconductors [1]. For that, they received a Nobel prize in 1987. This discovery excited great interest in the field of superconductivity, with rising expectations for the possible development of novel applications. Such unconventional superconductors are classified as a separate group with the overall name of high- temperature superconductors (HTS or High-Tc). At present, various types of High- Tc superconductors exist. Particularly promising are copper-based superconductors that hold a record for critical transition temperature (Tc) at ambient pressure. The most well-known among them are those that contain bismuth-strontium-calcium-copper-oxide (BSCCO) and yttrium-barium-copper-oxide (YBCO) compounds. They have critical temperatures of around 100 K. However, there are HTS with even higher transitional temperatures, e.g. thallium [2] and mercury-based cuprates [3]. The latter has the highest Tc among cuprates: ~153 K under high pressure [3]. Today, however, the record Tc no longer belongs to cuprates. A recent study of H2S under an extremely high pressure of 150 GPa indicated the record high of Tc ~203 K [4]. This suggests that hydrogen-based compounds under higher pressures may likely reach even room-temperature superconductivity. High Tc is not the only advantage of HTS. They also have a larger superconducting gap. Furthermore, many cuprates are quasi-two-dimensional materials with high anisotropy. The layered structure of cuprates leads to the formation of natural stacks of atomic-scale “intrinsic” Josephson junctions (which will be studied in this thesis) because interlayer transport between conducting CuO2 planes occurs via tunneling [5, 6]. Conventional low-Tc superconductors have a gap in the range of 1 meV. This corresponds to microwave to far-infrared frequencies in the sub-THz range. However, HTS have tenfold higher values with regard to the superconducting gap. This allows usage of such materials in the terahertz range [7, 8]. It is advantageous for the creation of generators and detectors in the region between 0.1 and 10 THz, i.e, within the so-called “terahertz gap” [9]. There are several competing technologies (for example, quantum-cascade lasers) for the creation of emitters and detectors in this range, but they are mostly inefficient and limited for practical applications due to their size and cost. Furthermore, they are usually not tunable. Josephson junctions allow the direct conversion of DC voltage into high- frequency electromagnetic waves [10]. Employment of intrinsic Josephson

1 junctions in cuprate HTS provides an alternative way to create THz sources that can cover the frequency span of the terahertz gap. The goal of this thesis is to study the possibility of creating compact, continuous-wave and highly tunable THz sources based on Josephson junction arrays.

1.1.1 Overview of Terahertz sources

The Terahertz radiation in the range from 1-30THz attracts tremendous growing interest in material science, imaging, and safety, defense applications [11]. This type of radiation was first observed at the beginning of the 20th century and been poorly investigated for a long time. But in the past twenty year’s situation changed towards the rapid development of various THz sources [12]. Here I will briefly cover existing THz sources and also successes in the superconducting direction. The semiconductor oscillators or Solid-State Oscillators are a compact source in a frequency range of 100GHz to 1THz, and due to their compactness, the application range is continuously growing. The outcome power in the range of 100GHz is about 100mW while with increasing the frequency the power drops to 0.1-1mW [12, 13]. The Quantum Cascade Laser sources are one of the new inventions in the Terahertz range. Here electrons are injected to the periodic structure of a superlattice under applied bias where during the transition, a THz photon emission occurs with correspondent excitation by resonant tunneling [12, 14]. The first commercial Quantum cascade laser emitted 4.4THz and provided 2mW of power at an operating temperature of 50K [15]. But the average power from QCL is rapidly decreased by lowering the emitted frequency. The laser-driven THz sources are based on frequency conversion from the optical range. There are two techniques used to achieve THz emission, one is from a femtosecond laser with a wide range of THz frequencies where the upper limit is settled by carrier recombination time[16,17], and another way to get THz spectrum is thought a sub-picosecond laser pulse to a crystal with a large second- order recipiency [18]. Those sources are mainly operated in the range of 0.2 to 2 THz. Other THz sources can be organized in a category as Free Electron Based sources. Here are such examples as Travelling Wave Tubes, Backward Wave Oscillators, and Klystrons. Those sources mainly suffer from metallic wall losses and the need for high magnetic and electrical fields [12]. But BWO is the candidate that can operate by moderate power levels up to 100mW and can be tuned in the range of 30GHz to 1.2THz. In parallel to semiconducting THz sources, a completely different technology for THz wave generation was discovered by Ozyuzer [8, 19]. Where the sub- micro-watt power at a frequency range of 0.36 to 0.86THz coherent emission was obtained from a Bi2212 single crystal mesa. Further improvement in the fabrication processes and experimenting with mesa shapes and amount of the

2 intrinsic Josephson junctions by the research groups came to a 2.4THz frequency obtained from an inner branch of IV from cylindrical mesa [20]. While for rectangular mesa were observed in the frequency range of 0.3THz to 1.6THz [19, 21-23]. The most important feature for superconducting THz emission from intrinsic Josephson junction remains the output power that nowadays varies from 1 to 110μW for different types of mesa structures [23, 24]. And 620μW power at 0.51THz frequency from synchronization of an array of three conventional mesas [24]. That multi-mesa synchronization mechanism is essential for the future development of high-power and tunable High-Tc THz generators.

3 1.2 Josephson Effect in BSCCO

1.2.1 Tunnel junction

In tunnel junctions, a charged carrier performs quantum-mechanical tunneling trough an insulating barrier. A tunnel current is strongly depends on an applied voltage and keeps essential information about the electronic density of states. On this principle the scanning tunneling spectroscopy is based [25]. When a voltage (eV) is applied to the tip, electrons from occupied states in the conduction band are caused to tunnel through the barrier to unoccupied states. A normal metal-insulator-normal metal (NIN) junction IV characteristic will be linear at small voltages, as shown in Fig. 1.1, and asymptotically rises as the bias eV approaches the barrier height value [26].

Figure 1.1: Current-voltage characteristics of a NIN junction, where ϕ ~1 eV the barrier height [26].

Consider the tunnel junction made of a normal metal-insulator-superconductor (NIS); the correspondent IV will change, at bias voltages around ~1–10 mV corresponding to the energy gap of a superconductor will be visible [25]. The following equation can describe the tunnel current:

1 ∞ |퐸| 퐼푡 = ⁄ ∫ ⁄ 2 2 1/2 [푓(퐸) − 푓(퐸 + 푒푉)]푑퐸 (1.1) 푒푅푛 −∞ [퐸 − ∆ ]

where ∆ is an energy gap of the superconductor, f(E) is the Fermi-Dirac distribution function. Fig.1.2 (below) shows the corresponding IV for a NIS junction where differences with respect to NIN case, Fig.1.1. The step in the current at eV=∆ reflects the singularity of the electronic density of the states in a superconductor.

4 For a superconducting SIS tunnel junction, with two superconducting electrodes, there are two transport channels: for Cooper pairs, residing at the Fermi level and for single electrons (quasiparticles). The density of states for the latter is split into valence and the conducting bands separated by twice the superconducting energy gap. When a small voltage, eV<2∆ is applied, a quasiparticle current cannot flow through the junction , as quasiparticles below the gap on the right electrode do not have access to empty states on the left electrode. When applied voltage exceeds this limit, the quasiparticle current becomes possible and the current increases rapidly due to singularities in the density of states. At significantly large voltages the current-voltage characteristics become ohmic with a normal resistance Rn [26].

Figure 1.2: Current-voltage characteristics of the NIS junction, the convolution of the tunneling densities of state [26].

If the superconducting tunnel junction consists of two different types of superconducting materials, each superconductor has a different energy gap that are marked as ∆1 and ∆2 respectively. Fig. 1.3 shows band structure for such junction. An expression for tunnel current is given by [26]:

1 1 ∞ 2 2 퐼 = 1⁄푒푅 |퐸|⁄[퐸2 − ∆ ]2 × |퐸 + 푒푉|⁄[(퐸 + 푒푉)2 − ∆ ]2 × 푠푠 푛 ∫−∞ 1 2 [푓(퐸) − 푓(퐸 + 푒푉)]푑퐸 (1.2)

Where |퐸| > ∆1 and |퐸 + 푒푉| > ∆2. Current-voltage characteristics for such junction shown in Fig. 1.4. At a finite temperature T>0, in addition to a current step at a sum-gap voltage 푒푉 = ∆1 + ∆2, there is also a peculiarity at a difference voltage 푒푉 = |∆1 − ∆2|.

Figure 1.3: Energy diagram for a superconductor-insulator- superconductor (SIS) junction, in this particular case for Sb/Sb- oxide/Pb [26, 27].

Figure 1.4: Current-voltage characteristics for SIS tunnel junction [26].

1.2.2 High-Tc BSCCO crystals

Bi2Sr2Can-1CunO2n+4+δ (BSCCO) or, to give the compound its familiar name, bismuth-strontium-calcium-copper-oxide, belongs to a group of high-Tc superconductors. When n = 2, the general formula changes to Bi2Sr2CaCu2O8+δ which is also called Bi-2212 due to the first four indices. It was discovered in 1988 by a Japanese group of physicists and was the first high-Tc superconductor

6 known at that time that did not consist of rare earth elements, in comparison with YBa2Cu3O7 [28]. As a cuprate superconductor, it has a perovskite-type structure with copper oxide layers where superconductivity occurs. Perovskites are a class of materials that have the same type of structure as calcium titanium oxide (CaTiO3), with oxygen atoms located at the edge centers [29]. The Bi-2212 unit cell (shown in Fig. 1.5) is orthorhombic with a scale in a and b planes of ≃ 0.544 nm and c ≃ 3.090 nm. It includes 15 layers or 2[Bi2Sr2CaCu2O8] due to reasons of symmetry [30].

Figure 1.5: A schematic structure of Bi-2212 with two copper oxide layers that form superconducting layers with thickness d = 3 Å and insulating layers BiO and SrO t = 12 Å [31].

Copper oxide layers have a thickness of d ≃ 3Å, while the thickness of the separating layer of BiO and SrO is t ≃ 12Å; this gives the superconducting layer periodicity of s=15Å. Bonding energies between different layers vary, with the weakest bonds located between the insulating BiO planes, which allows crystal splitting along them. The layered structure with a high anisotropy creates intrinsic Josephson junctions with a high-quality factor.

7 In parent, Bi-2212 compound is not superconducting. Superconducting ability can be reached by oxygen doping. A δ coefficient should be around 0.1-0.23. Additional oxygen atoms require two more electrons for each of them. To fulfill this requirement, transformation of the copper 2+ ions into 3+ state takes place, and finally leading to formation of superconducting hole-doped CuO2 planes [32]. Critical temperatures vary with δ. The best achieved Tc of 95 K was for δ = 0.16. However, it also depends on ion substitution in prepared crystals and can be increased by substitution of Pb (Bi, Pb)2Sr2CaCu2O8, which gives a maximum achieved Tc of 102 K [33].

1.2.3 DC Josephson effect

If a small current is sent through the Josephson junction or also called weak link, it would pass without resistance, even if the link material is non-superconducting. Similar wave functions describe superconductivity condensate on both sides of 푖휑푖 the junction 휓푖 = √푛푖 푒 [26] (ni are density of the superconducting Cooper pairs in electrodes, φi are phases). A potential energy of 푈2 − 푈1 = 2푒푉 that exists between electrodes allows writing of the following coupled Schrödinger equations:

휕휓 𝑖ℏ 1 = 푈 휓 + 퐾휓 , 푑푡 1 1 2 휕휓 𝑖ℏ 2 = 푈 휓 + 퐾휓 , (1.3) 푑푡 2 2 1

where K as coupling constant. For a finite phase difference Δ휑 = 휑2 − 휑1, it leads to a supercurrent flow:

퐼 = 퐼푐 sin ∆휑 (1.4)

This equation was predicted in 1962 by David Josephson [34] and is also named as the 1st Josephson equation. It represents the DC Josephson effect, where 1/2 퐼푐 = 2퐾(푛1푛2) /ℏ is the critical current of the junction.

1.2.4 AC Josephson effect

The 2nd Josephson equation, also called the voltage-phase relation is:

휕(Δ휑) 2푒푉 = , (1.5) 휕푡 ℏ

For the fixed applied voltage difference over the barrier, there is a continuous increase of the phase difference [26]

2푒푉 Δ휑(푡) = Δ휑(0) + 푡, (1.6) ℏ

The Josephson current will oscillate at a defined frequency, or so-called Josephson frequency:

2푒푉 푓 = , (1.7) ℎ

−1 Voltage-dependent frequency is 푓/푉 = 2푒/ℎ = 1/훷0 = 483.6 GHz m푉 . -15 2 Here Φ0 – flux quantum ≈ 2.07∙10 Tm [26]. Therefore, the Josephson junction allows direct conversion of the DC voltage into high-frequency electric current.

1.2.5 Current-voltage characteristics, RCSJ model, sine- Gordon equation

Josephson relations cannot entirely describe all the physics of the actual Josephson junction. A more detailed description is given by a resistively and capacitively shunted junction (RCSJ) model, where the sum of the supercurrent Is, the quasiparticle current Iqp and the displacement current Idis gives the total current through the junction. In terms of phase difference, the overall equation can be written out as:

2 푉 푑푉 Φ0 휕휑 퐶Φ0 휕 휑 퐼 = 퐼푠 + + 퐶 = 퐼푐푠𝑖푛Δ휑 + + 2 , (1.8) 푅푞푝 푑푡 2휋푅 휕푡 2휋 휕푡

Here Rqp is the quasiparticle resistance, and C is the capacitance of the junction. The IV curve shape depends on McCumbers parameter 훽푐 = 2 2휋퐼푐푅푞푝퐶/Φ0 [35]. The equation simplifies through introducing the Josephson plasma frequency 휔푝 = √2휋퐼푐/Φ0퐶 which defines 휏 = 휔푝푡 and the quality factor푄 = 휔푝푅퐶.

퐼 1 휕휑 휕2휑 = 푠𝑖푛Δ휑 + + 2 , (1.9) 퐼푐 푄 휕휏 휕휏

푄 related with so-called “damping factor” 훼 and the McCumbers parameter as following 푄 = √훽푐 = 1/훼. The quality factor influences the shape of the IVs. In other words, when 푄 or 훽푐 ≫ 1 the current-voltage characteristic become underdamped and, in the case of 푄 < 1, overdamped. Current-voltage

9 characteristics in underdamped and overdamped cases are presented in Fig. 1.6 where the difference between hysteresis type IV and non-hysteresis IV can be seen[35].

Figure 1.6: Two IV characteristics (a) in the underdamped case with the McCumbers parameter 훽푐 ≫ 1, large R and C, (b) in the overdamped case with the McCumbers parameter 훽푐 < 1 and small R and C.

However, the RCSJ model has a limitation. It neglects possible screening of the magnetic field by supercurrent in the junction. Therefore, it is valid only for “short” junctions. The phase variation over the sample length in the x-direction is caused by the magnetic field applied in the y-direction at the moment when the current flows perpendicular to both of them through the junction in the z- direction. In that case, an additional term is added to equation (1.9). It describes the phase dynamics over the junction [36].

2 2 푗 1 휕휑 휕 휑 2 휕 휑 = 푠𝑖푛Δ휑 + + 2 − 휆퐽 2 , (1.10) 푗푐 푄 휕휏 휕휏 휕푥

This equation is called a sine-Gordon equation. The Josephson penetration depth here 휆퐽 describes how deep the magnetic field penetrates into the junction.

Φ0 휆퐽 = √ (1.11) 2휋휇0푗푐Λ

Λ is an effective magnetic thickness (penetration of the magnetic field into the junction and electrodes in the z-direction). An equation for it is [35]:

10 푑 Λ = 2휆푠 tanh + 푡 (1.12) 2휆푠

The electrode thickness is represented by d, which in the case of BSCCO crystals is 3Ǻ. 휆푠 is the London penetration depth of a superconductor, while t represents the thickness of the insulating layer, which is 12Ǻ. Equation (1.12) is more general and can be simplified. For 푑 ≫ 휆푠when the electrode is thicker than the London penetration depth, it will transform to:

Λ = 2휆푠 + 푡 (1.13)

And when 푑 ≪ 휆푠 the equation transforms into an even simpler form:

훬 = 푑 + 푡 (1.14)

This equation will give a value of 훬 – 1.5nm, which is equal to the single junction thickness in the BSCCO crystal [35,36].

1.2.6 Intrinsic Josephson junctions

As has been mentioned above, the naturally created Josephson junctions inside the BSCCO crystals are atomically perfect and settle between double copper oxide planes. The total size of the junction due to the lattice structure is 1.5 nm in the c-axis direction. Strong anisotropy of the crystals in the normal state and a critical current with a high bypass resistance create the underdamped junctions with a high-quality factor Q. Bi-2212 has the London penetration depth 휆푠 of around 75-100 nm inside the copper oxide planes [37]. However, knowing that screening currents only fill d/s part of the total volume [38]. Therefore, in the ab-plane the effective London penetration depth for a field in the c-direction is:

푑 휆 = 휆 √ (1.15) 푎푏 푠 푠 while the effective penetration depth for a field in the ab-plane depends on the anisotropy 훾 and determined as:

휆푐 = 훾휆푎푏 (1.16)

Typical penetration depth values in Bi-2212 are much larger than the thickness of the junction in total (0.15 µm to 0.30 µm for 휆푎푏 and 15 to 180 µm for 휆푐

11 [37, 38]) and the effective magnetic thickness according to Eq. (1.14) is Λ = 푑 + 푡 = 푠 ~ 1.5푛푚. Its small value affects the Josephson penetration depth:

Φ0 휆퐽 = √ (1.17) 4휋휇0푗푐푠

Which corresponds to a large 휆푐, Eq. (1.16).

1.2.7 Washboard potential

A Josephson junction can be characterized by a Hamiltonian ℋ, as a function of the phase difference between two superconducting electrodes.

휕2 ℋ = −4퐸 − 퐸 cos 휑 (1.18) 푐 휕휑2 퐽

Where 퐸푐 and 퐸퐽 are the charging and Josephson energies, respectively [39]. 퐸푐 is usually much and can be neglected. In this case, the dynamics of phase in the junction can be represented as a motion of an imaginary particle locked into the potential gap of a washboard potential, shown in Fig.1.7.

퐼 푈(휑) = −퐸퐽[cos 휑 + ( )휑] (1.19) 퐼푐

If I

퐼 3/2 Δ푈 ≃ (4√2푈0/3) (1 − ) (1.20) 퐼푐

12 But in the presence of thermal fluctuations, the critical current is not well- defined, so only an escape rate or probability of switching from the stationary to the running state can be defined:

휔푝 Γ = 푎 ( ) 푒(−Δ푈/푘퐵푇) (1.21) 푡 푡 2휋

Here 푎푡 is an order unity coefficient. And here clearly it can be seen that the escape rate changes from rare occasions for a small current when Δ푈~2퐸퐽 ≫ 푘퐵푇 to a large rate 휔푝/2휋 for I=I0.

Thermal escape

ΔU

Potential (a.u.)

Electromagnetic wave Phase

Fig. 1.7 Tilted washboard potential diagram of the Josephson junction. Arrow is showing possible escape of the particle via thermal or electromagnetic activation.

1.2.8 Switching current detection of electromagnetic radiation

The incoming electromagnetic wave can also cause the escape from the potential as thermal fluctuations do. The high frequency signal induces alternating current in the junction, which shakes the wash-board potential and, therefore, switching current. This allows usage of a Josephson junction as a sensitive detector for radiation detection. The sensitivity of such detector can be tuned by adjusting the amplitude of the low-frequency ac bias current Iac, which

13 determines the maximum value of the barrier height Eq. (1.20). The total current in the detector will be 퐼 = 퐼푎푐 + 퐼푇퐻푧. Where ITHz is the high-frequency current induced by the incoming THz radiation. Therefore, a reduction of the switching current in the presence of radiation directly indicates the amplitude of the induced current +ITHz as shown in Fig. 1.8.

I = 0 THz

I I THz

I ≠ 0 THz

Fig.1.8: Sketch of the switch-current detector principle. With an absence of incoming radiation the switching current is equal to the critical current of the junction, with incoming radiation switching occurring with suppressed switching current by THz signal.

1.3 Coherent superradiant emission

There are two steps to achieving coherent superradiant emission from Josephson junctions: firstly, by creating a stack of JJs using BSCCO crystals; secondly, by creating a large array of JJs. The total radiative power from such structures is proportional to the total number of active junctions squared.

2 푁 푃푟푎푑~퐸 퐸푎푐 = ∑푖=1 퐸푖 (1.22)

2 For the in-phase case the total power will be Ei = Ei+1, Eac = NEi, P~N . This represents the supperradiant amplification of radiation. On the other hand, for the out-of-phase state: Ei= - Ei+1, Eac = 0 and the total power will be P~ 0. This represent the coherent suppression of radiation (destructive interference).

14 1.3.1 Flux-flow emission from a single junction

Josephson junctions, due to their properties, can be used as electromagnetic generation sources [35]. One of possible ways to achieve generation is through motion of fluxons. A fluxon, is a vortex, circulation of a supercurrent within the junction. The supercurrent varies at a scale of a Josephson penetration depth from the center of the vortex and the total magnetic flux induced – equals to the single flux quantum Φ0. When a bias current is applied to the junction it exerts a Lorentz force on a vortex and causes its motion. This motion generates electromagnetic waves. Devices built on such a basis are called flux-flow oscillators or in short FFO [40-43]. The fluxon motion can be affected by interaction with Abrikosov vortices in junction electrodes, close to the junction. Unique designs of pinning centers for trapping Abrikosov vortices can be used for creating memory elements based on a single vortex and a single Josephson junction [44]. For a better understanding of how the flux-flow oscillator works, a simple illustration of a single JJ is given in Fig. 1.9. Here are some important notes about a junction for flux-flow generators. The long side length L of the junction should be larger than the Josephson penetration depth. An external magnetic field B should be applied perpendicular to the entire length of the junction and placed parallel to the dielectric layer [43].

I B

VFF

Figure 1.9: Flux-flow oscillator, I – bias current, B – applied magnetic field, VFF – fluxon velocity, electromagnetic wave radiated when fluxon escapes the junction

The repulsive forces between fluxons leads to the formation of a fluxon chain within the junction. This chain of fluxons is pinned at the edges of the junction. A Lorentz force pushes fluxons when the bias current is applied through the junction. Above some critical value, the Lorentz force becomes larger than the pinning force and the fluxon chain starts moving. As a result of this unidirectional movement, fluxons enter into the junction from one side and exit on the other side. A balance is establishing between the Lorentz and the viscous damping forces at any bias value, so fluxons move with the constant velocity vFF. Fluxon movement also induces a flux-flow voltage that can be defined via the AC-

15 Josephson relation 푉⊥ = Φ0푣퐹퐹/퐿. A phase shift inducing by each fluxon is ∆휑 = 2휋 [43]. Each fluxon requires some time to pass over the junction; this time is equal to 푡 = 퐿/푣퐹퐹 The total number of the fluxons in the junction linearly depends on the length and magnetic field B, and can be calculated as 푁 = 퐵푑푒푓푓퐿/Φ0. Therefore, the total voltage VFF is:

푉퐹퐹 = 푁푉⊥ = 퐵푑푒푓푓푣퐹퐹 (1.23)

This equation shows that the flux-flow voltage depends on the flux-flow velocity and the applied magnetic field but is utterly independent from the junction length. Current increase leads to an acceleration of fluxons to the limiting velocity, or Swihart velocity c0. It is the speed of light in the junction, which behaves as the superconducting transmission line. Electromagnetic waves appear when the fluxon escapes from the junction. The amount of fluxons that reach the edge of the junction per second affects the final frequency where 푓 = 퐵푑푒푓푓푣퐹퐹/Φ0 [43] The same frequency can be obtained via the AC-Josephson equation (1.7) 푓 = 푉퐹퐹/Φ0 . Some part of the emission is reflected back and thus excites cavity resonances and standing waves in the junction. As a result, geometrical (Fiske) resonances occur. Oscillators based on the single Josephson junction are well developed and show budding promise as local oscillators [45]. Increasing the total number of junctions can enable a higher emission power, but coherent oscillation for such purposes is required. Junctions should be coupled with each other for that. Such a result has been achieved in Ref. [46] with an array of 2D JJs where junctions have been synchronized by an external resonator.

1.3.2 The Coupled sine-Gordon equation for inductively coupled stacked Josephson junctions

As seen in part 1.2.6 above, superconducting layers in Bi-2212 are thinner in comparison with the penetration depth 휆푎푏. Therefore, magnetic field cannot be screened by a single layer and screening currents in one of the junctions will influence nearby junctions. This leads to all junctions being inductively coupled via a shared magnetic field.

A two-junction stack The simplest case is that for a stack with two identical junctions [47]. In this case coupled-sine Gordon equation can be written as:

2 2 휕 휑1 1 −푆 퐽1 휆퐽 2 ( ) = ( ) ( ) (1.24) 휕푥 휑2 −푆 1 퐽2

16 Where the coupling parameter is determined as

휆 푆 = 푠 (1.25) Λ sinh푑⁄휆푠

Where Λ an effective magnetic thickness and is given by Eq. (1.12) and 퐽1,2 are currents through the two junctions according to RCSJ model. This equation can be solved analytically under certain conditions. In the case 2 퐽푖 −2 휕 휑𝑖 of small Josephson current and zero bias current = 휔푝 2 and 휑푖 = 퐽푐 휕푡 𝑖푘푥(푥−푢푡) 퐴𝑖푒 the equation can be written as:

휑 휑 −2 1 −2 1 −푆 1 푢 ( ) = 푐0 ( ) ( ) (1.26) 휑2 −푆 1 휑2

1 Where 푐 = 휆 휔 = 푐√ is the Swihart velocity of the single junction. 0 퐽 푝 4휋Λ퐶 Calculation of eigenvalues will result in:

−2 −2 −2 푐0 − 푢 −푐0 푆 | −2 −2 −2| = 0 −푐0 푆 푐0 − 푢

푐0 푢± = (1.27) √1±푆

This equation gives two characteristic velocities in the stack of two junctions, and it is seen that one of them is higher, while another is lower than the velocity 푐0 for a single junction. Higher velocity corresponds to the in-phase mode 휑1 = 휑2; the lower corresponds to the out-of-phase mode 휑1 = −휑2.

A N-junction stack In the stack of N junctions, the phase change in i-junction is related to i±1 junction, and the sine-Gordon equation transforms to a coupled equation or CSGE [39, 47-53]. Considering the case when all junctions are identical, the CSGE equation is:

휑1 1 푆 0 퐽 1 ⋮ 푆 1 푆 ⋮ 휕2 0 휆2 = ⋮ ⋱ ⋱ ⋱ ⋱ ⋮ 퐽 (1.28) 퐽 휕푥2 푖 ⋮ 0 푆 1 푆 ⋮ (휑푁) ( 0 푆 1) (퐽푁)

17 where:

2 휕휑푖 1 휕휑푖 푗 퐽푖 = 2 + + sin 휑푖 − (1.29) 휕휏 푄 휕휏 푗푐

A system of coupled differential equations sets the boundary conditions in the external magnetic field [39, 48, 52]

휕휑푖 2휋휇0 + | = 퐻0Λ(1 − 2푆) (1.30) 휕푥 푥=0,퐿 Φ0

As the sine-Gordon equation has the form of a nonlinear wave equation, the Josephson junction can be represented as a chain of pendulums. For small amplitudes, plasma waves can exist in the junction with the following dispersion relation for a single junction:

2 2 2 2 휔(푘) = 휔푝 + 푘 푐0 (1.31)

As we have already seen for the two-junction stack, Eq. (1.27), coupling in the multi-junction stack with the coupled Sine-Gordon equation leads to splitting of dispersion relation of electromagnetic waves into N branches with different characteristic velocities [53].

푐 푐 = 0 , 푛 = 1, … , 푁 (1.32) 푛 푛휋 √1+2푆 cos 푁+1

Here N is the number of junctions in the stack With a few simplifications, it can be seen that the slowest velocity is

푐 N≈푐 0/√1 + 2푆 and almost does not depend on N [53] as it is shown in Fig. 1.10. For the single-junction the plasma waves 휔(푘) dispersion relation depends on the in-plane wave vector k. Meanwhile for stacked junctions, there is an additional component, the wave vector q for the c direction [53]. The amount of modes in the c direction is determined by the number of junctions, N, in the stack. 푛휋 Wave numbers are quantized, 푞 = n=1…, N, and characteristic velocities are 푛 푁푠 given by Eq. (1.32) cn. For standing waves, in-plane, there are another standing 푙휋 wave mode number l =1, 2…., 푘 = [39, 54], where L is the in-plane length of 푙 퐿 the stack.

1.3.3 Geometrical resonances in stacked junctions

For a single Josephson junction, geometrical resonances occur when integer number of half-wave length of electromagnetic waves fit into the junction length.

18 This leads to formation of standing waves in a transmission line, formed by the junction. Geometrical resonances lead to appearance of Fiske steps in current- Φ 퐶 voltage characteristics at 푉 = 0 0 푛, which correspond to the condition that 푛 2퐿 Josephson frequency coincides with the geometrical resonance (cavity mode) frequency. Fiske steps appear due to the interaction between the Josephson current and the standing electromagnetic wave. Such behavior forms step-like current levels which were firstly observed by M. Fiske in 1965 [55] and named after him. For stacked Josephson junctions the number of cavity modes is enhanced due to splitting of the dispersion relation of electromagnetic waves. Therefore, Fiske steps may appear at:

Φ 푉 = 0 푙푐 (1.33) 푛,푙 2퐿 푛

Different modes correspond to different configurations of electric fields in the stack. As for the two-junction stack, the slowest mode cN corresponds to the out- of phase state, 퐸푖 = −퐸푖+1, and the fastes mode c1, to the in-phase state 퐸푖 = 퐸푖+1. Consequently, the superradiant amplification of emission should occur only for the c1 mode. For a rectangular stack with in-plane sizes Lx, Ly two-dimensional cavity modes occur. The expecting frequencies of strongly emitting in-phase geometrical resonances are:

2 2 푐1 푙 푛 푓푛,푙 = √ 2 + 2 (1.34) 2 퐿푥 퐿푦

Figure 1.10: Velocities of the fastest c1 and the slowest cN electromagnetic wave modes in stacked Josephson junctions as a function of the number of junctions. cN almost does not depend on N. Calculation from [54].

From Eq. (1.32), c1 depends on N. the corresponding dependence is shown in Fig. 1.10. For Bi-2212 c1 ≈ 0.1c for 200 junctions (c – the speed of light in vacuum) as can be seen from Fig. 1.10 [54]. Fiske steps have since been observed in stacked junctions of Bi-2212 [56-59] as shown in Fig. 1.11.

Figure 1.11: Fiske steps observed in Bi-2212 mesastructure from Ref. [59]

One quite important notice is that the Fiske steps amplitudes depend on the applied external magnetic field. Step amplitudes oscillate with field those steps that close to velocity matching condition VFF~ c0 have the highest amplitude [35, 43]. Mode l calculated from simple equation VFF/NFF=Vn,l gives l=2Φ/Φ0. Even l steps oscillate in-phase while odd in anti-phase with Ic(H) oscillation. And the quality factor of geometrical resonances is Qn,l = 2πfn,lReffC, where Reff is effective damping resistance [44, 60].

1.3.4 Synchronization of large Josephson junction arrays

High-Tc superconductors have higher values for the superconducting gap in comparison with conventional superconductors. Using intrinsic Josephson junctions, it is possible to convert DC-voltage into electromagnetic radiation in the whole THz range. However, it is most challenging to let them oscillate in a synchronized way to reach a higher power of emitted radiation. To get a sufficient power output, huge arrays with thousands of Josephson junctions are required, and such arrays may easily be larger than 1 cm and larger than the wavelength 휆 for sub-THz frequencies.

20 One of the ways to synchronize junctions discussed above is based on a resonant electromagnetic mode by some external cavity [46] or within the junction [54, 60-62]. However, as we would like to employ very large arrays of junctions, it becomes progressively harder to achieve a synchronized superradiant emission. Junctions parameters may vary as well environmental conditions thus complicating synchronization.

The alternative proposal is to synchronize very large arrays of Josephson junctions in a non-resonant manner by travelling electromagnetic waves, similar to operation of traveling wave antenna. [63-65]. The primary feature of the traveling-wave antenna is the strong forward- backward asymmetry of the emission with a significant amount of power in the forward direction of propagation of the traveling wave [66]. In other words, coherent emission can occur due to the unidirectional propagating wave imprinting the defined phase distribution over the whole array. It has been suggested in Ref. [65, 67] that large Josephson junction arrays can work as a Josephson traveling-wave antenna with similarities to the operation of a Beverage antenna [64]. Such antenna has an asymmetric directionality diagram with a maximum in the direction of the wave propagation at the angle α = arccos ℎ/푘, where h is the wave number of current oscillations that occur in the antenna, and k is the wave number for the emitted wave. If the ratio between h/k < 1, the traveling wave will be radiating to the lateral direction, and h/k > 1, when the angle α becomes imaginary, our traveling wave turns into a surface plasmon that travels between the wafer and the electrodes, with radiation taking place from ends of the Josephson junction array.

21 II Experimental part

2.1 Sample fabrication and equipment

This section describes several significant steps: the micro- and nanofabrication tools; a measurement set-up; and the sample preparation steps. The fabrication process requires the selection of a BSCCO crystal and the creation of a final stack of Josephson junctions by various micro and nano-fabrication techniques. More- over, an important part of the process is to etch a significant amount of JJs and create defined shaped mesa structures for future measurements. All samples were fabricated at the AlbaNova NanoFabLab, and electrical measurements at low- temperatures were made at the CryoLab of the EKMF group. The key for the presented work is fabrication of high-quality samples. That fabrication process contains several steps, including: selecting a crystal; cleaving; e-beam evaporation; lithography processes; oxygen ashing; Ar ion etching; magnetron sputtering; bonding; and finally, SEM/FIB manipulation for curing some cracks or for cutting off short circuits and shaping final mesas. The technological process is similar for all devices that were produced in previous works [38, 43], but the experimental strategy entirely different.

Crystal cleaving The first and essential task is to select and cleave the initial crystal. I use sapphire substrates with dimensions of 5×5 mm; as crystal carriers for creating a final sample with contact pads, A BSCCO crystal should be small enough, around 200×200 µm, to be placed on the center of the sapphire to simplify the creation of future contact electrodes. If the crystal is too big, it should be cut with a scalpel into smaller pieces. The BSCCO crystal must be cleaved in two parts to create a fresh surface for future Josephson junction stacks, as a non-cleaved crystal has an oxidized surface, which does not allow sending current through it. After the crystals are selected, they are fixed for the cleaving process — an epoxy glue 353ND was used for this. I use sapphire substrates with dimensions of 5×5 mm; as crystal carriers for creating a final sample with contact pads. The small drop of epoxy is placed on top of the substrate and the crystal is placed on it. Due to capillary forces, epoxy will capsulate crystal, so another substrate is put on top. It is rotated by 45 degrees respectively to the lower one. This will minimize the hardness of the cleaving process and it will be easier to manipulate with substrates. The glued crystal between two sapphire substrates is shown in Fig. 2.1. It can be seen that the epoxy reaches the bottom part of the substrate as it became more viscous during heating. It also requires time to reach its full

22 strength and hardness. This can be achieved by leaving such sandwiches for 12 hours; also, it can be achieved more quickly by baking them in an oven for 4 hours at a temperature of about 110-120ºC. Afterwards, the stack of glued sapphire substrates can be cleaved by splitting two substrates with a scalpel. The BSCCO crystal cleaves in-between BiO planes similar to the behavior of an HOPG graphite when trying to create graphene layers. Bonds within isolating SrO-BiO-BiO-SrO layers are weaker than within conducting CuO2-Ca-CuO2 layers see Fig. 1.6 (crystal structure). Ideally, it should be cleaved over one smooth plane, but in practice there will be steps, cracks and surface roughness that relate to different thicknesses of the crystal on its different sides and stresses applied to the crystal during the gluing process. The epoxy that has hardened can be removed with a scalpel, with care being taken not to damage the crystal.

Figure 2.1: Two sapphire substrates with 5×5 mm and 0.5 mm thickness and BSCCO crystal (small black flake) glued in-between them.

Electron beam deposition/gold coating

After the crystal is cleaved, it cannot be exposed to the air for a long time as its surface will passivate rapidly, in roughly 10 minutes. That is why cleaved substrates are immediately put in a vacuum chamber and a 50-60 nm protective layer of gold is deposited on top. For this, the sample was placed into the vacuum chamber in the Eurovac system for E-beam evaporation. The electron beam deposition is one of the simplest techniques that can be used for depositing of various materials. The simplicity of that method is based on the fact that a high energy electron beam from a tungsten filament heats the

23 crucible with deposition material. Part of the material evaporates and atoms are ballistically transferred to the sample and are deposited. A high vacuum is needed for achieving a good purity of deposited film as any gases inside might affect it and the film properties could deteriorate. A high vacuum is also required for material particles to travel freely from the target to the substrate, so the mean free path should be significant enough (larger than the chamber size) to facilitate such deposition.

Figure 2.2: Eurovac E-beam deposition system: 1 the main chamber, where deposition occurs; 2 the load-lock for loading and unloading samples; 3 vacuum gauges, one for the load-lock to avoid a pressure drop in the main chamber before transporting samples and a gauge for monitoring pressure during deposition, there is a valve in-between them that separates the load-lock from the main chamber; 4 the transfer rod that allows samples to be transferred to the main chamber and taken out after deposition; 5 a tilting rod for the tilting deposition, rotates by 360˚; 6 power supply; 7 a thickness monitor for controlling deposition rates and the deposited film thickness.

The Eurovac is a custom-made electron beam evaporation system. It can be used for the deposition of various materials, layer by layer, without breaking a vacuum (see Fig. 2.2). Due to the simplicity of the system and easy maintenance, it is mainly used for the deposition of materials such as gold, cobalt, titanium, copper, and calcium-fluoride as an insulating layer. The system, shown in Fig.2.2, is constructed in such a way that the main-deposition chamber 1 is kept under a vacuum of 10-7 mbar, while a load lock 2 is separated by a safety valve and can be vented to atmospheric pressure for the sample mounting on a transfer rod 4. Transferring the sample can be tricky. In order not to drop it inside the

24 main chamber during transference to its final position, three clamps hold the sample carrier on a transfer rod, and three more are at the main chamber holder: the operator is required to catch it inside the main chamber by pressing and rotating the transfer rod. The sample holder in the main chamber can be tilted at different angles for an angular deposition 5. For example, this allows step coverage between crystal and substrate edges even if the crystal is rather high. A power supply 6 has a “remote” control panel that can be used to increase the applied beam power and to adjust the beam position over the target in x and y directions with a wobbling amplitude for smooth heating of the crucible. Thickness monitor 7 uses a quartz crystal with a known resonance frequency that changes when material is deposited. Calibration constants can be set with correspondence to the densities of different materials and the chamber’s geometry. As a result, a final thickness of the film can be measured and controlled in-situ, with an accuracy of up to a few Å. The deposited film thickness can be checked afterwards by a KLA Tencor P-15 surface profiler with a vertical resolution of 0.5Å and a maximum scan length of 200 mm.

Photolithography and etching The next step after the gold deposition will mainly determine the quality of the sample at the end of fabrication. Several sequences of photolithography were conducted during device fabrication, and different masks were used. Fig. 2.3 is a sketch of the photolithography and etching steps. Etching always occurs after lithography and completes the created structure. All lithography processes were done under a yellow room light for minimizing the chance of unwanted exposure of the resist to daylight sources. Photolithography is a method where the pattern on the mask is transferred to the sample using a UV light source. A Canon PPC 210 projection camera was used for that purpose, as shown in Fig. 2.4. Here the UV light from a mercury lamp with well-defined intensity shine on the mask with a pattern and then passed through the optical system and focus on the sample that was spin-coated with the resist. Before exposure, the yellow filter was used to align the sample properly to the mask pattern. Then the filter was removed, and UV light exposed the positive photoresist S1818/S1813. After the exposure, the resist was developed using a developer, in this case MF-319, a chemical reagent that removes exposed parts. In the case of negative photoresist, non-exposed parts will be removed, but another developer should be used. Further use of the photoresist on top of the sample can be used as a protection layer for a subsequent etching. Alternatively, a deposited material can be removed together with the photoresist via the lift-off process. The photoresists used, S1818 and S1813, differ in viscosity which gives different thicknesses of 1.8 µm and 1.3 µm respectively when spin coating them at 4000 rpm for 60 seconds. Due to the limitations of the PPC system and its age, the best-achieved resolution is ~2 µm. One minute of baking on a hot plate under 100ºC is needed

25 for the resist to harden before the actual lithography process takes place. Expo- sure takes place for 35-40 seconds, and the transmitted mask pattern should be developed for the next ~30 seconds in the developer. The sample should be checked under the optical microscope to ensure that the photolithography has taken place without any defects. If the pattern shows defects, the photoresist can be removed from the sample using acetone, then cleaned using isopropanol and distilled water, and the entire photolithography process is iterated again.

crystal Au layer substrate 3.Development

photoresist

1.Spin coating 4.Etching UV

mask

2.UV exposure 5.O2 ashing

Figure 2.3: Sketch of the photolithography and etching process.

The first step is needed to create a square pattern with side length of 100 µm on the top of our crystal to prepare a working space, where at the next step a mesa line will be made. The lithography of the square is simple due to its large size. However, the second step, with the thin 5 µm mesa line, should be done with exquisite accuracy.

Figure 2.4: Canon PPC 210 system: Mercury lamp is placed in light- house on top (not present on image due to lamp failure), then light passed across lens and retractable yellow filter (for alignment, not to expose resist before lithography), and shone on mask with pattern, transmitted through optical column to the substrate for alignment and exposure.

A KI+ water solution was used for removing the residual gold on top of the substrate and the crystal. The remaining resist preserves the gold layer from a wet gold etch. At the second step, a mesa line 50 µm long and 5µm wide was created simi- larly, using another mask with a line pattern. After that all the remaining gold around the mesa line should be etched away. The etching is used for creation the final shape of the mesa line with a desired number of Josephson junctions. The etching process can be divided into physical and chemical etching techniques. The physical etching occurs when the material that is to be etched is bombarded by ions and then sputtered away. Ar ions being used for this purpose. Chemical etching involves a chemical reaction with good selectivity to the different materials. For dry chemical etching volatile products that form during the chemical reactions are pumped away. A wet chemical etching was performed with a KI+ water solution where the gold was etched with excellent selectivity to the BSCCO and the photoresist. The dry chemical etching is performed in the gas atmosphere. The chemically active gas reacts with the sample, and the reaction takes place in the inductively coupled plasma. In addition, the physical sputtering may occur if the kinetic energy of atoms is high enough.

Figure 2.5: Oxford Instruments PlasmaLab 80 RIE-ICP used for oxygen ashing of photoresist and cleanup processes (left); Oxford Plas- maLab System 100 used for argon sputtering and chemical etching (right).

An oxygen ashing process can easily remove organic materials such as the photoresist by using the Oxford Instruments PlasmaLab 80 RIE-ICP shown in Fig. 2.5 (left) during the chemical reaction where burning of the photoresist took place, with good tolerance to the BSCCO and deposited films. The sample was placed on a power electrode in the process chamber. First, the lithographed square can be ashed away with a soft oxygen ashing recipe (if acetone was not used for that), under a pressure of 100mTorr to prevent sputtering and damage of unprotected parts, with a low RF (radio frequency) generator power of 10W and an applied ICP (inducted coupled plasma) power of 50W. Increasing the ICP power will lead to an increasing etching rate and ionization, and that will affect the ashing speed, which can reach up to 70 nm/min. A hard ashing recipe is used for the hard-baked photoresist when a soft etch takes con- siderable time. The argon sputtering process was performed on an Oxford PlasmaLab System 100, as seen in Fig. 2.5 (right). This system is more advanced, with a separate load lock and an automatic wafer transfer arm to the main process chamber. Other gases can be used here for different purposes, depending on the physical and chemical etching recipes, such as CF4, SF6, CHF3, and Cl2. The PlasmaLab 100 system has a temperature-controlled stage that can be cooled down to -150ºC

28 (Cryo-RIE) by liquid nitrogen from a Dewar that is placed in the process corridor of the cleanroom. The increase of power can increase etching rates. The RF power was set for 300W and ICP 500W, the argon pressure set at 7mBar, with a DC bias voltage of 300V, while the sample was kept under -50ºC. Ar ions are not very selective; the sputtering occurs on any surface and on any material that is placed under such conditions. This is an example of the pure physical sputtering process. Depending on the material of the layers that cover the sample, each layer will be etched at different rates. This requires accurate control of the etching depth. Otherwise, it is possible to etch away needed parts. Under such parameters, S1813/S1818 has an etching rate of approximately 40 nm/min, Au ~80 nm/min and BSCCO ~15-20 nm/min. During sample fabrication, it is necessary to etch through a certain depth of BSCCO crystal to create several hundreds of Josephson junctions. Two hundred intrinsic Josephson junctions correspond to about 300 nm, as one Josephson junction is 1.5 nm in the c-direction. 1.3µm photoresist thickness can withstand the required etching time and etching can be done with precision. The total etching time was 20 minutes for the gold layer and BSCCO crystal to create the pedestal for mesa structures. In addition, Cryo-RIE was used to perform chemical etching of a niobium film during one of the final steps of the sample fabrication. For this purpose, a CF4 gas was used. It has a good selectivity and tolerance to other materials on a chip. The sample was kept under room temperature, with 55W RF and 100W ICP power.

Lift-off

The remaining parts of gold that were not etched due to shadows or cracks in the sample can create electrical shorts for future contacts. To avoid it, an isolating layer was made by electron beam deposition on top of the sample. In that in- stance, CaF2 was used, but SiO2 can be used as well. As a mesa line is covered by the photoresist, which protects the gold underneath it, the calcium fluoride covers the sample from the top with a 160 nm layer (due to the high mesa line sides that were etched beforehand). The open crystal surface is already passivated by exposure to air and dipping in liquids during. The lift-off process is needed for opening the gold surface from the photoresist and the CaF2 to continue the mesa fabrication. A weak ultrasound and bath of warm acetone dissolve the resist and create a small flare in places where the photoresist and the calcium fluoride present together, as show on sketch Fig.2.6.

29 Photoresist Gold covered Gold CaF2 mesa structure + Acetone Crystal + Ultrasound Substrate

Figure 2.6: Sketch of the lift-off process. Photoresist dissolved by the acetone, removes CaF2 layer from top of the mesa structure.

Thus, when the gold surface is opened on the mesa line, as shown in Fig. 2.7 the isolating layer preserves the rest of the sample.

Figure 2.7: Mesa line on top of the BSCCO crystal after the liftoff process, gold around crystal is covered by CaF2.

The planarization mask photolithography was used to create smooth coverage of the crystal edges and topography of the substrate. As they can affect the integrity of future contact electrodes. A specific mask was used for this purpose. This step is needed for creation of monotonous covering for future electrodes, as the photoresist thickness is around 1.5 µm.

Top electrode deposition

After lift-off the E-beam evaporation by Eurovac was used to deposit a thin 5 nm layer of Ti for better adhesion and a 150 nm layer of gold was laid with tilted

30 deposition of -45º, 0º and 45º in order to cover the sides and leave a uniform covering. Finally, a layer of Nb was deposited by an AJA Orion sputtering system (Fig. 2.8). AJA Orion is a multi-target system that can be used for the sputtering of various amounts of metals, alloys, and insulators, as can be seen from Fig. 2.9, it contains eight targets allowing simultaneous deposition. So, the deposition of a few different layers can be done layer by layer without taking the sample out. The aim of using Nb was to create superconducting electrodes on the surface and possibly, a Josephson junction at the top of the mesa. This minimizes heat effects while biasing the contacts. Another consideration was that Nb sputtering performs a conformal coverage of a complex sample topography with fairly vertical sides of the crystal and epoxy glue. Sputtering of the Nb layer on top of the sample was done under following parameters: At the beginning, 50W RF and 30mTorr pressure with 25sccm Ar flow were used to clean up the sample surface before deposition, at a low rate of sputtering. The actual deposition takes place with 250W DC applied and 5mTorr pressure and argon flow remaining the same all the time. Eight minutes of deposition creates an Nb film of 50 nm on top of the sample. The last but one of the sample fabrication is photolithography of electrodes, which is done after the Nb deposition. It creates the final rectangular mesa structures on the pre-etched mesa lines and contact pads for bonding connection wires for future measurements. The specific mask was chosen, and all process steps repeated as previously discussed, including spinning, backing, exposure, and development. There is no room for mistakes in the lithography process as the planarization layer would be destroyed along with all films deposited on top of it, due to acetone dissolving all the photoresist. After this, the sample is ready for the final etching of contacts and mesas by CF4 for an Nb chemical etch, the Ar milling for sputtering of Ti and Au, and creating the shapes of mesas and forming the stack of Josephson junctions. The etched sample is shown in Fig. 2.11. The finished and etched sample should be put into the oxygen plasma for 45 minutes of soft O2 ashing to remove the remaining resist.

Figure 2.8: AJA Orion sputtering system with control setup. 1 the main process chamber; 2 load-lock with separate pump and transfer road for sample transferring; 3 control setup computer with DC and RF power supplies for various deposition recipes.

Figure 2.9: Inside the main chamber of an AJA Orion sputtering system; eight different magnetrons for different materials can be seen.

Figure 2.10: Diagram of magnetron sputtering mechanism [66].

Figure 2.11: The finished sample after final etching and before the O2 ashing, the remaining photoresist can be seen from interference circles near the crystal.

The sample is now ready to be glued onto a printed circuit board (PCB), dried, and bonded with aluminum wires. To glue the sample on top of a PCB as shown in Fig. 2.12, a medical BF6 glue was used. A wire bonder it allows the creation of wire bonds between PCB contacts and niobium-gold electrodes; two bonds for each contact were made to exclude the possibility of wiring breaking during measurement.

Figure 2.12: PCB with bonded sample glued on top of it.

SEM/FIB manipulation

The SEM/FIB is used to create smaller mesas by splitting them for independent biasing of each. This will allow their manipulation with various configurations and will minimize risks if some of the contacts, due to circumstances, do not respond to the bias. An FEI Nova NanoLab 200 Dual Beam Microscope (Fig. 2.13) was used for manipulation and ultimate control of the sample. It consists of a conventional scanning electron microscope (SEM), a focused ion beam (FIB) column, and a platinum deposition gas containing system.

Figure 2.13: SEM/FIB system FEI Nova 200 with a gas injection system for platinum deposition.

34 The platinum system can be used to cure broken contacts and make patches on the sample by ion or electron beam induction deposition. Molecules that contain platinum are delivered to the surface by the injected needle and due to weak bonds of platinum to other organic matter in the gas, these bonds break by sec- ondary electrons from the sample while bombarding it with ions or electrons and platinum is deposited on top. The remaining components are pumped away. One disadvantage of this process is that the processed area can become contaminated by gallium from the ion gun or by organic ingredients in the platinum-containing gas. However, this may save the sample. The main reason for SEM inspection is to define shorts and then cut them by FIB and, where possible, to repair contacts. As can be seen from Fig. 2.14, the sharp and tall edges of the crystal can affect the integrity of the electrodes, and such a type cannot always be fixed.

Figure 2.14: SEM image of one of the samples. Lower two contact leads are not continuous due to the sharp edge of the Bi-2212 crystal; using a gas injection system some of them can be fixed.

The mesas were then trimmed by FIB to improve their size and shape. This manipulation allows us to create any mesa shape, but it also increases the number of junctions due to worse control of etching rates in comparison with Ar milling and plasma sputtering. In addition, gallium ions are trapped inside the structure after they reach the surface of the sample. In this particular case, this was not so

35 critical as the initial plan was to have more than 100 Josephson junctions in the stack and ions do not implant inside the actual mesas. The prepared sample before FIB is shown in Fig. 2.15 (left) and with cut mesas is shown in Fig. 2.15 (right) as an SEM image after all manipulations were finished.

Figure 2.15: A final SEM image of the processed sample, before FIB manipulation (left); after FIB manipulation, the upper mesa structure divided on two, the middle divided on four and the lower mesa on three different size mesas (right), zoomed image of the lower mesa cuts [69].

Using some steps of sample preparation, a wide range of other samples for different purposes can be made.

Figure 2.16: Sketch of a finalized iron-based superconductor (pnictide iron based Ba1−xNaxFe2As2 or FeTe1−xSex) (left) that been fabricated using the same techniques for BSCCO crystals, SEM image of the fabricated sample [70, 51].

36 The same techniques for fabrication were used to fabricate iron-based superconductors for the study of angular-dependent magnetoresistance [56]. In the sketch above of the prepared sample (Fig. 2.16), some steps are missing: for example, there is no gold deposition performed, while instead of calcium fluoride, SiO2 has been used. In that case, Nb was sputtered directly on top of the crystal. The manufacturing process allows us to fabricate a high-quality surface Jo- sephson junction on top of the crystal, as can be seen from Fig.2.17, where the Fraunhofer modulation pattern for such junction is shown.

Figure 2.17: Measured Fraunhofer modulation I(H) for positive and negative currents of the fabricated Josephson junction on top of the Ba1−xNaxFe2As2 crystal [71].

Created pnictide Ba1−xNaxFe2As2 and FeTe1−xSex were used for angular-dependent magnetoresistance studying [70].

2.2 Low-temperature setup

Two different closed-cycle cryostats from Cryogenic Ltd have been used for low- temperature measurements. The closed-cycle cryostat based on helium circulation involves liquification of the gas by cold heads installed inside. These cold heads are powered by He- gas compressors that are cooled by water flow, which also circulates in a closed cycle. This large cryostat is known as the 17 Tesla cryostat due to NbTi/Nb3Sn solenoid that reaches fields of up to ±17T (see Fig. 2.18 (left)). The base temperature is 1.8 K and can be heated up to 300 K without influencing the magnet. The sample is placed in a space with heat-exchange gas (helium) inside the cryostat by using a transfer rod with connectors for electrical measurements of the sample

37 and its surroundings, such as a thermometer and Hall probes for two field detection. The sample space is then cooled by the flow of liquified helium that collects in the He4 pot and flows via a needle valve to a variable temperature insert (VTI) where it is pumped out and liquified again to repeat the whole cycle. By operating the needle valve manually, it is possible to control the flow (pressure) and thus the sample cooling speed. Opening of the valve too much, while this would allow faster cooling, it would also affect the helium temperature in the system and in the matter of a moment there would be not enough liquid helium to cool down the sample. For reaching the lowest possible temperature, a pressure of around 5-9 mBar is needed. The sample rod allows sample rotation up to ±160º for different field orientation measurements. The second cryostat shown in Fig. 2.18 (right) is known as the Optical cryostat due to a window for optical access to the sample. It has a pulse-tube refrigerator and can reach a maximum 5T field. The system is based on He4 and He3 gases: the He4 enables cooling down to 3.2 K and lowering the temperature is possible by pumping the He3 at the range of 300 mK; depending on how well the pumping is performed, the hold time can be around 10 hours. Magnet operation is stable only at low temperatures, and the sample is cooled only via the thermal contact with the sample holder, without heat exchange gas (sample in vacuum).

Figure 2.18: Big cryostat (left) with a 17T magnet with com-pressed helium storage tanks on the right and VTI pressure manometer on the top to control helium flow over the needle valve for smooth sample cooling. Op- tical cryostat (right) with 5T mag-net in it, with a valve unit seen on top, transfer rod connected to turbopump before mounting sample from the front, optical windows are placed on the sides.

The sample glued on the PCB allows independent biasing from 20 different contacts that were connected to the electrodes by aluminum bonding wires. The backside of the PCB has two male 10-pin connectors to plug in different sample

38 holders. For the 17T cryostat, the rotation rod has another PCB with female connectors, shown in Fig. 2.19 (left), for mounting the sample PCB. From another side of it, there is a thermometer, the Lakeshore CX-1030-SD-1.4, with good thermal contact with the sample and the two Lakeshore HGT-2101 Hall probes held perpendicular to each other for field registration and determining an angular position of the sample stage. Copper wires connect all this equipment to a side connector that is also connected to the upper plugs on top of the transfer rod for cable connections for a data readout. Additionally, on top of the rod, there is a stepper connector connected to a motor that allows rotation of the sample for suitable positions during measurements. The optical cryostat does not have such a rotator. Instead, there are two types of female PCB adapters to put the sample on for a perpendicular or parallel position respectively to the magnetic field of the cryostat shell deck. These are known as the L-shape and standard adapters. The L-shape adapter in Fig. 2.19 (right) has a mirroring matrix connection due to the tilted position of the PCB. The L-shape connector situates the sample PCB just in front of the optical window, from where optical measurements of the sample can be done. The measurement system of both cryostats is similar with slight differences (the main difference being the analog and digital switch matrixes on the 17T and Optical cryostats, respectively). Both are based on National Instruments PXI sys- tems under the control of LabVIEW and are already customized for measurement needs. There are several extension cards in PXI for providing analog and digital in- and outputs for waveform generation. There are also field-programmable gate arrays (FPGA) with eight lock-ins. The output voltage of generated waveforms is limited up to 10V that is converted into a current sent to the sample by using a linear multiturn potentiometer of up to 100kΩ but this can be changed manually to the MΩ scale if needed. The measured current is obtained by voltage through another series resistors of 100Ω or 1kΩ. Low-level signals are amplified to a maximum of 10V by using custom-made amplifiers for each of eight available channels. Amplifying gain can be controlled over FPGA in a range of 1 to 5,000 that can obtain a better signal/noise ratio. For driving Hall probes another FPGA is used that can give a readout for two Hall probes mounted under the sample and another separate Hall probe that is installed directly on the magnet. This enables the calculation of the sample angular position versus the field and precise positioning of it.

Figure 2.19: Sample holder from 17T cryostat at the end of transfer rod with a rotation stage (left): heater and two thermometers and two Hall probes for precise field orientation during measurements. Opti- cal holder (right) with L-shape PCB on top for parallel orientation for the field and access to optical window.

40 III Results and discussion

Recent progress in terahertz research demands qualitative devices in a range of 0.1-10 THz. While there is a wide availability of well-developed broadband sources, there is still not clearly defined technology to build a narrow line-width THz laser. Mesa structures based on high Tc superconductors with a large number of Josephson junctions look quite promising in this regard. A sub pW power achieved from small mesas with fewer than 60 [24] junctions did not prove the theoretical prediction of a significant emission from such mesas and so samples with around 200 junctions.

3.1 Small-but-high Bi-2212 mesa structures characterization

As discussed above a layered structure of cuprate crystal Bi2Sr2CaCu2O8+δ represents a stack of naturally formed atomic-scale intrinsic Josephson junctions. A large number of junctions is vital for the coherent enhancement of emission power [69]. However, it should be noticed that while trying to boost the emission, Joule heating will limit bias voltage and oscillation frequency. Small size mesa structures based on the BSCCO crystal have some ad- vantages, such as edge effects and capacitive coupling which encourage the in- phase synchronization of junctions. In addition, self-heating is reduced propor- tionally to the mesa size, allowing operation on higher biases and at higher frequencies, while the qualitative factor Q of the primary geometrical resonance (cavity mode) is inversely proportional to the size and should boost emission power ∝ 푄2. That encourages our expectations. Moreover, small mesas are free of defects, which can simplify the synchronization [69]. Therefore, we focus on analysis of properties of small-but-high mesa structures, i.e., mesas with a small area in the ab-plane for reduction of self heating and simplification of synchronization, but with a large height in the c-axis direction, so that the mesas contain many Josephson junctions, facilitating significant superradiant amplification of the emission. After putting the sample into the cryostat, it was checked for responses from all the contacts. The resistance versus temperature dependence during cooling was recorded. From the resistance versus temperature R(T) graph shown in Fig. 3.1 it can be seen that a kink on plot happened at 48 K that corresponds to transition temperature to the superconducting state of the BSCCO crystal and a second kink appeared at 8 K for Nb electrodes. The total resistance of the sample remains finite due to the thin deterioration layer between the crystal and the Au/Nb electrodes.

)



( 4

0 10 20 30 40 50 60 70 80 Ts (K)

Figure 3.1: Resistant versus temperature graph of the non-FIBed (cut) sample.

At the base temperature of 3 K, each mesa has been tested. Their current-voltage characteristics (IV) are shown in Figs. 3.2 and 3.3. The Fig.3.2 represents the current-voltage characteristic of the top mesa, it includes Josephson junctions form the mesa body and the pedestal. That difference can be clearly seen as the pedestal junctions have higher critical current values.

(V)

V -2

-4

-6

-8

-10 -600 -400 -200 0 200 400 600 I (A)

Figure 3.2: Current-voltage characteristic of the top mesa.

42 On Fig. 3.3 shown the current-voltage characteristics for the middle mesas, black and blue IVs correspond to mesa and pedestal junctions with higher critical current for pedestal junctions, as red and cyan IVs represent only upper part of the mesa Josephson junctions without pedestal.

Figure 3.3: Medium mesas current-voltage characteristic, blue and black lines correspond to mesa and pedestal, red and cyan are for only the upper part of the mesas.

The hysteresis behavior of the mesa IVs in Figs. 3.2 and Fig. 3.3 is caused by a significant capacitance (McCumber parameter 훽푐 ≫ 1 ) because our Josephson junctions are of superconductor-insulator-superconductor (SIS).

Figure 3.4: (left) SEM image of the sample and combinations of generator/detector #1/#4 and #2/#5; (right) a 3D sketch of the sample, where pedestal can be seen [69].

43 As each mesa on the sample can be biased independently and as we would like to achieve synchronized emission from the stack of Josephson junctions and detection of it by the single Josephson junction. One of the mesas will act as generator and other one will act as detector for incoming radiation. Two different combinations for future generator/detector mesas were chosen in a way to give the best response: large generators allow higher total emission power proportional to the area; smaller detectors have higher sensitivity (inversely proportional to the area) (see Fig. 3.4). Two generators have different shapes, the mesa #2 is almost square, while #4 is rectangular. In both configurations the smallest outlying mesas #5 and #1 been used as detectors. Size comparison can be seen from Table. 1.1. An important factor is the distance of 25 µm between the detector and the generator mesas to minimize the effect of direct heating and the injection of non- equilibrium particles.

Table.1.1: Main characteristics of the fabricated device.

Generator/Detector mesas Size Active junctions Gen #2/Det#5 5.2×2.3µm2/1.2×3.3µm2 250

Gen#4/Det#1 11.5×2.6µm2/5.2×2.33µm 110 2

Figure 3.5: Current-voltage characteristics with Josephson critical current of Ic ~ 50µA for generator #2, upper axis is voltage per junction [69].

44 For the mesa #2, can be seen in Fig.3.4 (left), current-voltage characteristics with Josephson critical current of Ic ~ 50µA, as shown in Fig. 3.5, the intrinsic Josephson junctions start switching and show excellent uniformity of the mesa due to similar critical currents [69]. A sum-gap kink at 2Δ ≈ 30meV is seen. The Δ is smaller than standard values for such types of crystals, but it is still large [72,73], indicating that the gap suppression by self-heating is moderate at high biases. The particular contact configuration for the generator and the detector mesas is shown on Fig. 3.7. The IV of the generator mesa was measured in the four- probe configuration as it has two electrodes. The small detector mesa had only one electrode so it been measured in the three-probe configuration.

Figure 3.7: The contact configuration for THz generation experiment with generator#2 and detector #5 used [69].

3.2 THz generation

The main goal of the experiment is to detect THz radiation generated by Bi-2212 mesa structures. As noted above, two pairs of detectors/generators were chosen. In Fig. 3.8 the IV of generator #2 is shown to be achieved during the sweep from the significant negative bias to the large positive bias. This mesa had been etched to reach a total number N ~ 250 of JJs. The IV looks asymmetric, as during the sweep from -10V to a zero voltage, all Josephson junctions are in the resistive state. After the sweep to zero voltage all junctions return to the superconducting state and, with a current increase, they start to switch one by one to the resistive state again. If we repeat such a sweep

45 from the + to – voltage values, the current-voltage characteristic will be mirrored to the present one.

Figure 3.8: Generator #2 current-voltage characteristics during swipe from -10 V to +10 V bias voltage [69].

As shown in Fig. 3.9 for generator #4, the same values of the voltage on rising and falling parts of the IV correspond to a different number of the active junctions. This is due to the generator mesa #4 being etched only halfway into the pedestal, as can be seen from a 3D sketch in Fig. 3.4. From counted number of branches in the IV it shows that mesa #4 contains only about N≈110 Josephson junctions, i.e., half of the total number of them. This fact limits its biasing to ± 2V, while the larger biasing leads to the pedestal junctions starting switching, which makes analysis somewhat complicated.

Figure 3.9: Generator #4 current-voltage characteristic with a total number of active junctions N ~110 during sweep from -2V to +2V bias voltage [69].

46 As the generator should radiate, this emission must be captured and detected by the first junction of the detector mesa, which acts as a switch current detector.

3.3 Switch current detector

A top junction of the detector mesa was used as the switching current detector which reacts to the oncoming radiation. The top junction has a lower critical current due to the degradation of the top CuO layer. This allows independent biasing of it and left other parts of the mesa in the zero-voltage state. [69, 72]. To operate the switching-current detector, a low AC current with low frequency 1-23Hz was sent. The low amplitude of the current also keeps it in a superconducting state just above the limit before it can switch to a resistive state. That keeps it in the state when no emission is generated, and only spontaneous switching may occur due to thermal fluctuations. When generated electromagnetic waves reach it, they induce a high-frequency current that forces switching of the junction into resistive state and allows the detection of the incoming radiation [74] can be seen in Fig. 3.10.

Figure 3.10: Current-voltage characteristics for mesa #5 detector with a reflection on different biases of generator mesa #2 [69].

With no bias on generator switching do not occur, while increasing the generator voltage. With a continuous increase of voltage on a generator, the switching probability increases non-monotonously. Form Fig 3.11 it is seen that it rises from 0 to -4.88 V but drops at voltage value of 5.84 V, then rises again. That is an important point, as such a response indicates that the response is not due to heating. Also, from a coincidence of resistivity, parts of detector IV heating can be excluded. That quasiparticle resistance strongly depends on temperature [71],

47 therefor, if there were significant heating, this would be visible in IV of the detector, which did not occur. This fact proves that the generator responds to emitted radiation in the form of electromagnetic waves. Nevertheless, there should be a limit where emission cannot be registered, and it shows up on higher biases close to the sum-gap where unwanted response appears and what determines the borders of high-frequency detection. This happens as the detector response rapidly increases at a large bias, near the sum-gap voltage at V/N = 2Δ/e=30mV. This response cannot be related to the only electromagnetic waves as the non-equilibrium particles start propagating through the base crystal. Thus, it limits the upper frequency for operation of the switch current detector. Detection takes place when the emitted electromagnetic wave travels across a free space in the sample and gets caught by the similarity antenna contact electrodes and thus driven to the detector. To be sure that the signal does not propa- gate through the crystal base, there is no apparent DC crosstalk evident from the detector IVs in Fig. 3.10. If it were to occur, there should be a shift on the detector's current-voltage characteristic when a high bias was applied to the generator.

Figure 3.11: Switching time dependence of detector voltage. When increasing negative bias on generator, switching probability non-monotonously increases, which indicates a response from inducted electromagnetic currents, not from heating. Base temperature 3 K [69].

A small bias current can explain the absence of crosstalk, so the base crystal keeps superconducting, and the significant distance between two mesas, in comparison to the mesa size, prevents quasiparticle penetration into the detector. At high frequencies, the crosstalk over the crystal base will be smaller due to a skin effect. A screening of the electromagnetic waves also occurs due to the nature of

48 superconductors. The depth of the skin effect is limited by the London penetration depth λ that is lower than 200 nm, while the separation distance is a tenth of a micrometer.

3.4 THz radiation detection

The detector with a stable low AC bias current responds on the electromagnetic wave by the change in its resistance due to switching. The higher the resistance, the higher the switching possibility, as can be seen in Fig. 3.12, where almost all switching takes place at Rdet~12kΩ. Additionally in Fig. 3.12, the detector response demonstrate some resonant peaks at certain generator voltages Vgen. The non-monotonous detector response with respect to the dissipation power in the generator proves nature of the detector response.

Figure 3.12: Measured detector #5 response from generator #2 (voltage per junction) [69].

Looking at the detecting plot Fig. 3.12, it is notable that the response from the detector is mirrored when sweeping from -10 to +10V and from +10 to -10V. That occurs due to the majority of detected signals that take place when all junctions are active and are in the resistive state during the falling part of the IV. There is no significant signal after passing zero-voltage until eventually, a certain number of Josephson junctions become active and some emission emerges. The emission at the rising parts of the IV is, however, very metastable as more junctions are joined to the oscillating state, those peaks disappear.

49 In Fig. 3.12, the mirror symmetric with respect to backward seep from +10V to -10V is a result of the state of the junctions in generator mesa, but not by the sing of the current in it. The asymmetry of the emission is expected from stacked Josephson junctions. [46] The resistive state of the junctions alleviates oscillation, and so produce coherent superradiant emission intensification. It is quite challenging to get an emission from the rising part, as emission in this part asso- ciates with chaotic unsynchronized state of the stack. In Fig 3.13 showing another generator/detector pair, it is seen that there is no significant emission when Vgen > 0 on the rising part while junctions are turned on one-by-one and remain non- synchronized.

Figure 3.13: Detector #1 response from generator #4 as a function of detector voltage per junction [69].

Falling sides of IVs allow us to obtain detection spectra as a function of the Josephson frequency as it show in Fig. 3.14.Where panel a corresponds to the generator #2 and the detector #5 with different sweeps from -10 to +10V shown in black, -2.5, -4.4V red and the small sweep -5 to -2.5V in blue; while panel b represents one sweep for the pair of generator #4 and the detector #1, with all data received from the resistive state junctions. The emission frequency range is quite high for both generators, as it can be seen from Fig. 3.14 it is 3-11THz for the generator #2 and 1-9THz for the generator#4. This is a record high for Josephson oscillators [69] with underlying that emission occurs in the whole frequency span.

Figure 3.14: Emission spectra from detectors response (a Generator 2 Detector 5 b Generator 4 and Detector 1) to Josephson frequency from falling parts of generators current-voltage characteristics. Dif- ferent swipes marked by arrows. Top bars represent positions of main cavity modes depending on generator geometry and shape (1.34).[69]

2 2 푐1 푙 푛 푓푛,푙 = √ 2 + 2 (1.34) 2 퐿푥 퐿푦

Vertical bars in Fig.3.14 represent the expected frequencies of the coherently emitting in-phase geometrical resonances with the correspondent n=1 cavity mode (equation 1.26). This correlation of the emission maximum with the cavity modes establishes a significant role of in-phase geometrical resonances. Geomet- rical resonances promote boosting of emission power ∝ 푄2, and also requires for coherent superradiant emission, and assist with synchronization of the Josephson junction stack [60, 69, 70, 74]. Thus, it can be assumed that there are two ways to tune the frequency: changing the bias of the voltage and/or changing the mesa geometry. The maximum emission takes place when the Josephson frequency matches with the one of the in-plane geometrical resonances (cavity modes). Also, from Fig.3.14 panel a it is seen that the peak amplitudes depend on the maximum bias current value with fixed voltages. Two backward sweeps from - 10V to 0V (black) and -10V to-2.5V (red) have different set of peaks. While other two sweeps within lower bias sweeps from -5V to 2.5V (blue) are fully repro- ducible with other set of peaks. This can be related with vortex-antivortex medi- ated mechanism of emission [69, 75]. Vortices can be realigned with high biases

51 [76], this can explain the peak realignment after applying high current, but nota- bly that the peak frequency did not changed. Overall, the ten-fold tunability from 1 to 11 THz that is achieved compares more than favorably with the results achieved by the semiconducting quantum cascade lasers. It reinforces expectations that the superconducting THz sources are superior at least with respect to the tuning range tuning.

3.5 Power efficiency

The switching current detector allows us to determine an absorbed power. Switching occurs under the influence of electromagnetic waves that induce THz- current to the junction. The junctions kept running within the characteristic voltage of 4mV, as shown in Fig. 3.5. Work to overcome the Josephson junction barrier is [69, 73]:

3 4√2 퐼 2 Φ 퐼 ∆푈 ≃ (1 − ) 0 0, (1.32) 3 퐼0 2휋 every cycle Δ푡 = 푉푐/Φ0, so absorbed power will be equal to:

2√2 퐼 3/2 푃푎 ≃ (1 − ) 퐼0푉푐 (1.33) 3휋 퐼0

Where 퐼0 is the fluctuation free Josephson critical current and 퐼푠 is the actual switching current suppressed by the incoming THz signal. When it is suppressed to zero, the absorbed power would be around 0.5nW for that specific junction. While at the largest peak (Fig. 3.11(a)) it is ~0.1nW. Calibration of the absorption efficiency been done by an external THz source. The frequency 1-1.2THz from an external Backward-Wave Oscillator (BWO) was guided through the optical window of the optical cryostat with usage of pol- yethylene lenses. The THz beam been focused into a spot with width of 3mm. The optoacoustic Golay cell detector been used for measurements of the transition power trough lens system without cryostat through air [38]. The detected power was reduced during transmission to the sample through cryostat as beam can be diffracted at apertures and absorption on the way through optical window and lenses to the sample take place. The beam power from the BWO is in range of 1-0.5mW. Knowing the factor of power reduction around 3, this corresponds to 0.2-0.3mW of power at the sample with the power density of the 1-2mW/cm2. The similar by size detector mesa with higher critical current from previous research [38] slightly detects emission. Thu, the absorption efficiency measured by

52 an external Backward-Wave Oscillator is shown to be lower than ≤10-4. This enables a rough estimation of the maximum emission power with an order of mag- nitude estimation is ~1µW [69].

3.6 Radiation from large Josephson arrays

In addition to the main experiment with BSCCO crystals, discussed above, measurements were also performed using large chain-like arrays of Nb/NbSi/Nb Josephson junctions. Two arrays with Josephson junctions with different arrangements were made and the properties of the configuration were tested with a separate n-doped InSb bolometer [76] to detect emitted radiation. The first array consists of linear one- by-one Josephson junctions with a total number of 6,972, a 2D sketch of it shown in Fig. 3.15, representing seven subarray lines with each of them containing three connected in series lines.

Figure. 3.15: a “linear” array layout with marked input and output current contacts [66].

In addition, a second ‘meander’ array was created with a total of 9,000 junctions consisting of six sub-arrays, 2D sketch presented in Fig. 3.16. Both arrays Josephson junctions have similar areas 8µm×8µm with separation between them of 7µm. The total size of both arrays is 0.5×0.5 cm. The fabrication process of the arrays can be found in [77, 78]. The InSb detector been calibrated by the BWO oscillator with frequency range of 100- 118GHz. Measurements were conducted in the closed-cycle 17T cryostat mentioned before but with a customized sample holder. Due to the requirement that the detector should be placed close to the sample, the detector holder was mounted inside the sample space just in front of the sample without blocking the sample rotation stage. The rotation allows detection feedback from the tested

53 samples from various angles, such constructions sketch can be seen in Fig. 3.17. Such customization also requires the current and the voltage wires in order to operate the detector. They were soldered to the sample PCB before the actual sample was glued and bonded to it.

Figure 3.16: A “meander” array layout with marker input and output current contacts [66].

Figure 3.17: Scheme of sample rotator with sample on it and the detector placed geometrically in front of the array center [66].

The detector was around 1 cm from the geometrical center of the array. Fig. 3.17 is a schematic draw of the mounted sample and the detector in its place (the detector holder is not shown). Experimental results obtained by biasing such arrays with one-by-one switching of Josephson junction from superconducting to resistive state are presented in Fig. 3.18 and Fig. 3.19.

54 Fig. 3.18 shows the emission power as a function of voltage that was detected from the Josephson junction arrays. Two graphs in Fig.3.18 show the linear array emission behavior with the two lines marked in blue for α=85˚and red line for the angles with the maximum achieved emission. The detection measurements were done on a reverse branch of the IVs [66].

Figure 3.18: (a) Linear array emitted power on α=85˚ blue line and maximum emission angle red line, (b) meander array electromagnetic wave emission power, blue line for α=85˚and maximum emission detection angle, red line [66].

The meander array emitted radiation on respect to the detector response is shown in Fig. 3.19. It is clearly seen that there is a rapid increase after some threshold number of active junctions. Followed decreasing on graph-related with self-heating of the sample as the number of active junctions exceeds 7000 of them. The replotted data for meander array where the detector signal is normalized by the total consumed power in the array is shown in Fig. 3.20. In other words, this shows the ratio between the emitted and the consumed power. From this graph, it is seen that the increasing number of oscillation junctions affect the quality of emission that grows rapidly and nonlinearly. Such evidence declares the presence of super-radiant emission from the array with a threshold number of JJs [79-81], with a record high amount of active Josephson junctions. Thus, it can be easily seen that the meander array is the best candidate with nonlinear power enhancement with a large number of junctions for coherent emission. The linear array shows that power rises with an increasing number of junctions that take place in the oscillation, while the meander array has a rapid increase of the emission power at U ~ 1.3 V due to all oscillation junctions being in an identical state; the emission power should rapidly increase as ∝ 푁2.

Figure 3.19: (b) meander array electromagnetic wave emission power, blue line for α=85˚and maximum emission detection angle, red line [66].

Figure 3.20: Normalized signal by total consumed power from meander array, the red line is maxima emission correspondent angle, blue for α=85˚ [66].

Oscillation frequency for both arrays was limited by the applied voltage, which was U1=1.879V for the linear array, and U2=2.223V for the meander array. These voltages correspond to the oscillation frequencies 130.2GHz and 119.3GHz. The estimation of maximum detected power for both arrays is 80- 90µW, respectively. The emission form both arrays presents a forward-backward asymmetry [66]. Observed difference in-between two different arrays suggests that a non-resonant

56 traveling wave mechanism of synchronization take part at meander array emission. A traveling wave allows getting significant emission power in the propagation direction due to the strong asymmetry of the radiation pattern. This is similar to how the Beverage antenna or the wave antenna work, and simulation performed for 10 to 11 JJs in [64] and such experiment shows that it can be used to synchronize a significant amount of the Josephson junctions. A direct confirmation for the traveling mechanism scenario of synchronization of those arrays has been obtained recently in paper V using the low temperature scanning laser microscopy technique.

57 Summary

The main novelty of this work was fabrication and analysis of small but tall micron-sized mesa structures with hundreds of Josephson junctions from Bi2Sr2CaCu2O8+δ high-Tc superconductors. A significant and broadly tunable emission from such mesas has been observed. It was shown that the emission frequency depended on the generator geometry and covered the ranges of 3-11 THz and 1-9 THz respectively. Maxima emission were achieved at the resonances when the Josephson frequency matches the geometry-dependent cavity modes in the mesa. This indicates that the superradiant coherent emission was achieved. A estimated output power is around 1µW. This is due to a substantial increase in the number of junctions taking part in the synchronized emission. It is concluded that a minimum number of junctions needed to achieve the coherent emission is N>100. Two ways to tune the radiating frequency have been demonstrated: one is by changing the bias voltage; the other is by changing geometrical resonance frequencies by varying the geometry of the mesas. Good emission power and high-frequency tunability make the HTS intrinsic Josephson junction stack a promising candidate for compact THz sources to cover the whole “THz-gap” using a single device. Other promising results have been achieved through the synchronization of large Nb/NbSi/Nb Josephson junction arrays with a total number of junctions up to nine thousand. Two types of chain-like arrays were studied. It is shown that a travelling wave non-resonant mechanism of synchronization can be effective for synchronization of such very large arrays with overall size. Such type of synchronization opens the possibility to synchronizing even larger arrays for achieving higher output powers. This way it would be also possible to combine and achieve the coherent emission from arrays of the Josephson junction stacks. From the technical point of view, the fabrication process for making junctions on single crystals of various unconventional high-Tc superconductors has been developed. It gives a variety of possibilities for creating different samples with different sizes and geometry for various purposes, not only in the field of the THz sources but also for other applications. The only limitation is the instrumental resolution and the imagination of the researcher. Therefore, the present work shows that arrays of Josephson junction both natural in HTS cuprate and artificial using low temperature superconductors can be employed for creation of compact and tunable THz sources that are needed for a large variety of applications. Due to their high tunability and superradiant emission nature, they are perfectly suited for creation of a single device covering the whole THz gap” region.

58 Acknowledgments

For helping me during the long process of arriving at a Ph.D. thesis, I would like to thank my supervisor Prof. Vladimir Krasnov. His patience, support, and knowledge helped easily steer the course of the Ph.D. over such an exciting topic of high-Tc superconductors. Also, I would like to say special thanks to Taras Golod, my co-supervisor, who helped with measurement set-ups and kept cleanroom equipment in a working condition after intensive usage of it. Additionally, I would like to pay my respect and say thanks to Alessandro Pagliero, who was my first office colleague and showed me how everything should be done to let things work. Hope this thesis will reach you. Additional thanks go to my colleague Roberto de Andreas Prada, with whom I lived together in my first year and who make everything go smoother due to his perfect sense of humor. Thanks, bro! Erik Holmgren, thanks for all the help you gave and for the interesting talks during breaks, you became a real Swedish friend of mine. Milton Persson, thank you also for cool moments and wise advices. I would also like to say thanks to Adrian Iovan, for his guidance for lithography equipment and help in the cleanroom and also for computer that I used. Moreover, I would like to say my special thanks to my wife, Olena Kapran, who has also become my colleague for long scientific talks, providing criticism and advice to achieve and perform better results and for pushing me toward my dreams. Also, I would like to say special acknowledgement to my family. My Mom who pushes me towards physics, my grandma who also take part in all my life movements, my grandpa for best advices. Also separate thanks to Prof. Oleg Vasylkiv for long scientific and not only discussions and suggestions. And to Prof. Petre Badica for his wise advises.

59 References

[1] Bednorz, J. G.; Müller, K. A. “Possible high Tс superconductivity in the Ba- La-Cu-O system.” Zeitschrift für Physik B. 64 (2): 189–193, 1986.

[2] Sheng, Z. Z.; Hermann A. M. “Bulk superconductivity at 120 K in the Tl– Ca/Ba–Cu–O system”. Nature. 332 (6160): 138–139, 1988

[3] Chu, C. W.; Gao, L.; Chen, F.; Huang, Z. J.; Meng, R. L.; Xue, Y. Y. “Superconductivity above 150 K in HgBa2Ca2Cu3O8+δ at high pressures”. Nature. 365 (6444): 323, 1993

[4] Drozdov, A. P.; Eremets, M. I.; Troyan, I. A.; Ksenofontov, V.; Shylin, S. I. “Conventional superconductivity at 203 kelvin at high pressures in the sulfur hydride system”. Nature. 525 (7567): 73–6, 2015

[5] Kleiner R, Steinmeyer F, Kunkel G and Muller P “Intrinsic Josephson effects in Bi2Sr2CaCu2O8 single crystals” Phys. Rev. Lett. 68 2394, 1992

[6] Kleiner R and Muller P “Intrinsic Josephson effects in high- Tc superconductors” Phys. Rev. B 49 1327, 1994

[7] F.Sizov and A. Rogalski, "THz detectors” Prog. Quant. Electron. 34, 278, 2010

[8] L. Ozyuzer et al., “Emission of Coherent THz Radiation from Superconductors”, Science 318, 1291 2, 49, 2007

[9] Masayoshi Tonouchi “Cutting-edge THz technology” Nature Photonics 1(2):97-105, 2007

[10] Welp, U., Kadowaki, K. & Kleiner, R. “Superconducting emitters of THz radiation.” Nat. Photonics 7, 702, 2013

[11] Jozsef Andras Fulop, Stelios Tzortzakis and Tobias Kampfrath, “Laser- Driven Strong-Field Terahertz Sources.”, Adv. Optical Mater. 8, 1900681, 2020

[12] G.P. Gallerano et al. ”Overview of Terahertz radiation sources.”, Proceed- ings of the 2004 FEL Conference, 216-221, 2004

60 [13] H. Eisele, “Recent advances in the performance of InP Gunn devices and GaAs TUNNETT diodes for 100-300 GHz frequency range and above”, IEEE Trans. On Microwave Theory and Techniques, 48, 626, 2000

[14] J. Faist et al., “Quantum cascade laser”, Science, 264, 553, 1994

[15] R. Kohler et al., “Terahertz semiconductor heterostructure laser”, Nature, 417, 156, 2002

[16] D.H. Auston, K.P. Cheung, J.A. Valdmanis, D.A. Kleinman, “Cherenkov Radiation from Femtosecond Optical Pulses in Electro-Optic Media”, Phys.Rev.Lett., 53, 1555, 1984

[17] C. Fattinger, D. Grischkowsky, “Terahertz beams” Appl. Phys. Lett., 54, 440, 1989

[18] Z. Jiang and X.C. Zhang, “Terahertz imaging via electro-optic effect”, IEEE Trans. Microwave Theory Tech., 47, 2644, 1999

[19] T. Kashiwagi et al., “The present status of high-Tc superconducting terahertz emitters”, Supercond. Sci. Technol., 30, 074008, 2017

[20] T. Kashiwagi et al., “A high-Tc intrinsic Josephson junction emitter tunable from 0.5 to 2.4 terahertz”, Appl. Phys. Lett., 107, 082601, 2015

[21] Kashiwagi T et al., “Generation of electromagnetic waves from 0.3 to 1.6 terahertz with a high-Tc superconducting Bi2Sr2CaCu2O8+δ intrinsic Joseph- son junction emitter”, Appl. Phys. Lett. 106, 092601, 2015

[22] Kitamura T et al., “Broadly tunable, high-power terahertz radiation up to 73 K from a stand-alone Bi2Sr2CaCu2O8+δ mesa”, Appl. Phys. Lett. 105, 202603, 2014

[23] Nakade K, Kashiwagi T, Saiwai Y, Minami H, Yamamoto T, Klemm R A and Kadowaki K, “Applications using high-Tc superconducting terahertz emitters”, Sci. Rep. 6, 23178, 2016

[24] Benseman T M, Gray K E, Koshelev A E, Kwok W-K, Welp U, Minami H, Kadowaki K and Yamamoto T, “Three-terminal stand-alone superconducting terahertz emitter”, Appl. Phys. Lett. 103, 022602, 2013

61 [25] I. Giaever, “Energy Gap in Superconductors Measured by Electron Tunneling” Phys. Rev. Lett. 5, 147 2, 1960

[26] Paul Seidel “Applied Superconductivity: Handbook on Devices and Applications”, Wiley-VCH, 2015

[27] P.W. Anderson and J.M. Rowell, “Probable observation of the Josephson superconducting tunneling effect”, Phys. Rev. Lett., 10, 1963

[28] H. Maeda; Y. Tanaka; M. Fukutumi & T. Asano “A New High-Tc Oxide Superconductor without a Rare Earth Element.” Jpn. J. Appl. Phys. 27 (2): L209– L210, 1988

[29] Wenk, Hans-Rudolf; Bulakh, Andrei. “Minerals: Their Constitution and Origin.” New York, NY: Cambridge University Press, 2004

[30] P. Bordet, J.J. Capponi, C. Chaillout, J. Chenavas, A.W. Hewat, E.A. Hewat, J.L. Hodeau, M. Marezio, “A review of the preparation and structure of Bi–Sr– Ca–Cu–O superconductors and Pb-substituted phases, in: A. Narliker (Ed.), Studies of High Temperature Superconductors.” vol. 2, Nova Science Publisher, pp. 171–198, 1991

[31] J. Slezal, “The unit cell of Bi-2212, a high-temperature superconductor”, CC-BY 2.5, 11, 2006

[32] H.P. Roeser et al. ”Doping patterns in N-type high-temperature superconductors PLCCO and NCCO” Acta Astronautica 63 1372 – 1375, 2008

[33] K Sugawara, C Sugimoto, T Luo, T Kawamata, T Noji, M Kato and Y Koike “Superconductivity above 100 K in the Bi-2212 phase of (Bi,Pb)2Sr2CaCu2O8” IOP Conf. Series: Journal of Physics: Conf. Series 1054, 2018

[34] B. Josephson,”Possible new effects in superconductive tunneling” Phys. Lett. 1, 251, 4, 1962

[35] A. Barone and G. Paterno, “Physics and Application of the Josephson effect. Tunneling and Superconductivity” New York: John Wiley and Sons, 1982

[36] L.Faddeev, and V. Korepin,. “Quntum theory of solitons.”, Phys.Rep. 42, 1, 6, 1978

[37] V. M. Krasnov, ”In-plane fluxon in layered superconductors with arbitrary number of layers” Phys.Rev. B 63. 2001

62 [38] Holger Motzkau “High-frequency phenomena in small Bi2Sr2CaCu2O8+δ intrinsic Josephson junctions”, Doctoral thesis in Physics, Stockholm University, 2015

[39] D. Stornaiuolo, G. Rotoli, D. Massarotti, F. Carillo, L. Longobardi, F. Beltram, and F. Tafuri, “Resolving the effects of frequency-dependent damping and quantum phase diffusion in YBa2Cu3O7−x Josephson junctions” Phys. Rev. B 87, 134517 2013

[40] T. Nagatsuma, K.Enpuku, F. Irie and K. Yoshida,” Flux-flow-type Joseph- son oscillator for millimeter and submillimeter-wave region.” J. Appl. Phys., 56, no.6, pp.3302-3309, 1983.

[41] T. Nagatsuma, K.Enpuku, K. Yoshida and F. Irie,”Flux-flow-type Joseph- son oscillator for millimeter ans submillimeter-wave region. II. Modeling” J. Appl. Phys., 56, no.11, pp.3284-3293, 1984.

[42] T. Nagatsuma, K.Enpuku, K. Sueoka, K. Yoshida and F. Irie,”Flux-flow- type Josephson oscillator for millimeter and submillimeter-wave region. III. Os- cillation stability” J. Appl. Phys. 58, no.1, pp.441-449, 1985.

[43] Sven-Olof Katterwe, “Properties of small Bi2Sr2CaCu2O8 intrinsic Joseph- son junctions: confinement, flux-flow and resonant phenomena”, Doctoral thesis in Physics, Stockholm University, 2011

[44] Golod T., Iovan, A. & Krasnov, V. “Single Abrikosov vortices as quantized information bits.” Nat Commun 6, 8628, 2015

[45] V.P. Koshelets and S.V. Shitov “Integrated superconducting receivers” Su- perconducting Science and Technology 13, no.5 p.,000

[46] P. Barbara et al. “Stimulated emission and amplification in Josephson junction arrays” Phys. Rev. Lett. 82 pp. 1963-1966, 1999.

[47] S. Sakai, A.V. Ustinov, H. Kohlstedt, A. Petraglia, and N.F. Pedersen” The- ory and experiment on electromagnetic-wave-propagation velocities in stacked superconducting tunnel junctions.”, Phys. Rev.B, 50, pp.12905-12914, 1994

[48] A. Irie and G.Oya, “Effect of thermal fluctuations on Josephson vortex dynamics in intrinsic Josephson junctions.” Supercond. Sci. Technol. 20, S18, 2007

63 [49] R.Kleiner et al., “Dynamic behavior of Josephson-coupled layered structures” Phys. Rev. B 50 3942, 1994

[50] S.Sakai. P.Bodin, N. Pedersen, “Fluxons in thin‐film superconductor‐insulator superlattices”, J.Appl. Phys. 73 2411, 1993

[51] R. Kleiner, “Two-dimensional resonant modes in stacked Josephson junctions.” Phys. Rev. B 50 6919 1994

[52] S.Sakai, et al., “Dynamics of multiple-junction stacked flux-flow oscillators: Comparison between theory and experiment” Phys. Rev. B, 58, 5777 1998

[53] N. F. Pedersen and S. Sakai, “Josephson plasma resonance in superconducting multilayers”, Phys. Rev. B, 58 2820, 1998

[54] Katterwe S.O and Krasnov V. M. Temperature dependences of geometrical and velocity-matching resonances in Bi2Sr2CaCu2O8+δ intrinsic Josephson junctions. Phys. Rev. B 84, 214519, 2011

[55] D.D. Coon and M.D. Fiske “Josephson ac and step structure in the supercurrent tunneling characteristic” Phys. Rev. 138 pp. 744-746, 1965

[56] A. Irie, Y. Hirai and G. Oya Fiske and flux-flow modes of the intrinsic Jo- sephson junctions in Bi2Sr2CaCu2Oy mesas. Appl. Phys. Lett. 72 no 17 2159- 2161, 1998

[57] V.M. Krasnov, N. Mors, A. Yurgens and D. Winkler “Fiske steps in intrinsic Bi2Sr2CaCu2O8+x stacked Josephson junctions”, Phys. Rev. B 59, 1999

[58] Y. Latyshev, A. Koshelev, V. Pavlenko M. Gaifullin, T. Yamashita and Y. Matsuda, “Novel features of Josephson flux flow in Bi2212: contribution of in- plane dissipation, coherent response to mm-wave radiation, size effect”, Physica C: Superconductivity 367 no1-4, 2002

[59] S. O. Katterwe, A. Rydh, H. Motzkau, A. B. Kulakov, and V. M. Krasnov, “Superluminal geometrical resonances observed in Bi2Sr2CaCu2O8+x intrinsic Josephson junctions”, Phys. Rev. B 82, 024517, 2010

[60] V. M. Krasnov “Coherent flux-flow emission from stacked Josephson junctions: Nonlocal radiative boundary conditions and the role of geometric resonances” Phys. Rev. B 82, 2010

64 [61] D. Stornaiuolo, G. Rotoli, D. Massarotti, F. Carillo, L. Longobardi, F. Beltram, and F. Tafuri, “Resolving the effects of frequency-dependent damping and quantum phase diffusion in YBa2Cu3O7−x Josephson junctions” Phys. Rev. B 87, 134517, 2013

[62] M.H. Devoret, J.M. Martinis and J. Clarke, “Measurements of Macroscopic Quantum Tunneling out of the Zero-Voltage State of a Current-Biased Josephson Junction”, Phys. Rev. Lett. 55, 1908, 1985

[63] H.B. Wang, S Guenon, J. Yuan, A. Iishi, S. Arisawa, T. Hatano, T. Yama- shita, D. Koelle and R. Kleiner, “Hot spots and Waves in Bi2Sr2CaCu2O8 Intrinsic Josephson junction stacks: A study by low temperature scanning laser microscopy”, Phys. Rev. Lett. 102, 2009

[64] C. A. Balanis in Antenna Theory: “Analysis and Design”, 3rd edition. Chap- ter 10 Wiley Interscience, New York, 2005

[65] V. V. Kurinm, N.K. Vdovicheva and I.A. Shereshevsky “Josephson traveling-wave antennas”, Radiophys. Quantum Electron 59, 922, 2017

[66] M. A. Galin, E. A. Borodianskyi, V. V. Kurin, I. A. Shereshevskiy, N. K. Vdovicheva, V. M. Krasnov and A. M. Klushin, “Synchronization of Large Josephson-Junction Arrays by Traveling Electromagnetic Waves” Phys. Rev. Applied 9 054032, 2018

[67] M. A. Galin, A. M. Klushin, V. V. Kurin, S. V. Seliverstov, M. I. Finkel, G. N. Goltsman, F. Müeller, T. Scheller, and A. D. Semenov, “Towards local oscillators based on arrays of niobium Josephson junctions”, Supercond. Sci. Technol. 28, 055002, 2015

[68] Atul Tiwari, “Handbook of Antimicrobial coatings”, Chapter 16, Moham- mad M. Hassan, Elsevier, 2018

[69] Borodianskyi E.A., Krasnov V.M., “Josephson emission with frequency span 1-11 THz from small Bi2Sr2CaCu2O8+δ mesa structures.”, Nat. Commun, 8 (1), art. No. 1742, 2017

[70] A.A. Kalenyuk, A. Pagliero, E.A. Borodianskyi, S. Aswartham, S. Wurmehl, B. Buchner, D. A. Chareev, A.A. Kordyuk and V.M. Krasnov, “Unu- sual two-dimensional behavior of iron-based superconductors with low anisotropy”, Phys. Rev. B 96 134512, 2017

65 [71] A. A. Kalenyuk, A. Pagliero, E. A. Borodianskyi, A. A. Kordyuk, and V. M. Krasnov “Phase-Sensitive Evidence for the Sign-Reversal s± Symmetry of the Order Parameter in an Iron-Pnictide Superconductor Using Nb/Ba1- xNaxFe2As2 Josephson Junctions” Phys. Rev. Lett. 120, 067001 (2018)

[72] Krasnov V.M. “Temperature dependence of the bulk energy gap in underdo- ped Bi2Sr2CaCu2O8+δ. Evidence of the mean-field superconducting transition.”, Phys.Rev.B 79 214510, 2009

[73] Jacobs Th., Simsek. Y., Koval Y., Muller P., Krasnov V.M., “Sequence of quantum phase transition in Bi2Sr2CaCu2O8+δ cuprates revealed by in situ electrical doping of one and the same sample.”, Phys. Rev. Lett, 116 067001, 2016 [74] Martinis J.M. Grabet H. “Thermal enhacement of macroscopic quantum tunneling: Derivation from noise theory.”, Phys. Rev. B 38, 2371, 1988

[75] Krasnov V.M. “Terahertz electromagnetic radiation from intrinsic Joseph- son junctions at zero magnetic field via breather type self-oscillations.”, Phys. Rev. B 83, 174517, 2011

[76] A. N. Vystavkin, V. N. Gubankov, V. N. Listvin and V.V. Migulin, “Limit sensitivity of detectors based on electron gas heating in n-InSb.”, Izv. Vyssh. Uchebn. Zaved., Radiofiz. 11, 602, 1968

[77] Golod. T., Iovan A. and Krasnov V.M. “Single Abrikosov vortices as quantized information bits” Nat.Commun. 6, 8628, 2015

[78] F. Müller, R. Behr, T. Weimann, L. Palafox, D. Olaya,P. D. Dresselhaus, and S. P. Benz, “1 V and 10 V SNS programmable voltage standards for 70 GHz.”, IEEE Trans.Appl. Supercond. 19, 981, 2009

[79] M. A. Galin, A. M. Klushin, V. V. Kurin, S. V. Seliverstov, M. I. Finkel, G. N. Goltsman, F. Müeller, T. Scheller, and A. D. Semenov, “Towards local oscillators based on arrays of niobium Josephson junctions.”, Supercond. Sci. Tech- nol. 28, 055002, 2015

[80] P. Barbara, A. B. Cawthorne, S. V. Shitov, and C. J. Lobb, “Stimulated Emission and Amplification in Josephson Junction Arrays.”, Phys. Rev. Lett. 82, 1963, 1999

[81] G. Filatrella, N. F. Pedersen, C. J. Lobb, and P. Barbara, “Synchronization of underdamped Josephson-junction arrays.”, Eur. Phys. J. B 34, 3, 2003

66 Appended Papers