Some Applications of the Josephson Effect
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Application of the Josephson Effect to Voltage Metrology
Application of the Josephson Effect to Voltage Metrology SAMUEL P. BENZ, SENIOR MEMBER, IEEE, AND CLARK A. HAMILTON, FELLOW, IEEE Invited Paper The unique ability of a Josephson junction to control the flow of worldwide set of units that is uniform and coherent. The am- magnetic flux quanta leads to a perfect relationship between fre- pere is the only electrical unit belonging to the seven base quency and voltage. Over the last 30 years, metrology laboratories units of the SI. The ampere is defined as “that constant cur- have used this effect to greatly improve the accuracy of dc voltage standards. More recent research is focused on combining the ideas rent which, if maintained in two parallel straight conduc- of digital signal processing with quantum voltage pulses to achieve tors of infinite length, of negligible circular cross section, similar gains in ac voltage metrology. The integrated circuits that and placed 1 meter apart in vacuum, would produce between implement these ideas are the only complex superconducting elec- these conductors a force equal to 2 10 newtons per meter tronic devices that have found wide commercial application. of length.” Keywords—Digital–analog conversion, Josephson arrays, quan- The volt, which is not a base unit, is defined through tization, standards. coherency of electrical power (current times voltage) and mechanical power (force times distance divided by time): I. INTRODUCTION “The volt is that electromotive force between two points on a conductor carrying a constant current of 1 ampere when In 1962, B. Josephson, a graduate student at Cambridge the power dissipated between the two points is 1 watt.” University, Cambridge, U.K., derived equations for the cur- Realization of the SI volt, therefore, depends on experiments rent and voltage across a junction consisting of two super- that relate the ampere and the volt to the mechanical units of conductors separated by a thin insulating barrier [1]. -
Monte Carlo Simulation Study of 1D Josephson Junction Arrays
Monte Carlo Simulation Study of 1D Josephson Junction Arrays OLIVER NIKOLIC Master Thesis Stockholm, Sweden 2016 Typeset in LATEX TRITA-FYS 2016:78 ISSN 0280-316X ISRN KTH/FYS/-16:78-SE Scientific thesis for the degree of Master of Engineering in the subject of theoretical physics. © Oliver Nikolic, December 2016 Printed in Sweden by Universitetsservice US AB iii Abstract The focus in this thesis is on small scale 1D Josephson junction arrays in the quantum regime where the charging energy is comparable to the Joseph- son energy. Starting from the general Bose-Hubbard model for interacting Cooper pairs on a 1D lattice the problem is mapped through a path integral transformation to a classical statistical mechanical (1+1)D model of diver- gence free space-time currents which is suitable for numerical simulations. This model is studied using periodic boundary conditions, in the absence of external current sources and in a statistical canonical ensemble. It is explained how Monte Carlo simulations of this model can be constructed based on the worm algorithm with efficiency comparable to the best cluster algorithms. A description of how the effective energy Ek, voltage Vk and inverse capacitance −1 Ck associated with an externally imposed charge displacement k can be ex- tracted from simulations is presented. Furthermore, the effect of inducing charge by connecting an external voltage source to one island in the chain via the ground capacitance is investigated. Simulation results display periodic −1 response functions Ek, Vk and Ck as the charge displacement is varied. The shape of these functions are largely influenced by the system parameters and evolves from sinusoidal with exponentially small amplitude deep inside the superconducting regime towards more intriguing shapes closer to the insulat- ing regime where interactions among quantum phase slips are present. -
Transition from Phase Slips to the Josephson Effect in a Superfluid 4He Weak Link
1 Transition from phase slips to the Josephson effect in a superfluid 4He weak link E. Hoskinson1, Y. Sato1, I. Hahn2 and R. E. Packard1 1Department of Physics, University of California, Berkeley, CA, 94720, USA. 2Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA The rich dynamics of flow between two weakly coupled macroscopic quantum reservoirs has led to a range of important technologies. Practical development has so far been limited to superconducting systems, for which the basic building block is the so-called superconducting Josephson weak link1. With the recent observation of quantum oscillations2 in superfluid 4He near 2K, we can now envision analogous practical superfluid helium devices. The characteristic function which determines the dynamics of such systems is the current-phase relation I s (ϕ) , which gives the relationship between the superfluid current I s flowing through a weak link and the quantum phase difference ϕ across it. Here we report the measurement of the current-phase relation of a superfluid 4He weak link formed by an array of nano- apertures separating two reservoirs of superfluid 4He. As we vary the coupling strength between the two reservoirs, we observe a transition from a strongly coupled regime in which I s (ϕ) is linear and flow is limited by 2π phase slips, to a weak coupling regime where I s (ϕ) becomes the sinusoidal signature of a Josephson weak link. The dynamics of flow between two weakly coupled macroscopic quantum reservoirs can be highly counterintuitive. In both superconductors and superfluids, 2 currents will oscillate through a constriction (weak link) between two reservoirs in response to a static driving force which, in a classical system, would simply yield flow in one direction. -
Superconductivity and SQUID Magnetometer
11 Superconductivity and SQUID magnetometer Basic knowledge Superconductivity (critical temperature, BCS-Theory, Cooper pairs, Type 1 and Type 2 superconductor, Penetration Depth, Meissner-Ochsenfeld effect, etc), High temperature superconductors, Weak links and Josephson effects (DC and AC), the voltage-current U(I) characteristic, SQUID: structure, applications, sensitivity, functionality, screening current, voltage-magnetic flux characteristic) Literature [1] Ibach, Lüth, Festkörperphysik, Springer Verlag [2] Buckel, Supraleitung, VCH Weinheim [3] Sawaritzki, Supraleitung, Harri Deutsch [4] C. Kittel, Introduction of the Solid State Physics, John Wiley & Sons Inc. [5] N. W. Ashcroft and N. D. Mermin, “Solid State Physics” [6] STAR Cryoelectronics, Mr. SQUID® User’s Guide [7] http://en.wikipedia.org/wiki/Superconductor [8] http://www.physnet.uni-hamburg.de/home/vms/reimer/htc/pt3.html [9] http://hyperphysics.phy-astr.gsu.edu/Hbase/solids/scond.html#c1 [10] http://www.lancs.ac.uk/ug/murrays1/bcs.html [11] http://www.superconductors.org/Type1.htm Experiment 11, Page 1 Content: 1. Introduction………………………………..…………………………… 3 2. Basic knowledge………………………………………..………………4 Superconductivity BCS theory Cooper pairs Type I and Type II superconductors Meissner-Ochsenfeld effect Josephson contacts Josephson effects U-I characteristic Dc SQUID 3. Experimental setup………………………………………….….….13 4. Experiment…………………………………….………………….…14 4.1 Preparing the SQUID 4.2 Determination of the critical temperature of the YBCO-SQUID 4.3 Voltage – current characteristic 4.4 Voltage – magnetic flux characteristic 4.5 Qualitative experiments 5. Schedule and analysis………………………………..………....19 Questions……………………………………………...……….……….19 Experiment 11, Page 2 1. Introduction The aim of the present experiment is to give an insight into the main properties of superconductivity in connection with the description of SQUID. -
Josephson Tunneling at the Atomic Scale: the Josephson EEct As a Local Probe
Josephson Tunneling at the Atomic Scale: The Josephson Eect as a Local Probe THIS IS A TEMPORARY TITLE PAGE It will be replaced for the nal print by a version provided by the service academique. Thèse n. 6750 2015 présentée le 22 juillet 2015 à la Faculté des Sciences des Bases Laboratoire á l'Echelle Nanométrique Programme Doctoral en Physique École Polytechnique Fédérale de Lausanne pour l'obtention du grade de Docteur des Sciences par Berthold Jäck acceptée sur proposition du jury: Prof. Andreas Pautz, président du jury Prof. Klaus Kern, directeur de thèse Prof. Davor Pavuna, rapporteur Prof. Hermann Suderow, rapporteur Dr. Fabien Portier, rapporteur Lausanne, EPFL, 2015 Non est ad astra mollis e terris via — Lucius Annaeus Seneca Acknowledgements It took me about three and a half years, with many ups and downs, to complete this thesis. At this point, I want to say thank you to all the people that supported me on my way by any means. First of all, I am grateful to Prof. Klaus Kern for giving me the opportunity to perform my doctoral studies under his supervision at the Max-Planck-Institute for Solid State Research in Stuttgart, Germany. For the entire time of my studies, I enjoyed a significant scientific freedom, such that I had the great possibility to pursue and realize my own ideas. In particular, I want to acknowledge his personal support, which allowed me to attend conferences, workshops and schools, have interesting scientific discussions as well as a wonderful time in the whole of Europe and across the USA. -
Cond-Mat.Mes-Hall] 28 Feb 2007 R Opligraost Eiv Htti Si Fact [7] Heeger in and Is Schrieffer Su, This Dimension, a That That One Showed Believe in to There So
Anyons in a weakly interacting system C. Weeks, G. Rosenberg, B. Seradjeh and M. Franz Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, Canada V6T 1Z1 (Dated: June 30, 2018) In quantum theory, indistinguishable particles in three-dimensional space behave in only two distinct ways. Upon interchange, their wavefunction maps either to itself if they are bosons, or to minus itself if they are fermions. In two dimensions a more exotic possibility arises: upon iθ exchange of two particles called “anyons” the wave function acquires phase e =6 ±1. Such fractional exchange statistics are normally regarded as the hallmark of strong correlations. Here we describe a theoretical proposal for a system whose excitations are anyons with the exchange phase θ = π/4 and charge −e/2, but, remarkably, can be built by filling a set of single-particle states of essentially noninteracting electrons. The system consists of an artificially structured type-II superconducting film adjacent to a 2D electron gas in the integer quantum Hall regime with unit filling fraction. The proposal rests on the observation that a vacancy in an otherwise periodic vortex lattice in the superconductor creates a bound state in the 2DEG with total charge −e/2. A composite of this fractionally charged hole and the missing flux due to the vacancy behaves as an anyon. The proposed setup allows for manipulation of these anyons and could prove useful in various schemes for fault-tolerant topological quantum computation. I. INTRODUCTION particle states. It has been pointed out very recently [9] that a two-dimensional version of the physics underly- Anyons and fractional charges appear in a variety of ing the above effect could be observable under certain theoretical models involving electron or spin degrees of conditions in graphene. -
Surprising New States of Matter Called Time Crystals Show the Same Symmetry Properties in Time That Ordinary Crystals Do in Space by Frank Wilczek
PHYSICS CRYSTAL S IN TIME Surprising new states of matter called time crystals show the same symmetry properties in time that ordinary crystals do in space By Frank Wilczek Illustration by Mark Ross Studio 28 Scientific American, November 2019 © 2019 Scientific American November 2019, ScientificAmerican.com 29 © 2019 Scientific American Frank Wilczek is a theoretical physicist at the Massachusetts Institute of Technology. He won the 2004 Nobel Prize in Physics for his work on the theory of the strong force, and in 2012 he proposed the concept of time crystals. CRYSTAL S are nature’s most orderly suBstances. InsIde them, atoms and molecules are arranged in regular, repeating structures, giving rise to solids that are stable and rigid—and often beautiful to behold. People have found crystals fascinating and attractive since before the dawn of modern science, often prizing them as jewels. In the 19th century scientists’ quest to classify forms of crystals and understand their effect on light catalyzed important progress in mathematics and physics. Then, in the 20th century, study of the fundamental quantum mechanics of elec- trons in crystals led directly to modern semiconductor electronics and eventually to smart- phones and the Internet. The next step in our understanding of crystals is oc- These examples show that the mathematical concept IN BRIEF curring now, thanks to a principle that arose from Al- of symmetry captures an essential aspect of its com- bert Einstein’s relativity theory: space and time are in- mon meaning while adding the virtue of precision. Crystals are orderly timately connected and ultimately on the same footing. -
1 Title Josephson Scanning Tunneling Microscopy
Title Josephson scanning tunneling microscopy – a local and direct probe of the superconducting order parameter Authors Hikari Kimura1,2,†, R. P. Barber, Jr.3, S. Ono4, Yoichi Ando5, and R. C. Dynes1,2,6* 1Department of Physics, University of California, Berkeley, California 94720, USA 2Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA 3Department of Physics, Santa Clara University, Santa Clara, California 95053, USA 4Central Research Institute of Electric Power Industry, Komae, Tokyo 201-8511, Japan 5Institute of Scientific and Industrial Research, Osaka University, Ibaraki, Osaka 567-0047, Japan 6Department of Physics, University of California, San Diego, La Jolla, California 92093-0319 *[email protected] †Present address: Department of Physics and Astronomy, University of California, Irvine, California 92697, USA Abstract Direct measurements of the superconducting superfluid on the surface of vacuum-cleaved Bi2Sr2CaCu2O8+δ (BSCCO) samples are reported. These measurements are accomplished via Josephson tunneling into the sample using a scanning tunneling microscope (STM) equipped with a superconducting tip. The spatial resolution of the STM of lateral distances less than the superconducting coherence length allows it to reveal local inhomogeneities in the pair wavefunction of the BSCCO. Instrument performance is demonstrated first with Josephson 1 measurements of Pb films followed by the layered superconductor NbSe2. The relevant measurement parameter, the Josephson ICRN product, is discussed within the context of both BCS superconductors and the high transition temperature superconductors. The local relationship between the ICRN product and the quasiparticle density of states (DOS) gap are presented within the context of phase diagrams for BSCCO. Excessive current densities can be produced with these measurements and have been found to alter the local DOS in the BSCCO. -
Eltsov, VB AC Josephson Effect Between Two
This is an electronic reprint of the original article. This reprint may differ from the original in pagination and typographic detail. Autti, S.; Heikkinen, P. J.; Mäkinen, J. T.; Volovik, G. E.; Zavjalov, V. V.; Eltsov, V. B. AC Josephson effect between two superfluid time crystals Published in: Nature Materials DOI: 10.1038/s41563-020-0780-y Published: 01/02/2021 Document Version Peer reviewed version Please cite the original version: Autti, S., Heikkinen, P. J., Mäkinen, J. T., Volovik, G. E., Zavjalov, V. V., & Eltsov, V. B. (2021). AC Josephson effect between two superfluid time crystals. Nature Materials, 20(2), 171-174. https://doi.org/10.1038/s41563- 020-0780-y This material is protected by copyright and other intellectual property rights, and duplication or sale of all or part of any of the repository collections is not permitted, except that material may be duplicated by you for your research use or educational purposes in electronic or print form. You must obtain permission for any other use. Electronic or print copies may not be offered, whether for sale or otherwise to anyone who is not an authorised user. Powered by TCPDF (www.tcpdf.org) AC Josephson effect between two superfluid time crystals S. Autti1;2∗, P.J. Heikkinen1;3, J.T. M¨akinen1;4;5, G.E. Volovik1;6, V.V. Zavjalov1;2, and V.B. Eltsov1y 1Low Temperature Laboratory, Department of Applied Physics, Aalto University, POB 15100, FI-00076 AALTO, Finland. yvladimir.eltsov@aalto.fi 2Department of Physics, Lancaster University, Lancaster LA1 4YB, UK. *[email protected] 3Department of Physics, Royal Holloway, University of London, Egham, Surrey, TW20 0EX, UK. -
Lecture 10: Superconducting Devices Introduction
Phys 769: Selected Topics in Condensed Matter Physics Summer 2010 Lecture 10: Superconducting devices Lecturer: Anthony J. Leggett TA: Bill Coish Introduction So far, we described only the superconducting ground state. Before proceeding to the main topic of this lecture, we need to say a little about the simplest excited states. For this purpose it is easier to use the original representation of BCS, in which the condition of particle number conservation is relaxed and the ground state has the form of a product of states referring to the occupation of the pair of states (k ↑, −k ↓): in obvious notation, 2 2 ΨBCS = Φk, Φk = uk |00i + vk |11i , |uk| + |vk| = 1 (1) Yk where |00i is the state in which neither k ↑ nor −k ↓ is occupied, |11i is that in which both are, and uk,vk are complex coefficients (though the usual convention is to take uk real). From the identification (lecture 9, Eq. (30)) of the Fourier-transformed wave function Fk with the “anomalous average” hN − 2| a−k↓ak↑ |Ni (which in the BCS representation becomes simply ha−k↓ak↑i we find ∗ Fk = ukvk. (2) In this representation we can associate a contribution to the kinetic and potential energy with each pair state (k ↑, −k ↓) separately (but must remember not to double-count). The contribution hV ik to the potential energy (excluding as usual the Hartree and Fock terms) is simply ∗ hV ik = −2∆kFk. (3) In the case of the kinetic energy, it is most convenient to calculate it relative to the value in the normal ground state (hnki = θ(kF − k)), which is 0 for ǫk > 0 and −2|ǫk| for ǫk < 0. -
Tunnel Junction I ( V ) Characteristics: Review and a New Model for P-N Homojunctions N
Tunnel junction I ( V ) characteristics: Review and a new model for p-n homojunctions N. Moulin, Mohamed Amara, F. Mandorlo, M. Lemiti To cite this version: N. Moulin, Mohamed Amara, F. Mandorlo, M. Lemiti. Tunnel junction I ( V ) characteristics: Review and a new model for p-n homojunctions. Journal of Applied Physics, American Institute of Physics, 2019, 126 (3), pp.033105. 10.1063/1.5104314. hal-03035269 HAL Id: hal-03035269 https://hal.archives-ouvertes.fr/hal-03035269 Submitted on 2 Dec 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Tunnel junction model Tunnel junction I(V) characteristics: review and a new model for p-n homojunctions N. Moulin,1 M. Amara,1, a) F. Mandorlo,1, b) and M. Lemiti1, c) University of Lyon, Lyon Institute of Nanotechnology (INL) UMR CNRS 5270, INSA de Lyon, Villeurbanne, F-69621, FRANCE (Dated: 1 December 2020) Despite the widespread use of tunnel junctions in high-efficiency devices (e.g., multijunction solar cells, tunnel field effect transistors, and resonant tunneling diodes), simulating their behavior still remains a challenge. This paper presents a new model to complete that of Karlovsky and simulate an I(V ) characteristic of an Esaki tunnel junction. -
Lecture Notes 18: Magnetic Monopoles/Magnetic Charges
UIUC Physics 435 EM Fields & Sources I Fall Semester, 2007 Lecture Notes 18 Prof. Steven Errede LECTURE NOTES 18 MAGNETIC MONOPOLES – FUNDAMENTAL / POINTLIKE MAGNETIC CHARGES No fundamental, point-like isolated separate North or South magnetic poles – i.e. N or S magnetic charges have ever been conclusively / reproducibly observed. In principle, there is no physical law, or theory, that forbids their existence. So we may well ask, why did “nature” not “choose” to have magnetic monopoles in our universe – or, if so, why are they so extremely rare, given that many people (including myself) have looked for / tried to detect their existence… If magnetic monopoles / fundamental point magnetic charges did exist in nature, they would obey a Coulomb-type force law (just as electric charges do): ⎛⎞μ ggtest src test ommˆ Frmmm()== gBr () ⎜⎟ 2 r ⎝⎠4π r Source point Sr′( ′) src src test Where: gm = magnetic charge of source particle gm r =−rr′ gm test gm = magnetic charge of test particle zˆ gm ≡+ g() ≡ North pole r′ r gm ≡− g() ≡ South pole SI units of magnetic charge g = Ampere-meters (A-m) ϑ yˆ xˆ Field / observation point Pr( ) 2 ⎛⎞μomg −7 Newtons N Units check: Fm () Newtons = ⎜⎟2 μπo =×410 22 ⎝⎠4π r Ampere( A ) 2 ⎛⎞NN()Am− ⎛⎞A2 − m2 Newton = N = ⎜⎟22= ⎜⎟ = N ⎝⎠Am ⎝⎠A2 m2 Newton Then (the radial) B -field of a magnetic monopole is: 1 Tesla ≡1 Ampere− meter ⎛⎞μ g src N N omˆ Brm ()= ⎜⎟2 r (SI units = Tesla = ) 1 T = 1 ⎝⎠4π r Am− Am− NN⎛⎞A2 − m N Units check: Tesla == = gm = Ampere-meters (A-m) ⎜⎟2 2 Am− ⎝⎠A m Am− © Professor Steven Errede, Department of Physics, University of Illinois at Urbana-Champaign, Illinois 1 2005-2008.