Josephson and nonJosephson emission from

Bi 2Sr 2CaCu2O8+δ mesa structures

Vladimir Krasnov Experimental Condensed Matter Physics Group Condensed Matter and Quantum Optics Division Department of Physics Stockholm University AlbaNova University Center SE-10691 Stockholm, Sweden

P.L. Kapitza Institute of Physical Problems, Moscow, 22 November 2018 The THz gap

From: B.Ferguson and X.C.Zhang Nature Mat. 1, 26 (2002)

Where are Superconductors ?

From: M.Tonouchi Nature Photon. 1, 97 (2007) Outline: I. Josephson emission of EM waves: • Emission via the ac-Josephson effect : hννν= 2eV • Flux-flow oscillator • Geometrical (Fiske) resonances Stacked Josephson junctions • Coherent superradiant ac-Josephson emission • Zero-field emission via breather type self-oscillations II. Semi-Josephson emission : Monochromatic phonon and phonon-polariton emission via the piezoelectric effect III. Non-Josephson emission of non-equilibrium bosons: Superconducting cascade laser

Conclusions I. Josephson emission: ac-J.E. + more

= sin (ϕ) The dc - Josephson effect I S I c h The ac - Josephson effect ω J = 2eV I. Josephson junctions can generate EM-waves / Photons

Low-Tc Josephson flux- flow oscillator phase locked to an external reference oscillator

V. P. Koshelets and S. V. Shitov, Supercond. Sci. Technol. 13 , R53 2000.

But the devil is in the details: Supercurrent is nondissipative need not only dc voltage to ac(super)current conversion, but dctoac POWER conversion EMwave emission by a single junction

S = [Eac H ac ] w S 2πd E H t0 ∇ϕ = H Φ0 Magnetic field or spatially inhomogeneous phase VK, PRB 82, 134524 (2010) are needed for dc-to-ac POWER conversion

Need a Lorentz force = finite B!

Flux-flow oscillator

Problem with radiative Impedance matching (outside the JJ):

Z = Eac / H ac ??? ~ µ 0 /ε 0 =119 .917 Ω Bulaevskii, Koshelev, PRL (2006) 2 = w / Z Langenberg etal, PRL 15, 294 (1965) Radiation power: Prad = wt0 Eac H ac t0 Eac + self-heating limitations = low emission power ~ µµµW + Energy storage in relativistic fluxons

I

Lorentz contraction

V

u=c 0 Zero field steps in linear junctions

c 0 Φ 0 V ZFS = n cL

VZFS = 2V FS

From: A. Barone and G. Paterno Geometrical resonances: Impedance mismatching is not totally bad

2 A. High-Q resonances enhance the emission power: Prad ~ Q B. High-Q resonances reduce the linewidth: ∆f / f =1/ Q

V. P. Koshelets and S. V. Shitov, Supercond. Sci. Technol. 13 , R53 2000.

Flux-flow emission is a 3-step process: 1. Lorentz force accelerates fluxons to the speed of light and store energy. 2. Upon collision with the edge the fluxon energy is given to EM waves. 3. Waves at the cavity mode resonance are amplified, leading to emission. Where is the ac-J.E. here? Coherent EM emission from STACKED Josephson junctions

Radiation power: ??? Ei+1

Ei Outside the stack (far field):

Z = Eac / H ac VK, PRB 82, 134524 (2010)

2 In-phase state: Ei = Ei+1 , Eac = NE i, P ~ N Coherent amplification of radiation ☺

Out-of-phase state: Ei= - Ei+1 , Eac = 0, P ~ 0

Coherent suppression of radiation 2D - cavity modes in stacked Josephson junctions

E.N. Economou, Phys.Rev. 182, 539 (1969)

R.Kleiner, Phys.Rev.B 50, 6919 (1994)

S.Sakai, A.V.Ustinov, H. Kohlstedt, A.Petraglia, N.F. Pedersen, Phys.Rev.B 50, 12905 (1994)

S.O. Katterwe and VK, PRB 84, 214519 (2011) Intrinsic STACKED Josephson junctions in strongly anisotropic HTSC

Bi 2Sr 2CaCu 2O8+x (Bi-2212)

c-axis

Courtesy of A.Yurgens From presentation of P.Mueller

~700 stacked junctions per µµµm of crystal Intrinsic Tunneling Characteristics of small Bi-2212 mesas

Advantages of High-Tc intrinsic Josephson junctions:

* High Tc ≈ 95K: allows high power * High ∆~30-40 meV: allows operation up to 20 THz * Integration of a large amount of stronglySum coupled-gap kink:junction Vsg =2 ∆Ν/e ~700/mm of a crystal: coherent high power superradiation emission 2 2 P ~ N 1.0 SMa, A=1.8x2 µm . T(K)= 30, 53, 65, 75, 82, 95, 0.5 a) Au 125, 175.

0.0

(mA) I Mesa 50 N=9 FIB -0.5

A) 0 cut µ (

-1.0 I -50 T= 30 K CaF 2 -1 0-0.2 0.0 1 0.2 Bi-2212 d) V (V) V (V)

S.O.Katterwe et al, PRL 101, 087003 (2008) Zero-field EM-wave emission from Bi 2Sr 2CaCu 2O8+x mesa structures

L. Ozyuzer et al, Science 318 , 1291 (2007)

Emission at H=0 , Follows ac- Josephson relation Scales as f~1/w – geometrical resonance Superradiant: P~N 2 Mechanism of emission at H = 0 ??? (No Lorentz force)

Standing waves (cavity modes)

H.B.Wang et al., PRL 102, 017006 (2009) Calculation of fluxflow emission from stacked junctions

VK, PRB 82, 134524 (2010) Zero-field emission via breather type self-oscillations

VK, PRB 83, 174517 (2011) Motivation for the search of emission from SMALL Bi-2212 mesas

Advantages of small: • High uniformity of junctions (no deffects) • High Q of geometrical resonances (~1/L) • Low heating = high frequency up to ∆∆∆ ~ 30 meV > 15 THz • Fully (?) understood theoretically: MUST emit!

II. But No emission in mesas with N ~ 20-50 (P<1pW)

III. Detection of emission from SMALL-but-HIGH mesas with N >100 with f ~ 1-11 THz THz generation by small-but-high mesas

From E.A. Borodianskyi & VMK, Nat. Commun . 8, 1742 (2017) Detection of emission: Surface junction as a switching current detector

T = 3 K

Switching condition: I = I + I = I (T) dc rf sw Absorbed power: ~1 nW Irf = Isw - Idc ~ 0.1 µA Emitted power ~1 mW (BWO – test experiment) Generator 2, Detector 5

Generator 4, Detector 1

From E.A. Borodianskyi & VMK, Nat. Commun . 8, 1742 (2017) Emission occurs only when all IJJs are active - superradiant Estimation of in-phase geometrical resonances

7 f(1,0) = c 1/2 L c1(N~250) ≈ 0.1c ≈3x10 m/s

Gen#2: L≈5µm, f(1,0) ≈ 3 THz

Katterwe, VMK, PRB 84, 214519 (2011)

Gen#4: L≈12 µm, f(1,0) ≈ 1.3 THz

Efficiency: Prf ~ 1 µµµW, Pdc ~ 0.1 mW -> 1% Power density (5x5 µµµm2) : ~ 4 W/cm 2 Scaled P to 200x200 µµµm2 : ~ 1.6 mW Conclusion- 1 AC-Josephson emission of EM waves from Bi-2212 mesas: Large mesas – high power, low-f due to heating. Small-but-high mesas emit high-f with high efficiency. • Emission at in-phase cavity modes = coherent emission • Small = Low heating = high V = high f • Record high frequency and fr. span 1-11 THz, • Close to theoretical limit ∆∆∆ ~ 15 THz • Achieved (unoptimized) power density ~ to large mesas. • Tunable in the whole THz gap region and beyond by geometry and Bias • Seemingly, there is a threshold N ~ 100 • Not just N2 effect • Not present in CSGE theory. Why? Power- synchronization, Cascade amplification, Collective cavity pumping - stimulated emission…

See: E.A. Borodianskyi & VMK, Nat. Commun . 8, 1742 (2017) II. Semi-Josephson generation of phonons by the ac-Josephson effect in junctions with polar barrier ( electrostriction )

Eac

First demonstration: In Low-Tc : H. Kinder, Phys. Rev. Lett. 28, 1564 (1972) In High-Tc (Bi-2212 and Tl-2212): A.Yurgens, Supercond. Sci. Technol. 13, R85 (2000); K. Schlenga et al., Phys.Rev.B 57, 14518 (1998).

S.O.Katterwe, et al, Phys. Rev. B 83, 100510(R) (2011).

In Bi 2Sr 2CaCu 2O8+x single crystal – sharp, high quality phonon resonances (7 IR + 7 Raman optical phonons) Tuning the phonon wavelength by magnetic field

H=0 k = 0 Longitudinal Optical (LO) Phonons,

C.Preis, C.Helm, et al Physica C 362, 51 (2001)

H>0 Transverse Optical (TO) Phonons Direct determination of the dispersion relation via the velocity-matching resonance: Power density at phonon - flux-flow resonances: ~1-10 kW/cm2

S.O.Katterwe, et al, PRB 83, 100510(R) (2011) Phonon-Polariton dispersion

LO TO

Direct determination of the dispersionω = cn k relation via the velocity-matching resonance: dω/dk →0 Slow light – a fingerprint of Phonon-Polaritons III. Non -Josephson emission upon non -equilibrium E quasiparticle relaxation

Junction-1 E Junction-2 N(E) h ωB ≤ eV -2∆ Braking phonon h ωR ≥ 2∆ Recomb.

In stacks: eV Cascade amplification of non-equilibrium bosons 2∆ Superconducting cascade laser

V.M.Krasnov, Phys.Rev.Lett. 97,257003 (2006), ibid., 103, 227002 (2009). Quantum cascade laser

J.Faist, et al., Science 264 (1994) 553

Operation principle: •Coupled quantum wells •Population inversion by resonant tunneling •Cascade amplification of light intensity Effect of stacking in semiconducting heterostructure lasers

Stacking leads to : QP confinement (no leakage) Cascading From Z.I.Alferov, Nobel lecture Rev.Mod.Phys. 73, 767 (2001) Superconducting gap unlike the semiconducting gap is naturally placed in the THz frequency range Factors enhancing nonequilibrium effects in IJJs J ⋅τ Very rough estimation: DoS ⋅δf ~ I ⋅τ ⇒ δf ~ d ⋅dos (cm3)

Al/AlOx/Al Nb/AlOx/Nb IJJs Bi-2212 2 2 3 2 3 Jc (A/cm ) ~10 10 -10 3x10 -3x10 ∆ (meV) 0.4 1.4 30-40 2 2 3 3 4 J(Vg) (A/cm ) ~10 10 -10 ~ 10 -10 dos (1/eVcm3) ~2x10 22 ~2x10 22 ~10 22 d (nm) ~100 ~200 ~0.4 τ (ns) ~1000 ~0.2 ~2x10 -3 (opt.)

δf (Vg) (a.u.) ~50 0.05-0.5 5-50 Additional effects of stacking Bosons Cascading N = 10-10 3 QPs Confinement no leakage Kinetic balance equations ∂δN(E,Ω) ∂δN ∂δN ∂δN = + + ∂t ∂t (rel ) ∂t (inj ) ∂t (esc )

Tunnel QP injection rate (bias dependent) ∂δN(E) ∆ dE (E) (E eV )[]f (E eV ) f (E) = 2 ρ ρ − − − ∂t (inj ) e Rn ∆ QP escape rate (via tunneling) ∂δN(E) ∆ dE (E) (E eV )[]f (E) f (E eV ) = − 2 ρ ρ + − + ∂t (esc ) e Rn ∆

Phonon injection rate ∂δN(Ω) ∂δN(Ω) (bias independent) = − βN J ∂t (inj ) ∂t (esc )

∂δN(Ω) vs Phonon escape rate = −δN()Ω ∂t (esc ) d Quasiparticle relaxation rate

∂δN(E) 4πV DQP (0)dE = − × ∂t (rel ) h ∞  2  2  ∆  ∫ dΩα DPh ()()()Ω ρ E ρ E + Ω 1− {f (E)[1− f (E + Ω) g(Ω) ]− f (E + Ω) 1− f (E) 1+ [g(Ω) } ][ ] 0  E(E + Ω)  absorption-emission Relaxation: emission-absorption

E ∆−  2  2  ∆  + ∫ dΩα DPh ()()()Ω ρ E ρ E − Ω 1− {f (E)[1− f (E − Ω) 1+ g ][(Ω) − f (E − ]Ω) 1− f (E) g(Ω [)} ] 0  E(E − Ω) 

Recombination – pair breaking

∞  2  2  ∆  + ∫ dΩα DPh ()()()Ω ρ E ρ Ω − E 1+ {f (E) f (Ω − E)[1+ g(Ω) − 1 ]− f [(E) 1− f (Ω ][− E) g(Ω)} ] E ∆+  E(Ω − E) 

Absorption Spontaneous emission Stimulated emission Phonon relaxation rate

2 ∂δN(Ω) 8πV DQP (0)α DPh (Ω)dΩ = − × ∂t (rel ) h

∞  ∆2  ∫ dE ρ()()E ρ E + Ω 1− {f (E)[1− f (E + Ω) g(Ω) ]− f (E + Ω) 1− f (E) 1+ [g(Ω) } ][ ] ∆  E(E + Ω) 

1 ∞  ∆2  + ∫ dE ρ()()E ρ Ω − E 1+ {[1− f (E) 1− ][f (Ω − E) g(Ω) − f ](E) f (Ω − E) 1+ g(Ω) } [ ] 2 ∆  E(Ω − E) 

Absorption Spontaneous emission Stimulated emission Self-consistency equation:

Equilibrium ∆∆∆0 (((Τ ))) Τ:

1 ΩD tanh( E / 2kT ) = ∫ dE 2 2 λ ∆ 0 E − ∆0

1 ΩD 1 − 2 f (E) ΩD tanh( E / 2kT ) ΩD δf (E) = ∫ dE = ∫ dE − 2 ∫ dE 2 2 2 2 2 2 λ ∆ E − ∆ ∆ E − ∆ ∆ E − ∆

Numerical solution for non-equilibrium ∆/∆ 000:

ε ∆0 T c ε ∆ ∆0 T c tanh( ) − tanh( ) ∞ ∞ 2 k T c T 2 ∆0 k T c T δf (E) ∫ dε = −2∫ dE 2 2 2 1 ε −1 ∆ E − ∆ QP’s at the bottom of the gap are most important Nonlinear effects at even-gap bias: Secondary nonequilibrium QP and bosons E eV < 4 ∆∆∆

Bremsstrahlung Recombination bosons bosons E N(E) 2∆∆∆ Phonon intensity Phonon Bremsstr boson eV -2∆∆∆ 2∆∆∆ Energy

Recomb. eV = 4∆∆∆ Bremsstrahlung •Enhanced depairing Recombination bosons Secondary QP-band bosons 0< E-∆∆∆< eV -4∆∆∆

New bands appear at intensity Phonon eV=2 n∆∆∆ eV -2∆∆∆ 2∆∆∆ Energy Stimulated emission Observation of even-gap peculiarities in Bi-2212 intrinsic tunneling characteristics

69.7K S811b 6 75.0K 811b 6∆ /e 80.0K S 40 84.1K 4∆ /e S 87.5K

89.9K 30 4 92.0K 2∆ /e S

20 (100K) (mS) (100K) σ σ σ σ

- 2 10 σ σ σ σ Voltage per junction (mV) junction per Voltage

0 0 20 40 60 80 0 T (K)

-400 -200 0 200 400 Overdoped Bi-2212 V (mV) V.M.Krasnov, Phys.Rev.Lett. 97,257003 (2006) Changing the QP injection rate:

3 0,10 γ Linear( i=0.05) ) 0,09 ∆ Secondary

= 0,08 γ =0.1 QP band i E 0,07

2 ( eV >4 ∆ i f

γ 0,06 / δ

I 0,05 γ =0.05, Non-linear Equilibr. i 0,04 γ =0.01, 1 i 0,03 γ =0.05, i 0,02 γ =0.01, a) b) i γ =0.1 0,01 i 0 0,00 1 2eV/∆ 3 0 1 2 3 4 5 0 eV /∆ 1,04 0 1,00 γ =0.01, n d)

i R 0,98 Non-eq. V

0 ∆=∆ 0 /d ∆

γ =0.05, I 0,96 i

d 1,02 / /

∆ 0,94 γ =0.01, i γ =0.05, 0,92 c) i V.M.Krasnov, γ =0.1 γ =0.1, Phys.Rev.Lett. 103, i i 227002 (2009) 0,90 1,00 0 1 2 3 4 5 3,6 3,8 4,0 4,2 4,4 eV/∆ eV/∆ 0 0 Nonequilibrium I-V characteristics

V.M.Krasnov, Phys.Rev.Lett. 103, 227002 (2009)

Note, that I-V curves are very similar for both solutions. Therefore, power dissipation P=IV is also the same. However, suppression of ∆∆∆ is much smaller in the radiative state. This is due to radiative cooling = ballistic boson emission from the stack.

Radiative cooling is the only heat transport mechanism considered here, κκκ=0. The stack effectively (100% efficiency) converts electric power into boson emission without ac-Josephson effect. Non-equilibrium spectroscopy as a new tool for hunting down pairing bosons

Krasnov etal., Nat Commun. 4, 2970 (2013)

Relation to old Phonon generation-detection experiments in LTSC

Time of flight experiments through 0.4 cm (Ge)

1.5 cm (Al 2O3) W. Eisenmenger and A.H. Dayem, Phys.Rev.Lett. 18 (1967) 125. R.C.Dynes and V.Narayanamurti, Phys.Rev.B 6 (1972) 143 Krasnov etal., Nat Commun. 4, 2970 (2013) Krasnov etal., Nat Commun. 4, 2970 (2013) 6 3 vrecomb ~ Λ/τ ~ 10 m/s ~ v Fermi >> v phonon ~ v sound ~ 4x10 m/s

Conclusions Conclusions Intrinsic Josephson junctions in cuprates are interesting as possible candidates for coherent THz sources.

• Unlimited amount of high quality stacked Josephson junctions ~700/ µµµm • Several mechanisms of emission: • Coherent superradiant ac-Josephson emission (FFO) • Zero-field emission via breather type self-oscillations • TUNABLE CW operation up to ∆∆∆ ~ 30 meV > 15 THz

• Ionic single crystals – high quality phonons + polarization = Monochromatic phonon polariton emission via the piezoelectric effect • Non-Josephson emission via quasiparticle relaxation Superconducting cascade laser