Chernogolovka, October 2009

1. Phonon lasing in stacked intrinsic Josephson junctions Nolinear nonequilibrium phenomena in stacked junctions Vladimir Krasnov Experimental Condensed Matter Physics Fysikum, AlbaNova, Stockholm University • Motivation: • Non-equilibrium phenomena are central in many superconducting detectors, but may be detrimental for in superconducting electronics. • “Heat” (Energy) conduction at low T in the absence of thermal conductivity • Extreme non-equilibrium states in stacked JJ – new nonlinear phenomena. Superconducting Cascade Laser in THz frequency range Chernogolovka, October 2009

2. eV 2D Relaxation of non-equilibrium Quasi-Particles in Josephson junctions E Electron heating /cooling E Phonon heating / radiative cooling N(E) BeV-2 Bremsstr phonon R 2 Recomb. 2-stage: Phonon down conversion (luminescence) Reabsorption of non-eq. Phonons: QP excitation Pair breaking -> Secondary QP 1-stage: QP Relaxation – Bremsstrahlung phonons QP Recombination – Recombination phonons 3-stage: Relaxation of secondary QP And so on…

3. Intrinsic stacked Josephson junctions in layered HTSC Bi2Sr2CaCu2O8+x : anisotropy rc/rab ~106 c-axis

4. Factors enhancing nonequilibrium effects in IJJs Very rough estimation: Additional effects of stacking

5. 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

6. Cross-sectional STM of InAlAs/InGaAs quantum cascade laser J.Faist, et al., Science 264 (1994) 553 P.Offermans et al., Appl.Phys.Lett. 83 (2003) 4131

7. Effect of stacking in semiconducting heterostructure lasers From Z.I.Alferov, Nobel lecture Rev.Mod.Phys. 73, 767 (2001)

8. Tunnel QP injection rate (bias dependent) QP escape rate (via tunneling) Phonon injection rate (bias independent) Phonon escape rate Kinetic balance equations

9. Quasiparticle relaxation rate absorption-emission Relaxation: emission-absorption Recombination – pair breaking Absorption Spontaneous emission Stimulated emission

10. Phonon relaxation rate Absorption Spontaneous emission Stimulated emission

11. Expansion of the quasiparticle relaxation rate f(E) = F(E) + df(E) g(W) = G(W) + dg(W) Absorption Spontaneous emission Stimulated emission No equilibrium terms here

12. Expansion of the phonon relaxation rate Relaxation: absorption-emission Recombination – pair breaking Absorption Spontaneous emission Stimulated emission No equilibrium terms here

13. Equilibrium D0 (T ): Numerical solution for non-equilibrium D/D0: Self-consistency equation: QP’s at the bottom of the band are most important

14. Dayem & Wiegand PRB 5, 4390 (1972) Chang & Scalapino PRB 15, 2651 (1977) Itteration (n): Solve the system of 2K linear Eqs. QP balance Phonon balance Relaxation Escape Injection obtain Proceed with itteration (n+1) obtain Dn from the self-consistency Eq. calculate Numerical procedure:

15. Nonlinear solution for a double stacked junctions ordinary ”absorptive solution” Net accumulation of QPs at E’=0 and absorption of bosons with W=0. Slow QP relaxation due to reabsorption of bosons. Nonlinearity appears when df > F. QP relaxation is always nonlinear at low enough T or high enough E where F(T,E)→0. Nonlinearity stimulates QP relaxation dfn.l.< dflin.

16. Nonlinear effects at even-gap bias: Secondary nonequilibrium QP and bosons eV = 4 Bremsstrahlung phonons Recombination phonons Phonon intensity eV-2 2 Energy eV < 4 Bremsstrahlung phonons Recombination phonons Phonon intensity eV-2 2 Energy • Enhanced depairing • Secondary QP-band • 0<E-D< eV-4D New bands appear at eV=2nD Stimulated emission?

17. Bias-dependence of the nonlinear absorptive solution for a double stacked junctions

18. Time of flight experiments 0.4 cm (Ge) 1.5 cm (Al2O3) R.C.Dynes and V.Narayanamurti, Phys.Rev.B 6 (1972) 143 Phonon generation-detection experiment

19. Nonequilibrium I-V characteristics Note, that I-V curves are very similar for both solutions. Therefore, power dissipation P=IV is also the same. However, suppression of D 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, k=0. The stack effectively (100% efficiency) converts electric power into boson emission without ac-Josephson effect.

20. Observation of even-gap peculiarities in Bi-2212 intrinsic tunneling characteristics Overdoped Bi-2212 V.M.Krasnov, Phys.Rev.Lett. 97,257003 (2006)

21. V+ I+ Height of the mesa 4a 4b V- I- Tripple-mesa with common junctions for injection-detection experiments: Three and Four-probe measurements N=52 N=28 N=28 N=52 V.M.Krasnov, Phys.Rev.Lett. 97,257003 (2006)

22. V A B C E Detection of recombination radiation D I Bi2Sr2CaCu2O8+d V.M.Krasnov, Phys.Rev.Lett. 97,257003 (2006)

23. Appearance of a second ”radiative solution” at large bias No net accumulation of QPs at E’=0 – fast QP relaxation due to stimulated emission of low W bosons. Eistence of two solutions is a result of nonlinerity

24. Semiconducting Light Emitting Diode Absorptive and Radiative states in stacked IJJs bare some similarity with light emitting and lasing states in heterostructure injection diodes. Population inversion by electron injection in a superlattice. Note that in LED Jth=10-100 A/cm2 at 300K, Jth~exp(aT). For IJJs J = 104 A/cm2 at 4K. Mesa itself acts as a Fabry-Perot resonator, selecting cavity (Fiske) modes. From O.Heikkilä et al., J.Appl.Phys. 105, 093119 (2009)

25. Conclusions: • Linear approximation fails already at relatively small disequilibrium: the nonequilibrium part has to be small compared to thermal population. • Nonequilibrium effects are always nonlinear at low enough effects T. This has to be taken into account in analysis of superconducting devices at low T. • In stacked IJJ extreme nonequilibrium state can be achieved. The obtained radiative state indicates a possibility of realization of a new type of Superconducting Cascade Laser (SCL). Unlike existing Josephson oscillators which utilize the ac-Josephson effect for conversion of electric power into radiation, the SCL is based on direct conversion of electric power into boson emission via nonequilibrium QP relaxation upon sequential tunneling in stacked junctions. The mechanism is similar to lasing in semiconducting heterostructures and allows very high radiation efficiency. • Emitted are bosons that participate in pairing. Therefore, nonequilibrium intrinsic tunneling spectroscopy may provide a direct probe for HTSC coupling mechanism.