1. Coherent excited states in superconductors due to a microwave field
A.V. Semenov, I.A. Devyatov,
P.J. de Visser, T.M. Klapwijk
Coherent excited states in superconductors
due to a microwave field
XXI International Symposium “Nanophysics and Nanoelectronics”
Nizhny Novgorod, March 13-16, 2017

2. Outline (List of questions I’ll try to answer)
- How high-frequency EM field/current affects ground state
of (dirty) superconductor?
- What is high frequency?
- What is the effect on experimentally observable quantities
(DOS, admittance,…)?
- How to explain it on the fingers?
- Can the effect be seen against
the effects of nonequilibrium QPs?

3. Background: Direct depairing by dc current
P.W. Anderson, Coherent excited states in the theory of superconductivity:
Gauge invariance and the Meissner effect. Phys. Rev. 110, 827 (1958).
Γ≡2e2DA2 ≡2Dps2

4. Direct depairing by low-frequency current
Γ(t)≡2e2DA2(t) =2e2DE2(t+T/4)/ω2
Gurevich, A. (2014). Physical Review Letters, 113(8),

5. Direct depairing by low-frequency current
Γ(t)≡2e2DA2(t) =2e2DE2(t+T/4)/ω2
Gurevich, A. (2014). Physical review letters, 113(8),
BUT!
ћω<<?
What is in the opposite case?

6. Single electron in a periodic field

7. Single electron in a periodic field
ħω vs. (eA)2/2m
ħω <<. (eA)2/2m - classical e
ħω >>. (eA)2/2m - quantum
Diffuse limit ωτ << 1:
m -> ħ /D

8. Model Keldysh-Usadel formulation (Larkin, Ovchinnikov, 1977) E
Dirty superconductor
No spatial gradients
Keldysh-Usadel formulation (Larkin, Ovchinnikov, 1977)
Retarded Usadel equation
rf field term
Normalization condition

9. Model Monochromatic field, ω G and F are expanded
in even harmonics of ω
Retarded Usadel equation in E-ω representation
Normalization condition
α≡e2DE2/ω2
En≡E+nω/2

10. Closed equations for time-averaged
Green functions
Retarded Usadel equation
α<<ω
Normalization condition
rf field term
f± ≡ f(E ± ω)
For comparison,
α≡e2DE2/ω2
R Usadel equation in dc case
Essentially the same as
in MW absorption theory
ω<<α
Our R Usadel is
nonlocal in energy
Qualitatively different solution

11. Solution: Density of states
Time averaged DOS
N(E)=ReG0(E)
IDC=IRF=0.25Ic

12. Energy + A(t) Energy Quasi-energy Back to E Quasi-energy
ΔE~q2A2
Quasi-energy
Back to E
representation
Quasi-energy ω ω ω ω
Energy
Energy

13. Solution: conductivity
Linear conductivity
ħω<<Δ
α<<ħω<<Δ

14. Comparison with the experiment

15. Effect on quasiparticle number
Nqpth depends on DOS
Should increase with α and ω

16. Effect on quasiparticle number
Nqpth depends on DOS
Should increase with α and ω
Rapid increase expected above some threshold α and ω

18. Can this all be seen against the non-equilibrium effects in QPs?
Field cannot create QPs directly,
Can only move up the existing (thermal) QPs
ħω<<Δ
T<<Δ
Number of thermal QPs ~exp(- Δ/T)
BUT!
Lifetime of QPs ~exp(Δ/T)
When RF field is applied,
there should be a steady-state non-equilibrium
QP distribution. With number of QPs Nqp~α
One has to compare their effect with that of
direct RF depairing

19. Simplest model of inelastic interaction
(suggestion by M.A. Skvortsov)
Relaxation via tunneling to large normal reservoir
Usadel equation

20. Simplest model of inelastic interaction
Linearized retarded Usadel equation
Linearized kinetic equation
Solution of the kinetic
equation at T<<ω0

21. Simplest model of inelastic interaction
Effect of nonequilibrium QPs on Δ
Correction to Δ
(The same is for Lk)

22. Conclusion RF (ω>>α) field/current modifies the ground state
of dirty superconductor qualitatively
The effect can be seen against
the effects of nonequilibrium QPs

23. Thank you for your attention!