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

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?

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

Direct depairing by low-frequency current Γ(t)≡2e2DA2(t) =2e2DE2(t+T/4)/ω2 Gurevich, A. (2014). Physical Review Letters, 113(8), 087001.

Direct depairing by low-frequency current Γ(t)≡2e2DA2(t) =2e2DE2(t+T/4)/ω2 Gurevich, A. (2014). Physical review letters, 113(8), 087001. BUT! ћω<<? What is in the opposite case?

Single electron in a periodic field

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

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

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

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

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

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

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

Comparison with the experiment

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

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

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

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

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

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

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

Thank you for your attention!