Nonequilibrium dynamics of quasiparticles in superconductors

Small changes {δ}Rₛ in the 10-GHz surface resistance Rₛ of thin superconducting films of Sn and In, caused by an induced static current J₀ have been measured. {δ}Rₛ was quadratic in J₀ and both increases ({δ}Rₛ>0) and decreases ({δ}Rₛ0) of absorption were observed. The increase is associated mainly with thermodynamic depression of the gap parameter due to the static current. On the other hand, the decrease of absorption, which implies an enhancement of superconductivity, is incompatible with thermodynamic analysis. A nonequilibrium analysis is presented, according to which the combined static and high-frequency currents cause a nonthermal, time-dependent oscillation of the quasiparticle distribution, and which is out of phase with the driving high-frequency field. The counter oscillation leads to an enhancement of high-frequency supercurrent and decrease of dissipative normal current, and hence results in a decrease of absorption. The analysis describes the experimental results for very thin films of Sn both qualitatively and quantitatively, and with no adjustable parameters. These results lead to the conclusion that at high frequencies, the superconductor responds to time-dependent perturbations in an inherently nonadiabatic, nonequilibrium manner even for vanishingly small high-frequency fields. The implications for several unexplained experiments on the magnetic field dependence of Rₛ are discussed.