Theory of Disordered Superconductors with Applications to Nonlinear Current Response

TL;DR

This paper reviews the theoretical framework for charge transport in disordered superconductors, focusing on nonlinear current responses and their potential applications in dark matter detection and photon generation.

Contribution

It extends the quasiclassical transport equations to disordered superconductors, analyzing nonlinear current responses and their implications for applications like SRF cavities.

Findings

Derivation of Usadel's equations for nonlinear current response

Analysis of disorder's pair-breaking effects on superconducting current

Potential use of nonlinear currents in dark matter detection

Abstract

I present a review of the theory and basic equations for charge transport in superconducting alloys starting from the Keldysh formulation of the quasiclassical transport equations developed by Eilenberger, Larkin and Ovchinnikov and Eliashberg. This formulation is the natural extension of Landau's theory of normal Fermi liquids to the superconducting state of strongly correlated metals. For dirty metals the transport equations reduce to equations for charge diffusion, with the current response given by the Drude conductivity at low temperatures. The extension of the diffusion equation for the charge and current response of a strongly disordered normal metal to the superconducting state yields Usadel's equations for the non-equilibrium quasiclassical Keldysh propagator. The conditions for the applicability of the Usadel equations are discussed, the pair-breaking effect of disorder on the current response, including the nonlinear current response to an EM field in the dirty limit, $\tau \ll \hbar/\Delta$, are reported. The same nonlinearity is shown to lead to source currents for photon generation and nonlinear Kerr rotation driven by the nonlinear response to excitation of the superconductor by a multi-mode EM field. The potential relevance of the nonlinear source currents to SRF cavities as detectors of axion-like dark matter candidates is briefly discussed.