Relaxation and Electromagnetic Response of a Superconductor in a State of Supercurrent Flow

Abstract

The situation is investigated in which a superconductor in a state of supercurrent flow and near the transition temperature is exposed to an alternating electric field. The induced alternating current is shown to exhibit a frequency dependence ${(1-i\Omega {\tau }_{\mathrm{R}})}^{-1\mathrm{}}$, which is due to a relaxation process in the Cooper-pair density. The relaxation time ${\tau }_{\mathrm{R}}$ is determined by electron-phonon collisions (collision time ${\tau }_c$), in which case ${\tau }_{\mathrm{R}}\simeq {\tau }_c{\left[\frac{T_c}{(T_c-T)}\right]}^{\frac{1}{2}}$; impurity scattering is important only under certain conditions, in which case ${\tau }_{\mathrm{R}}\simeq {10}^{-11\mathrm{}}{\left[\frac{T_c}{(T_c-T)}\right]}^{-5\mathrm{}}$ sec.