Effect of charge-imbalance potential relaxation on the high-frequency vortex dynamics and kinetic inductance of superconducting circuits

Abstract

We show that relaxation of the charge-imbalance potential plays a key role in the retarded dynamics of Abrikosov vortices in a type-II superconducting sample carrying a microwave current. Starting from the time-dependent Ginzburg--Landau equations we derive the vortex equation of motion accounting both the dissipation and retardation effects. The retardation is governed by the dynamics of the charge-imbalance potential and reveals itself at characteristic timescales diverging near the superconducting critical temperature $T_{c}$. These retardation effects in vortex dynamics strongly affect the kinetic inductance of superconducting circuits being, thus, responsible for the magnetic field dependence of characteristics of different superconducting devices in the high frequency range.