Time-dependent Ginzburg-Landau equation and Boltzmann transport equation for charge-density-wave conductors

TL;DR

This paper derives coupled equations for charge-density-wave conductors from a microscopic model, enabling detailed analysis of their nonequilibrium dynamics and nonlinear conductivity behavior.

Contribution

It introduces a microscopic derivation of the time-dependent Ginzburg-Landau and Boltzmann equations for CDW conductors, incorporating electric fields and impurity effects without phenomenology.

Findings

Equations accurately describe nonlinear electric conductivity.

Model captures spatiotemporal dynamics of CDW and quasiparticles.

Framework applicable to analyze phase slip phenomena.

Abstract

The time-dependent Ginzburg-Landau equation and the Boltzmann transport equation for one-dimensional charge-density-wave (CDW) conductors are derived from a microscopic model by applying the Keldysh Green's function approach under a quasiclassical approximation. The effects of external electric field and impurity pinning of the CDW are fully taken into account without relying on a phenomenological argument. These equations simultaneously describe spatiotemporal dynamics of both the CDW and quasiparticles, so they serve as a powerful tool to analyze various nonequilibrium phenomena, such as the current conversion between the CDW condensate and quasiparticles mediated by phase slips. It is shown that, in typical situations, the equations correctly describe the nonlinear behavior of electric conductivity in a simpler manner.