Zero-frequency anomaly in quasiclassical ac transport: Memory effects in a two-dimensional metal with a long-range random potential or random magnetic field

TL;DR

This paper investigates the low-frequency ac conductivity of a two-dimensional fermion gas with long-range disorder, revealing a non-analytic correction due to memory effects, supported by analytical and numerical methods.

Contribution

It uncovers a universal non-analytic || correction to ac conductivity caused by return processes in 2D fermion systems with long-range disorder, extending understanding beyond Boltzmann theory.

Findings

Identifies a || correction to Re  in 2D fermion gases.

Shows the correction's sign and magnitude depend on disorder type and parameters.

Supports analytical results with numerical simulations.

Abstract

We study the low-frequency behavior of the {\it ac} conductivity $\sigma(\omega)$ of a two-dimensional fermion gas subject to a smooth random potential (RP) or random magnetic field (RMF). We find a non-analytic $\propto|\omega|$ correction to ${\rm Re} \sigma$, which corresponds to a $1/t^2$ long-time tail in the velocity correlation function. This contribution is induced by return processes neglected in Boltzmann transport theory. The prefactor of this $|\omega|$-term is positive and proportional to $(d/l)^2$ for RP, while it is of opposite sign and proportional to $d/l$ in the weak RMF case, where $l$ is the mean free path and $d$ the disorder correlation length. This non-analytic correction also exists in the strong RMF regime, when the transport is of a percolating nature. The analytical results are supported and complemented by numerical simulations.