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

Abstract

We study the low-frequency behavior of the ac conductivity (Formula presented) of a two-dimensional fermion gas subject to a smooth random potential (RP) or random magnetic field (RMF). We find a nonanalytic (Formula presented) correction to (Formula presented) which corresponds to a (Formula presented) long-time tail in the velocity correlation function. This contribution is induced by return processes neglected in Boltzmann transport theory. The prefactor of this (Formula presented) term is positive and proportional to (Formula presented) for the RP, while it is of opposite sign and proportional to (Formula presented) in the weak RMF case, where l is the mean free path and d the disorder correlation length. This nonanalytic 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. © 2000 The American Physical Society.