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 {\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 $\mathrm{Re}\sigma$, 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.

12 pages, RevTeX, 7 figures

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