Linear response theory of Coulomb drag in coupled electron systems

TL;DR

This paper develops a comprehensive microscopic theory for Coulomb drag in coupled electron systems using the Kubo formalism, unifying previous results and revealing new frequency and localization effects.

Contribution

It introduces a general expression for transconductivity based on fluctuation diagrams, extending prior models and analyzing energy-dependent relaxation times and weak localization corrections.

Findings

At T=0, transfer rate frequency dependence is proportional to Ω and Ω^2 below and above impurity scattering rate.

The theory recovers Boltzmann and memory function results in appropriate limits.

Weak localization correction to transconductivity relates to corrections in individual layers.

Abstract

We report a fully microscopic theory for transconductivity, or, equivalently, momentum transfer rate, of Coulomb coupled electron systems. We use the Kubo linear response formalism, and our main formal result expresses the transconductivity in terms of two fluctuation diagrams, which are topologically related, but not equivalent to, the Aslamazov-Larkin diagrams known for superconductivity. Previously reported results are shown to be special cases of our general expression; specifically, for constant impurity scattering rates, we recover the Boltzmann equation results in the semiclassical clean limit, and the memory function results in dirty systems. Furthermore, we show that for energy dependent relaxation times, the final result is not expressible in terms of standard density-response functions. Other new results include: (i) at T=0, the frequency dependence of the transfer rate is found to be proportional to $\Omega$ and $\Omega^2$ for frequencies below and above the impurity scattering rate, respectively and (ii) the weak localization correction to the transconductivity is given by $\delta\sigma^{WL}_{21} \propto \delta\sigma^{WL}_{11} +\delta\sigma^{WL}_{22}$.