Boltzmann-Langevin theory of Coulomb drag

TL;DR

This paper develops a comprehensive Boltzmann-Langevin framework to describe Coulomb drag in double-layer systems, capturing both collisionless and hydrodynamic regimes and revealing a nonmonotonic temperature dependence of drag resistivity.

Contribution

It introduces a unified theory for Coulomb drag that covers the crossover from collisionless to hydrodynamic regimes, including the effects of electron-electron scattering.

Findings

Drag resistivity shows nonmonotonic temperature dependence.

At low temperatures, drag is dominated by particle-hole continuum.

At higher temperatures, plasmon modes govern the drag.

Abstract

We develop a Boltzmann-Langevin description of Coulomb drag effect in clean double-layer systems with large interlayer separation $d$ as compared to the average interelectron distance $\lambda_F$. Coulomb drag arises from density fluctuations with spatial scales of order $d$. At low temperatures, their characteristic frequencies exceed the intralayer equilibration rate of the electron liquid, and Coulomb drag may be treated in the collisionless approximation. As temperature is raised, the electron mean free path becomes short due to electron-electron scattering. This leads to local equilibration of electron liquid, and consequently drag is determined by hydrodynamic density modes. Our theory applies to both the collisionless and the hydrodynamic regimes, and it enables us to describe the crossover between them. We find that drag resistivity exhibits a nonmonotonic temperature dependence with multiple crossovers at distinct energy scales. At the lowest temperatures, Coulomb drag is dominated by the particle-hole continuum, whereas at higher temperatures of the collision-dominated regime it is governed by the plasmon modes. We observe that fast intralayer equilibration mediated by electron-electron collisions ultimately renders a stronger drag effect.