Coulomb drag in graphene: perturbation theory

TL;DR

This paper analyzes Coulomb drag in graphene monolayers, deriving universal functions and asymptotic behaviors of the drag coefficient under various doping and temperature regimes, including effects of interactions and impurity scattering.

Contribution

It provides a comprehensive theoretical analysis of Coulomb drag in graphene, including universal functions, asymptotic limits, and corrections for different doping, temperature, and interaction regimes.

Findings

Drag coefficient proportional to μ₁μ₂ near Dirac point

Inverse proportionality of drag to μ₁μ₂ at low T

Logarithmic corrections for stronger interactions and larger d

Abstract

We study the effect of Coulomb drag between two closely positioned graphene monolayers. In the limit of weak electron-electron interaction and small inter-layer spacing ($\mu_{1(2)}, T\ll v/d$) the drag is described by a universal function of the chemical potentials of the layers $\mu_{1(2)}$ measured in the units of temperature $T$. When both layers are tuned close to the Dirac point, then the drag coefficient is proportional to the product of the chemical potentials $\rho_D\propto\mu_1\mu_2$. In the opposite limit of low temperature the drag is inversely proportional to both chemical potentials $\rho_D\propto T^2/(\mu_1\mu_2)$. In the mixed case where the chemical potentials of the two layers belong to the opposite limits $\mu_1\ll T\ll\mu_2$ we find $\rho_D\propto \mu_1/\mu_2$. For stronger interaction and larger values of $d$ the drag coefficient acquires logarithmic corrections and can no longer be described by a power law. Further logarithmic corrections are due to the energy dependence of the impurity scattering time in graphene (for $\mu_{1(2)}\gg T$ these are small and may be neglected). In the case of strongly doped (or gated) graphene $\mu_{1(2)}\gg v/d\gg T$ the drag coefficient acquires additional dependence on the inter-layer spacing and we recover the usual Fermi-liquid result if the screening length is smaller than $d$.