Quantum critical transport in clean graphene

TL;DR

This paper investigates electrical transport in ideal single-layer graphene at zero bias, revealing a crossover from collisionless to collision-dominated regimes and providing an exact calculation of quantum critical conductivity.

Contribution

It presents an exact leading-order calculation of quantum critical conductivity in graphene considering relativistic dispersion and collinear scattering effects.

Findings

Identifies a crossover from collisionless to collision-dominated transport regimes.

Derives the non-equilibrium distribution functions for quasi-particles and holes.

Calculates the quantum critical conductivity to leading order in 1/|ln(alpha)|.

Abstract

We describe electrical transport in ideal single-layer graphene at zero applied bias. There is a crossover from collisionless transport at frequencies larger than k_B T/hbar (T is the temperature) to collision-dominated transport at lower frequencies. The d.c. conductivity is computed by the solution of a quantum Boltzmann equation. Due to a logarithmic singularity in the collinear scattering amplitude (a consequence of relativistic dispersion in two dimensions) quasi-particles and -holes moving in the same direction tend to an effective equilibrium distribution whose parameters depend on the direction of motion. This property allows us to find the non-equilibrium distribution functions and the quantum critical conductivity exactly to leading order in 1/|ln(alpha)| where alpha is the coupling constant characterizing the Coulomb interactions.