Crossover from quantum to Boltzmann transport in graphene

TL;DR

This paper investigates the transition from quantum to classical (Boltzmann) transport in graphene by comparing numerical quantum calculations with semiclassical theory, revealing agreement away from the Dirac point and a crossover behavior.

Contribution

It provides a quantitative analysis of the crossover between quantum and semiclassical transport regimes in graphene considering smooth disorder potentials.

Findings

Quantum and semiclassical results agree away from the Dirac point.

Discrepancies occur at the Dirac point under weak disorder.

Numerical results describe the full crossover between transport regimes.

Abstract

We compare a fully quantum mechanical numerical calculation of the conductivity of graphene to the semiclassical Boltzmann theory. Considering a disorder potential that is smooth on the scale of the lattice spacing, we find quantitative agreement between the two approaches away from the Dirac point. At the Dirac point the two theories are incompatible at weak disorder, although they may be compatible for strong disorder. Our numerical calculations provide a quantitative description of the full crossover between the quantum and semiclassical graphene transport regimes.