Full counting statistics in disordered graphene at Dirac point: From ballistics to diffusion

TL;DR

This paper investigates the full counting statistics of charge transport in disordered graphene at the Dirac point, analyzing the transition from ballistic to diffusive regimes using analytical methods and confirming results with numerical simulations.

Contribution

It provides a comprehensive analytical study of transport statistics in disordered graphene, bridging ballistic and diffusive regimes with new diagrammatic and sigma model techniques.

Findings

Universal Dorokhov distribution describes transport at the Dirac point.

Deviations from universality occur in the crossover regime.

Results agree with recent numerical simulations.

Abstract

The full counting statistics of the charge transport through an undoped graphene sheet in the presence of smooth disorder is studied. At the Dirac point both in clean and diffusive limits, transport properties of a graphene sample are described by the universal Dorokhov distribution of transmission probabilities. In the crossover regime, deviations from universality occur which can be studied analytically both on ballistic and diffusive sides. In the ballistic regime, we use a diagrammatic technique with matrix Green functions. For a diffusive system, the sigma model is applied. Our results are in good agreement with recent numerical simulations of electron transport in disordered graphene.