Exact results for intrinsic electronic transport in graphene

TL;DR

This paper provides exact analytical results for the electronic transport properties of graphene sheets, revealing how topology and electronic structure influence conductivity and noise characteristics.

Contribution

It offers the first exact transfer-matrix solutions for graphene's transport properties across all geometries and sizes, clarifying the intrinsic transport mechanisms.

Findings

Dirac-point conductivity of 2e^2/√3h for large sheets

Fano factor of approximately 0.346 for armchair graphene

Zero conductivity and Poissonian noise for zigzag graphene

Abstract

We present exact results for the electronic transport properties of graphene sheets connected to two metallic electrodes. Our results, obtained by transfer-matrix methods, are valid for all sheet widths and lengths. In the limit of large width-to-length ratio relevant to recent experiments, we find a Dirac-point conductivity of $2e^2/\sqrt{3}h$ and a sub-Poissonian Fano factor of $2 - 3\sqrt{3}/\pi \simeq 0.346$ for armchair graphene; for the zigzag geometry these are respectively 0 and 1. Our results reflect essential effects from both the topology of graphene and the electronic structure of the leads, giving a complete microscopic understanding of the unique intrinsic transport in graphene.