Quantum transport via evanescent waves in undoped graphene

TL;DR

This paper reviews the quantum transport phenomena in undoped graphene, focusing on pseudodiffusive behavior at zero charge density and employing conformal mapping techniques to analyze effects like the Aharonov-Bohm effect.

Contribution

It introduces a theoretical framework for understanding pseudodiffusive transport in undoped graphene using conformal mapping methods.

Findings

Pseudodiffusive transport arises from zero-modes of the Dirac operator.

Conformal mapping effectively analyzes quantum effects in graphene rings.

The Aharonov-Bohm effect is used as an example to demonstrate these phenomena.

Abstract

Charge carriers in graphene are chiral quasiparticles ("massless Dirac fermions"). Graphene provides therefore an amazing opportunity to study subtle quantum relativistic effects in condensed matter experiment. Here I review a theory of one of these unusual features of graphene, a "pseudodiffusive" transport in the limit of zero charge carrier concentration, which is related to existence of zero-modes of the Dirac operator and to the Zitterbewegung of unltrarelativistic particles. A conformal mapping technique is a powerful mathematical tool to study these phenomena, as demonstrated here, using the Aharonov-Bohm effect in graphene rings with Corbino geometry as an example.