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arXiv · 1101.2542

Quantum transport via evanescent waves in undoped graphene

M. I. Katsnelson
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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.

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M. I. Katsnelson. 2011-01-13. Quantum transport via evanescent waves in undoped graphene. https://doi.org/10.1166/jctn.2011.1770

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