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arXiv · 1104.5621

The quantum Hall effect in graphene - a theoretical perspective

M. O. Goerbig
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Abstract

This short theoretical review deals with some essential ingredients for the understanding of the quantum Hall effect in graphene in comparison with the effect in conventional two-dimensional electron systems with a parabolic band dispersion. The main difference between the two systems stems from the "ultra-relativistic" character of the low-energy carriers in graphene, which are described in terms of a Dirac equation, as compared to the non-relativistic Schrödinger equation used for electrons with a parabolic band dispersion. In spite of this fundamental difference, the Hall resistance quantisation is universal in the sense that it is given in terms of the universal constant h/e^2 and an integer number, regardless of whether the charge carriers are characterised by Galilean or Lorentz invariance, for non-relativistic or relativistic carriers, respectively.

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M. O. Goerbig. 2011-05-11. The quantum Hall effect in graphene - a theoretical perspective. https://doi.org/10.1016/j.crhy.2011.04.012

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