The quantum Hall effect in graphene - a theoretical perspective

Details The quantum Hall effect in graphene - a theoretical perspective The quantum Hall effect in graphene - a theoretical perspective

2011-04-29

arxiv.org/abs/1104.5621v2

C. R. Physique 12, 369 (2011)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

9 pages, 4 figures; brief review article for Comptes Rendus de l'Academie des Sciences; references added with respect to previ

Scientific paper

10.1016/j.crhy.2011.04.012

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 Schr\"odinger 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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