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Two-Dimensional Gas of Massless Dirac Fermions in Graphene

K. S. Novoselov·A. K. Geim·S. V. Morozov·D. Jiang·M. I. Katsnelson·I. V. Grigorieva·S. V. Dubonos·A. A. Firsov
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Abstract

Electronic properties of materials are commonly described by quasiparticles that behave as non-relativistic electrons with a finite mass and obey the Schroedinger equation. Here we report a condensed matter system where electron transport is essentially governed by the Dirac equation and charge carriers mimic relativistic particles with zero mass and an effective "speed of light" c* ~10^6m/s. Our studies of graphene - a single atomic layer of carbon - have revealed a variety of unusual phenomena characteristic of two-dimensional (2D) Dirac fermions. In particular, we have observed that a) the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; b) graphene's conductivity never falls below a minimum value corresponding to the conductance quantum e^2/h, even when carrier concentrations tend to zero; c) the cyclotron mass m of massless carriers with energy E in graphene is described by equation E =mc*^2; and d) Shubnikov-de Haas oscillations in graphene exhibit a phase shift of pi due to Berry's phase.

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K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, A. A. Firsov. 2005-09-13. Two-Dimensional Gas of Massless Dirac Fermions in Graphene. https://doi.org/10.1038/nature04233

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