Twodimensional gas of massless Dirac fermions in graphene
Abstract
Quantum electrodynamics (resulting from the merger of quantum mechanics and relativity theory) has provided a clear understanding of phenomena ranging from particle physics to cosmology and from astrophysics to quantum chemistry. The ideas underlying quantum electrodynamics also influence the theory of condensed matter, but quantum relativistic effects are usually minute in the known experimental systems that can be described accurately by the nonrelativistic Schrödinger equation. Here we report an experimental study of a condensedmatter system (graphene, a single atomic layer of carbon) in which electron transport is essentially governed by Dirac's (relativistic) equation. The charge carriers in graphene mimic relativistic particles with zero rest mass and have an effective `speed of light' c_{*} ~ 10^{6}ms^{1}. Our study reveals a variety of unusual phenomena that are characteristic of twodimensional Dirac fermions. In particular we have observed the following: first, graphene's conductivity never falls below a minimum value corresponding to the quantum unit of conductance, even when concentrations of charge carriers tend to zero; second, the integer quantum Hall effect in graphene is anomalous in that it occurs at halfinteger filling factors; and third, the cyclotron mass m_{c} of massless carriers in graphene is described by E = m_{c}c_{*}^{2}. This twodimensional system is not only interesting in itself but also allows access to the subtle and rich physics of quantum electrodynamics in a benchtop experiment.
 Publication:

Nature
 Pub Date:
 November 2005
 DOI:
 10.1038/nature04233
 arXiv:
 arXiv:condmat/0509330
 Bibcode:
 2005Natur.438..197N
 Keywords:

 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Strongly Correlated Electrons;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 Nature 438:197,2005