The electronic properties of graphene and carbon nanotubes

A brief review is given on the characteristic features of electronic states and transport in graphene consisting of a single sheet of graphite, and its cylinder form called a carbon nanotube. Electron motion in graphene is equivalent to that of a neutrino or a relativistic Dirac electron with vanishing rest mass. This causes the appearance of a nontrivial Berry's phase under 2 pi rotation in wave-vector space, leading to the absence of backscattering and in the metallic carbon nanotube resulting in perfect conduction even in the presence of scatterers. The energy bands in carbon nanotubes are determined by periodic boundary conditions with a fictitious Aharonov-Bohm flux determined uniquely by the circumferential chiral vector. A nanotube becomes metallic when the flux vanishes and semiconducting when the flux is nonzero. The conductivity of graphene is essentially independent of the Fermi energy and the electron concentration as long as variations in effective scattering strength are neglected, and therefore graphene should be regarded as a metal rather than a zero-gap semiconductor. Various schemes are now being proposed and tested for the purpose of opening the band gap in graphene.