Monolayer graphite films, or graphene, have quasiparticle excitations that can be described by (2+1)-dimensional Dirac theory. We demonstrate that this produces an unconventional form of the quantized Hall conductivity sigma(xy) = -(2e2/h)(2n+1) with n = 0, 1, ..., which notably distinguishes graphene from other materials where the integer quantum Hall effect was observed. This unconventional quantization is caused by the quantum anomaly of the n=0 Landau level and was discovered in recent experiments on ultrathin graphite films.

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A theory of the magnetic field driven (semi-)metal-insulator phase transition is developed for planar systems with a low density of carriers and a linear (i.e., relativistic like) dispersion relation for low energy quasiparticles. The general structure of the phase diagram of the theory with respect to the coupling constant, the chemical potential and temperature is derived in two cases, with and without an external magnetic field. The conductivity and resistivity as functions of temperature and magnetic field are studied in detail. An exact relation for the value of the "offset" magnetic field $B_c$, determining the threshold for the realization of the phase transition at zero temperature, is established. The theory is applied to the description of a recently observed phase transition induced by a magnetic field in highly oriented pyrolytic graphite.Comment: 22 pages, REVTeX, 16 figures. The version corresponding to that published in Phys.Rev.

Landau level quantization in graphene reflects the Dirac nature of its quasiparticles and has been found to exhibit an unusual integer quantum Hall effect. In particular, the lowest Landau level can be thought of as shared equally by electrons and holes, and this leads to characteristic behaviour of the magneto-optical conductivity as a function of frequency for various values of the chemical potential μ. Particular attention is paid to the optical spectral weight under various absorption peaks and its redistribution as μ is varied. We also provide results for magnetic field B as well as chemical potential sweeps at selected fixed frequencies, which can be particularly useful for possible measurements in graphene. Both diagonal and Hall conductivities are considered.