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 ${\sigma }_{xy}=-(2e^2/h)(2n+1)$ with $n=0,1,\dots$, 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.

• Received 26 June 2005

DOI:https://doi.org/10.1103/PhysRevLett.95.146801