The paper discusses the unconventional integer quantum Hall effect (IQHE) observed in graphene, a monolayer of graphite. The authors, V.P. Gusynin and S.G. Sharapov, demonstrate that the quasiparticle excitations in graphene can be described by a 2+1 dimensional Dirac theory, leading to a quantized Hall conductivity given by \(\sigma_{xy} = -(2e^2/h)(2n+1)\), where \(n\) is an integer. This quantization rule is distinct from the conventional IQHE observed in other materials and is attributed to the quantum anomaly of the \(n = 0\) Landau level, which has half the degeneracy of the higher Landau levels. The authors provide a theoretical framework based on the Dirac theory and show that this unconventional quantization is supported by recent experimental results on ultrathin graphite films. They also discuss the implications of this quantization for the de Haas van Alphen and Shubnikov de Haas oscillations in graphene.The paper discusses the unconventional integer quantum Hall effect (IQHE) observed in graphene, a monolayer of graphite. The authors, V.P. Gusynin and S.G. Sharapov, demonstrate that the quasiparticle excitations in graphene can be described by a 2+1 dimensional Dirac theory, leading to a quantized Hall conductivity given by \(\sigma_{xy} = -(2e^2/h)(2n+1)\), where \(n\) is an integer. This quantization rule is distinct from the conventional IQHE observed in other materials and is attributed to the quantum anomaly of the \(n = 0\) Landau level, which has half the degeneracy of the higher Landau levels. The authors provide a theoretical framework based on the Dirac theory and show that this unconventional quantization is supported by recent experimental results on ultrathin graphite films. They also discuss the implications of this quantization for the de Haas van Alphen and Shubnikov de Haas oscillations in graphene.