Unconventional integer quantum Hall effect in graphene.

@article{Gusynin2005UnconventionalIQ,
  title={Unconventional integer quantum Hall effect in graphene.},
  author={V. P. Gusynin and S. G. Sharapov},
  journal={Physical review letters},
  year={2005},
  volume={95 14},
  pages={
          146801
        }
}
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… 

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Part 1 Introduction - Basic Facts: The Integer Quantum Hall Effect Classical Dynamics Quantizing Magnetic Fields The Eigenvalue Problem The Landau Model Models of Confinement Bloch Representation

but with a twice smaller size of the steps of σxy, and without making a link between the unusual behavior of σxy and the quantum anomaly of

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that asserts that in condensed matter systems diabolic points come in parity-inavariant pairs. Accordingly the Dirac Lagrangian (2) which embedes a pair of such points

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The corresponding analytical expression for Axy(ω, B, Γ) is simple, but rather lengthy