Quantized Hall conductance in a two-dimensional periodic potential

@article{Thouless1992QuantizedHC,
  title={Quantized Hall conductance in a two-dimensional periodic potential},
  author={David J. Thouless and Mahito Kohmoto and M. P. S. Nightingale and Monique de Nijs},
  journal={Physical Review Letters},
  year={1992},
  volume={49},
  pages={41-44}
}
The Hall conductance of a two-dimensional electron gas has been studied in a uniform magnetic field and a periodic substrate potential U. The Kubo formula is written in a form that makes apparent the quantization when the Fermi energy lies in a gap. Explicit expressions have been obtained for the Hall conductance for both large and small Uℏωc. 

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