Quantized Hall effect in a hexagonal periodic potential

The Hall conductivity of a two-dimensional electron gas in a strong magnetic field and a hexagonal periodic potential is discussed. The hexagonal potential is treated by separating it into a term which depends on only one coordinate and a second term, treated perturbatively, which depends on both coordinates. Emphasis is placed on the origin of the differences between the hexagonal potential case and the square-lattice potential case discussed earlier by Thouless et al. [Phys. Rev. Lett. 49, 405 (1982)]. The calculations are based on a simple physical criterion for determining the Hall conductivity which has been justified starting from the Kubo formula.