On the conductivity of lateral-surface superlattices in magnetic fields

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Abstract
The authors present results for the band conductivity and the density of states of electrons in realistic two-dimensional periodic potentials and magnetic fields. They show the effects of the number of flux quanta per unit cell in producing Hofstader's-butterfly-like splittings in the limit of small field, but outside the simple tight-binding limit, and for high fields where the dominant effect is the local splitting of Landau levels to form weakly coupled edge states round the minima and maxima of the potential. The broadening and splitting of these states to form Hofstader's butterfly then occurs on a much finer energy scale.