MAGNETORESISTANCE OSCILLATIONS OF A 2DEG IN A WEAK LATERAL SUPERLATTICE - MANIFESTATION OF HOFSTADTER BUTTERFLY

The resistance oscillations of a two-dimensional electron gas subject to a weak periodic modulation in both lateral directions are calculated as a function of the applied perpendicular magnetic field B. The calculation is based on a quantum-mechanical picture taking consistently into account the effect of the lateral superlattice on the energy spectrum and the effect of randomly distributed impurities on collision broadening and transport scattering rate. The superlattice potential splits each Landau level into a complicated energy spectrum, visualized by the famous self-similar "Hofstadter butterfly". The effect of this peculiar energy spectrum on the magnetoresistance is investigated and provides the key for the understanding of recent experiments by D. Weiss, A. Menschig, K. von Klitzing and G. Weimann.