Effects of large disorder on the Hofstadter butterfly

Motivated by the recent experiments on periodically modulated, two-dimensional electron systems placed in large transversal magnetic fields [S. Melinte et al., Phys. Rev. Lett. 92, 036802 (2004)], we investigate the interplay between the effects of disorder and periodic potentials in the integer quantum Hall regime. In particular, we study the case where disorder is larger than the periodic modulation, but both are small enough that Landau level mixing is negligible. We carry extensive numerical calculations to understand the relevant physics in the lowest Landau level, such as the spectrum and nature (localized or extended) of the wave functions. Based on our results, we propose a qualitative explanation of the new features uncovered recently in these transport measurements.