Quantum Hall Effect on the Hofstadter Butterfly
arXiv:cond-mat/0507594 · doi:10.1143/JPSJ.73.3243
Abstract
Motivated by recent experimental attempts to detect the Hofstadter butterfly, we numerically calculate the Hall conductivity in a modulated two-dimensional electron system with disorder in the quantum Hall regime. We identify the critical energies where the states are extended for each of butterfly subbands, and obtain the trajectory as a function of the disorder. Remarkably, we find that when the modulation becomes anisotropic, the critical energy branches accompanying a change of the Hall conductivity.
4 pages, 6 figures
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