Quantum Hall Effect on the Hofstadter Butterfly

Details Quantum Hall Effect on the Hofstadter Butterfly Quantum Hall Effect on the Hofstadter Butterfly

2005-07-26

arxiv.org/abs/cond-mat/0507594v1

J. Phys. Soc. Jpn. 73, 3243 (2004)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 6 figures

Scientific paper

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.

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