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Quantum Hall Effect on the Hofstadter Butterfly

Mikito Koshino·Tsuneya Ando
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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.

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Mikito Koshino, Tsuneya Ando. 2005-07-26. Quantum Hall Effect on the Hofstadter Butterfly. https://doi.org/10.1143/jpsj.73.3243

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