Effects of large disorder on the Hofstadter butterfly

Abstract

Motivated by the recent experiments on periodically modulated, two dimensional electron systems placed in large transversal magnetic fields, 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. In this limit, the self-consistent Born approximation is inadequate. 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 transport measurements.

arXiv comment15 pages, 13 figures, several pictures have been shrunk to comply with the size requirements

References in corpus (6)

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• Hall conductance of Bloch electrons in a magnetic field
• Heat Capacity Evidence for the Suppression of Skyrmions at Large Zeeman Energy
• One Dimensional Chain with Long Range Hopping
• A Convergent Method for Calculating the Properties of Many Interacting Electrons
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Cited by in corpus (6)

• Artificial Gauge Field for Photons in Coupled Cavity Arrays
• Hofstadter butterflies of carbon nanotubes: Pseudofractality of the magnetoelectronic spectrum
• Fractal defect states in the Hofstadter butterfly
• Hofstadter butterfly in the Falicov-Kimball model on some finite 2D lattices
• Floquet engineering the Hofstadter butterfly in the square lattice and its effective Hamiltonian
• Interacting fermions in two dimension in simultaneous presence of disorder and magnetic field