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arXiv · 1609.07729

Hofstadter butterfly of a quasicrystal

J. -N Fuchs·J. Vidal
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Abstract

The energy spectrum of a tight-binding Hamiltonian is studied for the two-dimensional quasiperiodic Rauzy tiling in a perpendicular magnetic field. This spectrum known as a Hofstadter butterfly displays a very rich pattern of bulk gaps that are labeled by four integers, instead of two for periodic systems. The role of phason-flip disorder is also investigated in order to extract genuinely quasiperiodic properties. This geometric disorder is found to only preserve main quantum Hall gaps.

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J. -N Fuchs, J. Vidal. 2016-09-25. Hofstadter butterfly of a quasicrystal. https://doi.org/10.1103/physrevb.94.205437

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