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arXiv · 1807.10032

Landau levels in quasicrystals

Jean-Noël Fuchs·Rémy Mosseri·Julien Vidal
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Abstract

Two-dimensional tight-binding models for quasicrystals made of plaquettes with commensurate areas are considered. Their energy spectrum is computed as a function of an applied perpendicular magnetic field. Landau levels are found to emerge near band edges in the zero-field limit. Their existence is related to an effective zero-field dispersion relation valid in the continuum limit. For quasicrystals studied here, an underlying periodic crystal exists and provides a natural interpretation to this dispersion relation. In addition to the slope (effective mass) of Landau levels, we also study their width as a function of the magnetic flux per plaquette and identify two fundamental broadening mechanisms: (i) tunneling between closed cyclotron orbits and (ii) individual energy displacement of states within a Landau level. Interestingly, the typical broadening of the Landau levels is found to behave algebraically with the magnetic field with a nonuniversal exponent.

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Jean-Noël Fuchs, Rémy Mosseri, Julien Vidal. 2018-07-26. Landau levels in quasicrystals. https://doi.org/10.1103/physrevb.98.165427

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