Landau levels in quasicrystals

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 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. PACS numbers: 71.23.Ft,71.70.Di,73.43.-f 1 These commensurate quasicrystals have perfect long-range order and are no less quasicrystalline than the original ones. The adjective "commensurate" only refers to the fact that the ratios of their plaquette areas are rational numbers. arXiv:1807.10032v2 [cond-mat.dis-nn]

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