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 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.

arXiv comment14 pages, 9 figures

References in corpus (7)

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• Hofstadter butterfly of a quasicrystal
• Electrons in deterministic quasicrystalline potentials and hidden conserved quantities
• Brillouin zone labelling for quasicrystals
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• Bulk Localised Transport States in Infinite and Finite Quasicrystals via Magnetic Aperiodicity
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• Confined states and topological phases in two-dimensional quasicrystalline $\pi$-flux model
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• Topological phases of amorphous matter
• Family of Aperiodic Tilings with Tunable Quantum Geometric Tensor
• Localization and topological signatures under periodic twisting