Hofstadter butterfly of a quasicrystal

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.

arXiv comment9 pages, 5 figures, published version

References in corpus (17)

• Topological States and Adiabatic Pumping in Quasicrystals
• Aharonov-Bohm cages in two-dimensional structures
• Topological Phases for Fermionic Cold Atoms on the Lieb Lattice
• Topological Photonic Quasicrystals: Fractal Topological Spectrum and Protected Transport
• Fractal energy spectrum of a polariton gas in a Fibonacci quasi-periodic potential
• Topological Hofstadter Insulators in a Two-Dimensional Quasicrystal
• Hofstadter butterflies for flat bands
• Aperiodic Weak Topological Superconductors
• Quantum dynamics in two and three-dimensional quasiperiodic tilings
• Landau levels in the case of two degenerate coupled bands: kagome lattice tight-binding spectrum
• Energy landscape in two-dimensional Penrose-tiled quasicrystal
• Flip dynamics in octagonal rhombus tiling sets
• Generalized quasiperiodic Rauzy tilings
• Quasiperiodic tilings under magnetic field
• Anderson Localization and Quantum Hall Effect: Numerical Observation of Two Parameter Scaling
• Topological properties of Fibonacci quasicrystals : A scattering analysis of Chern numbers
• Less singular quasicrystals: life in low codimensions

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• Bulk Localised Transport States in Infinite and Finite Quasicrystals via Magnetic Aperiodicity
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