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.

9 pages, 5 figures, published version

References in corpus (4)

• Topological Phases for Fermionic Cold Atoms on the Lieb Lattice
• Topological Photonic Quasicrystals: Fractal Topological Spectrum and Protected Transport
• Topological Hofstadter Insulators in a Two-Dimensional Quasicrystal
• Quasiperiodic tilings under magnetic field

Cited by in corpus (25)

• Topological and geometrical aspects of band theory
• Universality of Hofstadter butterflies on hyperbolic lattices
• Topological states in quasicrystals
• Realization of quasicrystalline quadrupole topological insulators in electrical circuits
• Quasicrystalline Chern Insulators
• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Topological Anderson insulators in an Ammann-Beenker quasicrystal and a snub-square crystal
• Two-dimensional optical quasicrystal potentials for ultracold atom experiments
• Physical properties of an Aperiodic monotile: Graphene-like features, chirality and zero-modes
• Topological Gaps in Quasi-Periodic Spin Chains: A Numerical and K-Theoretic Analysis
• Bulk Localised Transport States in Infinite and Finite Quasicrystals via Magnetic Aperiodicity
• Higher-dimensional Hofstadter butterfly on Penrose lattice
• Topological gap labeling with the third Chern numbers in three-dimensional quasicrystals
• Closing of gaps and gap labeling and passage from molecular states to critical states in a 2D quasicrystal
• Confined states and topological phases in two-dimensional quasicrystalline $\pi$-flux model
• Finding spectral gaps in quasicrystals
• Ising model on the aperiodic Smith hat
• Elastodynamical properties of Sturmian structured media
• High-Quality Resonances in Quasi-Periodic Clusters of Scatterers for Flexural Waves
• Multifractal Properties of Tribonacci Chains
• Quasicrystalline Spin Liquid
• Topological phases of amorphous matter
• Family of Aperiodic Tilings with Tunable Quantum Geometric Tensor
• Missing link between the 2D Quantum Hall problem and 1D quasicrystals
• Mapping Chern numbers in quasi-periodic interacting spin chains