Topological equivalence of crystal and quasicrystal band structures

Abstract

A number of recent articles have reported the existence of topologically non-trivial states and associated end states in one-dimensional incommensurate lattice models that would usually only be expected in higher dimensions. Using an explicit construction, we here argue that the end states have precisely the same origin as their counterparts in commensurate models and that incommensurability does not in fact provide a meaningful connection to the topological classification of systems in higher dimensions. In particular, we show that it is possible to smoothly interpolate between states with commensurate and incommensurate modulation parameters without closing the band gap and without states crossing the band gap.

arXiv comment7 pages, 9 figures. Editors' Suggestion

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Cited by in corpus (59)

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• Topological Hofstadter Insulators in a Two-Dimensional Quasicrystal
• Localization and topological transitions in non-Hermitian quasiperiodic lattices
• Radiative topological states in resonant photonic crystals
• The Aubry-André model as the hobbyhorse for understanding localization phenomenon
• Virtual Topological Insulators with Real Quantized Physics
• Kaleidoscope of symmetry protected topological phases in one-dimensional periodically modulated lattices
• Constructing a Weyl semimetal by stacking one dimensional topological phases
• Fibonacci optical lattices for tunable quantum quasicrystals
• Electromagnetic response of quantum Hall systems in dimensions five and six and beyond
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• Topological superconductivity in quasicrystals
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• Boundary spin polarization as robust signature of topological phase transition in Majorana nanowires
• Topological properties of the long-range Kitaev chain with Aubry-André-Harper modulation
• Fractional boundary charges in quantum dot arrays with density modulation
• Topological mechanics in quasicrystals
• Breakdown of the correspondence between the real-complex and delocalization-localization transitions in non-Hermitian quasicrystals
• Tunable Band Topology Reflected by Fractional Quantum Hall States in Two-Dimensional Lattices
• Theory of a 3+1D fractional chiral metal: interacting variant of the Weyl semimetal
• From fractional boundary charges to quantized Hall conductance
• Realizing the Harper model with Ultracold Atoms in a Ring Lattice
• The K-Theoretic Bulk-Boundary Principle for Dynamically Patterned Resonators
• Topological Anderson insulators in an Ammann-Beenker quasicrystal and a snub-square crystal
• Phasonic Spectroscopy of a Quantum Gas in a Quasicrystalline Lattice
• Classical Dimers on Penrose Tilings
• Topological Properties of Ultracold Bosons in One-Dimensional Quasiperiodic Optical Lattice
• Anomalous charge pumping in a one-dimensional optical superlattice
• Time Quasilattices in Dissipative Dynamical Systems
• Rational Approximations of Quasi-Periodic Problems via Projected Green's Functions
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• Quantum Emulation of Extreme Non-equilibrium Phenomena with Trapped Atoms
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• Quasiperiodicity and 2D Topology in 1D Charge Ordered Materials
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• Bulk-boundary correspondance for Sturmian Kohmoto like models
• Colloquium: Synthetic quantum matter in non-standard geometries
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• Unraveling Multifractality and Mobility Edges in Quasiperiodic Aubry-André-Harper Chains through High-Harmonic Generation
• Superconductivity and charge-density-wave in the Holstein model on the Penrose Lattice
• Compressibility enhancement in an almost staggered interacting Harper model
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• Topological end states in two-orbital double-exchange model for colossal magnetoresistive manganites
• Nonlinear topological Toda quasicrystal
• Two-strand ladder network variants: localization, multifractality, and quantum dynamics under an Aubry-André-Harper kind of quasiperiodicity
• Disorder-induced chiral and helical Majorana edge modes in a two-dimensional Ammann-Beenker quasicrystal
• Quantum state transfer and maximal entanglement between distant qubits using a minimal quasicrystal pump
• Localization and multifractal properties of the long-range Kitaev chain in the presence of an Aubry-André-Harper modulation