Topological Hofstadter Insulators in a Two-Dimensional Quasicrystal

Abstract

We investigate the properties of a two-dimensional quasicrystal in the presence of a uniform magnetic field. In this configuration, the density of states (DOS) displays a Hofstadter butterfly-like structure when it is represented as a function of the magnetic flux per tile. We show that the low-DOS regions of the energy spectrum are associated with chiral edge states, in direct analogy with the Chern insulators realized with periodic lattices. We establish the topological nature of the edge states by computing the topological Chern number associated with the bulk of the quasicrystal. This topological characterization of the non-periodic lattice is achieved through a local (real-space) topological marker. This work opens a route for the exploration of topological insulating materials in a wide range of non-periodic lattice systems, including photonic crystals and cold atoms in optical lattices.

10 pages, 9 figures. Published version

References in corpus (10)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• Topological Anderson Insulator
• Observation of Topological Phase Transitions in Photonic Quasicrystals
• Quench-induced supercurrents in an annular Bose gas
• Direct imaging of topological edge states in cold-atom systems
• Detecting Chiral Edge States in the Hofstadter Optical Lattice
• Topological meaning of Z${}_2$ numbers in time reversal invariant systems
• Quasiperiodic tilings under magnetic field

Cited by in corpus (13)

• Topological phase transition in non-Hermitian quasicrystals
• Topological Photonic Quasicrystals: Fractal Topological Spectrum and Protected Transport
• Topological and geometrical aspects of band theory
• Topological states in quasicrystals
• Hofstadter butterfly of a quasicrystal
• Quasicrystalline Chern Insulators
• Topological Anderson insulators in an Ammann-Beenker quasicrystal and a snub-square crystal
• Anomalous charge pumping in a one-dimensional optical superlattice
• Topological gap labeling with the third Chern numbers in three-dimensional quasicrystals
• Higher-dimensional Hofstadter butterfly on Penrose lattice
• Non-diagonal disorder enhanced topological properties of graphene with laser irradiation
• Transport through Quantum Anomalous Hall Bilayers with Lattice Mismatch
• Disorder-induced chiral and helical Majorana edge modes in a two-dimensional Ammann-Beenker quasicrystal