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

Abstract

Robust edge transport can occur when particles in crystalline lattices interact with an external magnetic field. This system is well described by Bloch's theorem, with the spectrum being composed of bands of bulk states and in-gap edge states. When the confining lattice geometry is altered to be quasicrystaline, then Bloch's theorem breaks down. However, we still expect to observe the basic characteristics of bulk states and current carrying edge states. Here, we show that for quasicrystals in magnetic fields, there is also a third option; the bulk localised transport states. These states share the in-gap nature of the well-known edge states and can support transport along them, but they are fully contained within the bulk of the system, with no support along the edge. We consider both finite and infinite systems, using rigorous error controlled computational techniques that are not prone to finite-size effects. The bulk localised transport states are preserved for infinite systems, in stark contrast to the normal edge states. This allows for transport to be observed in infinite systems, without any perturbations, defects, or boundaries being introduced. We confirm the in-gap topological nature of the bulk localised transport states for finite and infinite systems by computing common topological measures; namely the Bott index and local Chern marker. The bulk localised transport states form due to a magnetic aperiodicity arising from the interplay of length scales between the magnetic field and quasiperiodic lattice. Bulk localised transport could have interesting applications similar to those of the edge states on the boundary, but that could now take advantage of the larger bulk of the lattice. The infinite size techniques introduced here, especially the calculation of topological measures, could also be widely applied to other crystalline, quasicrystalline, and disordered models.

23 pages, 23 figures, comments welcome

References in corpus (21)

• The density-matrix renormalization group in the age of matrix product states
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Helical Metal Inside a Topological Band Insulator
• Topological Photonic Quasicrystals: Fractal Topological Spectrum and Protected Transport
• Periodically-driven quantum matter: the case of resonant modulations
• Topological Hofstadter Insulators in a Two-Dimensional Quasicrystal
• Observation of Protected Photonic Edge States Induced By Real-Space Topological Lattice Defects
• Hofstadter Topology: Non-crystalline Topological Materials at High Flux
• Strongly-Interacting Bosons in a Two-Dimensional Quasicrystal Lattice
• Higher-Order topological insulator in a dodecagonal quasicrystal
• Topological models in rotationally symmetric quasicrystals
• Hofstadter butterfly of a quasicrystal
• Bosonic Bott Index and Disorder-Induced Topological Transitions of Magnons
• Perturbative Approach to Flat Chern Bands in the Hofstadter Model
• Landau levels in strained two-dimensional photonic crystals
• Non-adiabatic quantum state preparation and quantum state transport in chains of Rydberg atoms
• Impurity bound states as detectors of topological band structures revisited
• The Mean-Field Bose Glass in Quasicrystalline Systems
• Quasiperiodic tilings under magnetic field
• Effect of coordination on topological phases on self-similar structures
• Flat band of topological states bound to a mobile impurity

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• Physical properties of an Aperiodic monotile: Graphene-like features, chirality and zero-modes
• Identification and properties of topological states in the bulk of quasicrystals
• Topological states and flat bands in exactly solvable decorated Cayley trees
• Localization and topological signatures under periodic twisting