Fractal Surface States in Three-Dimensional Topological Quasicrystals
arXiv:2401.11497 · doi:10.1103/PhysRevResearch.6.043054
Abstract
We study topological states of matter in quasicrystals, which do not rely on crystalline orders. In the absence of a bandstructure description and spin-orbit coupling, we show that a three-dimensional quasicrystal can nevertheless form a topological insulator. It relies on a combination of noncrystallographic rotational symmetry of quasicrystals and electronic orbital space symmetry, which is the quasicrystalline counterpart of topological crystalline insulator. The resulting topological state obeys a non-trivial twisted bulk-boundary correspondence and lacks a good metallic surface. The topological surface states, localized on the top and bottom planes respecting the quasicrystalline symmetry, exhibit a new kind of multifractality with probability density concentrates mostly on high symmetry patches. They form a near-degenerate manifold of 'immobile' states whose number scales proportionally with the macroscopic sample size. This can open the door to a novel platform for topological surface physics distinct from the crystalline counterpart.
References in corpus (47)
- Topological Insulators
- Topological insulators and superconductors
- Anyons in an exactly solved model and beyond
- Topological Crystalline Insulators
- Anderson Transitions
- Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
- Topological States and Adiabatic Pumping in Quasicrystals
- -dimensional edge states of rotation symmetry protected topological states
- The space group classification of topological band insulators
- Fragile Topology and Wannier Obstructions
- Amorphous topological insulators constructed from random point sets
- Mapping topological order in coordinate space
- Angle-resolved photoemission spectroscopy and its application to topological materials
- Higher-Order Topological Insulators in Quasicrystals
- Disordered Topological Insulators via -Algebras
- Topological Insulators in Random Lattices
- Topological Photonic Quasicrystals: Fractal Topological Spectrum and Protected Transport
- Quantum Spin Hall Effect and Spin Bott Index in a Quasicrystal Lattice
- Matter-wave diffraction from a quasicrystalline optical lattice
- Real Space Invariants: Twisted Bulk-Boundary Correspondence of Fragile Topology
- Disordered Topological Insulators: A Non-Commutative Geometry Perspective
- Superconductivity and strong interactions in a tunable moiré quasiperiodic crystal
- Topological phases without crystalline counterparts
- Higher-order topological insulators in amorphous solids
- Topology of Disconnected Elementary Band Representations
- Experimental characterization of fragile topology in an acoustic metamaterial
- Aperiodic Weak Topological Superconductors
- Topological Amorphous Metals
- Berry-phase description of Topological Crystalline Insulators
- Structural Disorder Induced Second-order Topological Insulators in Three Dimensions
- Topological Weaire-Thorpe models of amorphous matter
- Robust Edge States in Amorphous Gyromagnetic Photonic Lattices
- Amorphous topological superconductivity in a Shiba glass
- Critical eigenstates and their properties in one and two dimensional quasicrystals
- Crystallographic splitting theorem for band representations and fragile topological photonic crystals
- Effective Model for Fractional Topological Corner Modes in Quasicrystals
- Kohn-Luttinger mechanism driven exotic topological superconductivity on the Penrose lattice
- Photonic Chern insulator through homogenization of an array of particles
- Universal topological marker
- Local Topological Markers in Odd Spatial Dimensions and Their Application to Amorphous Topological Matter
- Exact Eigenstates of Tight-Binding Hamiltonians on the Penrose Tiling
- Topological phase transitions in glassy quantum matter
- Energy landscape in two-dimensional Penrose-tiled quasicrystal
- Strictly localized states in the octagonal Ammann-Beenker quasicrystal
- Quasicrystalline Weyl points and dense Fermi-Bragg arcs
- Higher-order Topological Insulators and Semimetals in Three Dimensions without Crystalline Counterparts
- Calculations of Chern number: equivalence of real-space and twisted-boundary-condition formulae