Topological phases of amorphous matter

Abstract

Topological phases of matter are often understood and predicted with the help of crystal symmetries, although they don't rely on them to exist. In this chapter we review how topological phases have been recently shown to emerge in amorphous systems. We summarize the properties of topological states and discuss how disposing of translational invariance has motivated the surge of new tools to characterize topological states in amorphous systems, both theoretically and experimentally. The ubiquity of amorphous systems combined with the robustness of topology has the potential to bring new fundamental understanding in our classification of phases of matter, and inspire new technological developments.

arXiv comment44 pages, 5 Figures. v3 updated references. Contributed chapter to "Low-Temperature Thermal and Vibrational Properties of Disordered Solids" (A Half-Century of universal "anomalies" of glasses), Ed. M. A. Ramos, to appear

References in corpus (75)

• Topological Insulators
• Topological insulators and superconductors
• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Anyons in an exactly solved model and beyond
• Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
• Topological Insulators with Inversion Symmetry
• Photonic Floquet Topological Insulators
• Moire bands in twisted double-layer graphene
• Classification of topological quantum matter with symmetries
• Topological Crystalline Insulators
• Topological Crystalline Insulators in the SnTe Material Class
• Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals
• Topological States and Adiabatic Pumping in Quasicrystals
• The (High Quality) Topological Materials In The World
• Magnetoelectric polarizability and axion electrodynamics in crystalline insulators
• Catalogue of Topological Electronic Materials
• Zoo of quantum-topological phases of matter
• Higher-Order Topology in Bismuth
• Topological Boundary Modes in Isostatic Lattices
• Towards ideal topological materials: Comprehensive database searches using symmetry indicators
• Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property
• Quantized circular photogalvanic effect in Weyl semimetals
• Topological Anderson Insulator
• Room-temperature perpendicular magnetization switching through giant spin-orbit torque from sputtered BixSe(1-x) topological insulator material
• Designer disordered materials with large complete photonic band gaps
• Theory of the topological Anderson insulator
• Wannier representation of Z_2 topological insulators
• Topological quantum properties of chiral crystals
• Multiple types of topological fermions in transition metal silicides
• High-throughput calculations of magnetic topological materials
• Large Fermi Arcs in Unconventional Weyl Semimetal RhSi
• Fragile Topology and Wannier Obstructions
• Observation of the topological Anderson insulator in disordered atomic wires
• Quantized Faraday and Kerr rotation and axion electrodynamics of a 3D topological insulator
• Mapping topological order in coordinate space
• Chiral Topological Semimetal with Multifold Band Crossings and Long Fermi arcs
• Magnetic Topological Quantum Chemistry
• Numerical study of the topological Anderson insulator in HgTe/CdTe quantum wells
• Structure and Topology of Band Structures in the 1651 Magnetic Space Groups
• Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time reversal symmetry
• Higher-Order Topological Insulators in Quasicrystals
• Topological Origin of Equatorial Waves
• Disordered Topological Insulators via $C^{\ast }$-Algebras
• Chiral Optical Response of Multifold Fermions
• Existence of bulk chiral fermions and crystal symmetry
• Scattering theory of topological insulators and superconductors
• Quantum interference and Aharonov-Bohm oscillations in topological insulators
• Real Space Invariants: Twisted Bulk-Boundary Correspondence of Fragile Topology
• Theory of orbital magnetoelectric response
• Dichroic f-sum rule and the orbital magnetization of crystals
• Topological phases without crystalline counterparts
• Topological Hofstadter Insulators in a Two-Dimensional Quasicrystal
• Witten effect in a crystalline topological insulator
• Probing topology by "heating": Quantized circular dichroism in ultracold atoms
• Theory of spin Bott index for quantum spin Hall states in non-periodic systems
• Chern-Simons orbital magnetoelectric coupling in generic insulators
• Aperiodic Weak Topological Superconductors
• Probing two topological surface bands of Sb2Te3 by spin-polarized photoemission spectroscopy
• Topological Amorphous Metals
• Topological Weaire-Thorpe models of amorphous matter
• Topological states on fractal lattices
• Topology in the Sierpiński-Hofstadter problem
• The existence of robust edge currents in Sierpinsky Fractals
• Robust Edge States in Amorphous Gyromagnetic Photonic Lattices
• Hofstadter butterfly of a quasicrystal
• Surface theorem for the Chern-Simons axion coupling
• Topological Anderson insulator phase in a quasicrystal lattice
• Edge states reconstruction from strong correlations in quantum spin Hall insulators
• Pairing Obstructions in Topological Superconductors
• Topological phase transitions in glassy quantum matter
• Geometric and nongeometric contributions to the surface anomalous Hall conductivity
• Topological and conventional phases of a three dimensional electron glass
• Landau levels in quasicrystals
• Microscopic characteristics and tomography scheme of the local Chern marker
• Local formula for the $Z_2$ invariant of topological insulators

Cited by in corpus (4)

• Plasticity in amorphous solids is mediated by topological defects in the displacement field
• Symmetry-Protected Topological Phases in a Rydberg Glass
• Robustness of chiral edge modes in fractal-like-lattices below two dimensions: A case study
• Linear magnetization dependence and large intrinsic anomalous Hall effect in Fe78Si9B13 metallic glasses