Amorphous topological matter: theory and experiment

Abstract

Topological phases of matter are ubiquitous in crystals, but less is known about their existence in amorphous systems, that lack long-range order. In this perspective, we review the recent progress made on theoretically defining amorphous topological phases and the new phenomenology that they can open. We revisit key experiments suggesting that amorphous topological phases exist in both solid-state and synthetic amorphous systems. We finish by discussing the open questions in the field, that promises to significantly enlarge the set of materials and synthetic systems benefiting from the robustness of topological matter.

arXiv commentThis is an extended version of the article accepted in EPL

References in corpus (56)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Anyons in an exactly solved model and beyond
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Anderson Transitions
• Topological quantum chemistry
• Quantization of fractional corner charge in $C_n$-symmetric higher-order topological crystalline insulators
• Room-temperature perpendicular magnetization switching through giant spin-orbit torque from sputtered BixSe(1-x) topological insulator material
• Quantitative mappings between symmetry and topology in solids
• Amorphous topological insulators constructed from random point sets
• Disordered Topological Insulators via $C^{\ast }$-Algebras
• Topological Materials Discovery from Crystal Symmetry
• Scattering theory of topological insulators and superconductors
• Bulk-boundary correspondence from the inter-cellular Zak phase
• Topological phases without crystalline counterparts
• Higher-order topological insulators in amorphous solids
• K-Theory and Pseudospectra for Topological Insulators
• Fractional corner charges in spin-orbit coupled crystals
• Statistical Topological Insulators
• Non-Commutative Tools for Topological Insulators
• Amorphous photonic topological insulator
• Topological Weaire-Thorpe models of amorphous matter
• Observation of spin-momentum locked surface states in amorphous Bi${}_2$Se${}_3$
• Toward Realistic Amorphous Topological Insulators
• Robust Edge States in Amorphous Gyromagnetic Photonic Lattices
• Amorphous topological superconductivity in a Shiba glass
• Local invariants identify topology in metals and gapless systems
• Non-Commutative Chern Numbers for Generic Aperiodic Discrete Systems
• Geometrically disordered network models, quenched quantum gravity, and critical behavior at quantum Hall plateau transitions
• Local Topological Markers in Odd Spatial Dimensions and Their Application to Amorphous Topological Matter
• An operator-based approach to topological photonics
• Topological phase transitions in glassy quantum matter
• Orbital magnetization and Chern number in a supercell framework: Single k-point formula
• Amorphous topological phases protected by continuous rotation symmetry
• Quantised Bulk Conductivity as a Local Chern Marker
• Extended topological group structure due to average reflection symmetry
• Criticality in amorphous topological matter -- beyond the universal scaling paradigm
• Structural and electronic properties of realistic two-dimensional amorphous topological insulators
• Topological and conventional phases of a three dimensional electron glass
• Amorphous Bi${}_2$Se${}_3$ structural, electronic, and topological nature by first-principles
• Topology invisible to eigenvalues in obstructed atomic insulators
• Topological Insulator Thin Films Starting from the Amorphous Phase - Bi${}_2$Se${}_3$ as Example
• Random network models with variable disorder of geometry
• Disorder-driven topological phase transition in Bi2Se3 films
• Microscopic characteristics and tomography scheme of the local Chern marker
• Application of Convolutional Neural Network to Quantum Percolation in Topological Insulators
• Origin and localization of topological band gaps in gyroscopic metamaterials
• Geometry and Topology Tango in Ordered and Amorphous Chiral Matter
• Correlated quantum percolation in the lowest Landau level
• Topological Insulator in an Atomic Liquid
• Topological transitions and Anderson localization of light in disordered atomic arrays
• Spin memory of the topological material under strong disorder
• Single-point spin Chern number in a supercell framework
• Engineering of Chern insulators and circuits of topological edge states
• Fermionic Topological Order on Generic Triangulations

Cited by in corpus (26)

• Higher-order topological phases in crystalline and non-crystalline systems: a review
• The Wannier Function Software Ecosystem for Materials Simulations
• Average Symmetry Protected Higher-order Topological Amorphous Insulators
• Phase transitions and scale invariance in topological Anderson insulators
• Local Chern Marker for Periodic Systems
• Topological superconductivity in Fibonacci quasicrystals
• Structural spillage: an efficient method to identify non-crystalline topological materials
• Topological diffusive metal in amorphous transition metal monosilicides
• Theory of local ${\mathbb{Z}}_2$ topological markers for finite and periodic two-dimensional systems
• Establishing Coherent Momentum-Space Electronic States in Locally Ordered Materials
• Amorphous quantum magnets in a two-dimensional Rydberg atom array
• Interacting Local Topological Markers: A one-particle density matrix approach for characterizing the topology of interacting and disordered states
• Quantum Hall effect and Landau levels without spatial long-range correlations
• Structure-driven phase transitions in paracrystalline topological insulators
• Topological zero-modes of the spectral localizer of trivial metals
• Floquet Amorphous Topological Orders in a One-dimensional Rydberg Glass
• Quantum Hall criticality in an amorphous Chern insulator
• Signatures of Amorphous Shiba State in FeTe${}_{0.55}$Se${}_{0.45}$
• Global and Local Topological Crystalline Markers for Rotation-Symmetric Insulators
• Fluctuations and Correlations of Local Topological Order Parameters in Disordered Two-dimensional Topological Insulators
• Magnon topology driven by altermagnetism
• Laser-induced topological phases in monolayer amorphous carbon
• Aharanov-Bohm oscillations and perfectly transmitted mode in amorphous topological insulator nanowires
• Three-Dimensional Quantum Hall Effect in Topological Amorphous Metals
• Coarse geometric approach to topological phases: Invariants from real-space representations
• Topological transition induced by selective random defects on a honeycomb lattice