Topological Weaire-Thorpe models of amorphous matter

Abstract

Amorphous solids remain outside of the classification and systematic discovery of new topological materials, partially due to the lack of realistic models that are analytically tractable. Here we introduce the topological Weaire-Thorpe class of models, which are defined on amorphous lattices with fixed coordination number, a realistic feature of covalently bonded amorphous solids. Their short-range properties allow us to analytically predict spectral gaps. Their symmetry under permutation of orbitals allows us to analytically compute topological phase diagrams, which determine quantized observables like circular dichroism, by introducing symmetry indicators for the first time in amorphous systems. These models and our procedures to define invariants are generalizable to higher coordination number and dimensions, opening a route towards a complete classification of amorphous topological states in real space using quasilocal properties.

6+11 pages, 9 figures. Upgraded discussion, including coordination $z=4$ phase diagram and symmetry indicators

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Cited by in corpus (52)

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• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Local Topological Markers in Odd Spatial Dimensions and Their Application to Amorphous Topological Matter
• Symmetry-Protected Topological Phases in a Rydberg Glass
• Amorphous topological phases protected by continuous rotation symmetry
• Criticality in amorphous topological matter -- beyond the universal scaling paradigm
• Fractionalization and topology in amorphous electronic solids
• Structural and electronic properties of realistic two-dimensional amorphous topological insulators
• Topological Random Fractals
• Bootstrapping Bloch bands
• Noncrystalline topological superconductors
• An Exact Chiral Amorphous Spin Liquid
• Signatures of two- and three-dimensional semimetals from circular dichroism
• Obstructed insulators and flat bands in topological phase-change materials
• Geometry and Topology Tango in Ordered and Amorphous Chiral Matter
• Origin and localization of topological band gaps in gyroscopic metamaterials
• Average Symmetry Protected Higher-order Topological Amorphous Insulators
• Physical properties of an Aperiodic monotile: Graphene-like features, chirality and zero-modes
• Probing Chern number by opacity and topological phase transition by a nonlocal Chern marker
• Density-driven higher-order topological phase transitions in amorphous solids
• Bootstrapping the Kronig-Penney Model
• Structural disorder-driven topological phase transition in noncentrosymmetric BiTeI
• Non-Hermitian topology and criticality in photonic arrays with engineered losses
• Local Chern Marker for Periodic Systems
• Topological superconductivity in Fibonacci quasicrystals
• Structural spillage: an efficient method to identify non-crystalline topological materials
• Theory of local ${\mathbb{Z}}_2$ topological markers for finite and periodic two-dimensional systems
• Topological diffusive metal in amorphous transition metal monosilicides
• Enhanced quantum metric due to vacancies in graphene
• Disordered topological graphs enhancing nonlinear phenomena
• Scaling of the Integrated Quantum Metric in Disordered Topological Phases
• Establishing Coherent Momentum-Space Electronic States in Locally Ordered Materials
• Amorphous quantum magnets in a two-dimensional Rydberg atom array
• Quantum Hall effect and Landau levels without spatial long-range correlations
• Fractal Surface States in Three-Dimensional Topological Quasicrystals
• Robustness of topological magnons in disordered arrays of skyrmions
• Structure-driven phase transitions in paracrystalline topological insulators
• A tale of two localizations: coexistence of flat bands and Anderson localization in a photonics-inspired amorphous system
• Topological phases of amorphous matter
• Topological zero-modes of the spectral localizer of trivial metals
• Topology of ultra-localized insulators and superconductors
• Linear magnetization dependence and large intrinsic anomalous Hall effect in Fe78Si9B13 metallic glasses
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• Aharanov-Bohm oscillations and perfectly transmitted mode in amorphous topological insulator nanowires
• Topological band insulators without translational symmetry
• Laser-induced topological phases in monolayer amorphous carbon
• Isotropic 3D topological phases with broken time reversal symmetry
• Three-Dimensional Quantum Hall Effect in Topological Amorphous Metals
• Non-self-averaging topological Anderson insulator