Topological phase transitions in glassy quantum matter

Abstract

Amorphous systems have rapidly gained promise as novel platforms for topological matter. In this work we establish a scaling theory of amorphous topological phase transitions driven by the density of lattice points in two dimensions. By carrying out a finite-size scaling analysis of topological invariants averaged over discrete and continuum random geometries, we discover unique critical properties of Chern and ${\mathbb{Z}}_2$ glass transitions. Even for short-range hopping models the Chern glass phase may persist down to the fundamental lower bound given by the classical percolation threshold. While the topological indices accurately satisfy the postulated one-parameter scaling, they do not generally flow to the closest integer value in the thermodynamic limit. Furthermore, the value of the critical exponent describing the diverging localization length varies continuously along the phase boundary and is not fixed by the symmetry class of the Hamiltonian. We conclude that the critical behaviour of amorphous topological systems exhibit characteristic features not observed in disordered systems, motivating a wealth of new research directions.

5.5 pages + 2.5-page appendix, 3+3 figures, updated figures in the appendix

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• Criticality in amorphous topological matter -- beyond the universal scaling paradigm
• Topological Random Fractals
• Average Symmetry Protected Higher-order Topological Amorphous Insulators
• Origin and localization of topological band gaps in gyroscopic metamaterials
• Density-driven higher-order topological phase transitions in amorphous solids
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• Quantum walks on random lattices: Diffusion, localization and the absence of parametric quantum speed-up
• Structural spillage: an efficient method to identify non-crystalline topological materials
• Topological diffusive metal in amorphous transition metal monosilicides
• Fractal Surface States in Three-Dimensional Topological Quasicrystals
• Floquet Amorphous Topological Orders in a One-dimensional Rydberg Glass
• Percolation Transition in a Topological Phase
• Topological phases of amorphous matter
• Emergent fractals in dirty topological crystals
• Three-Dimensional Quantum Hall Effect in Topological Amorphous Metals
• Topological band insulators without translational symmetry
• Laser-induced topological phases in monolayer amorphous carbon
• Recent progress on disorder-induced topological phases
• Symmetry-protected topological wire in a topological vacuum
• Entanglement signatures of a percolating quantum system
• Non-self-averaging topological Anderson insulator