Criticality in amorphous topological matter -- beyond the universal scaling paradigm

Abstract

We establish the theory of critical transport in amorphous Chern insulators and show that it lies beyond the current paradigm of topological criticality epitomized by the quantum Hall transitions. We consider models of Chern insulators on percolation-type random lattices where the average density determines the statistical properties of geometry. While these systems display a two-parameter scaling behaviour near the critical density, the critical exponents and the critical conductance distributions are strikingly nonuniversal. Our analysis indicates that the amorphous topological criticality results from an interpolation of a geometric-type transition at low density and an Anderson localization-type transition at high density. Our work demonstrates how the recently discovered amorphous topological systems display unique phenomena distinct from their conventionally-studied counterparts.

5+7 pages. 3+4 figures

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Cited by in corpus (24)

• Structural Disorder Induced Second-order Topological Insulators in Three Dimensions
• Topological Weaire-Thorpe models of amorphous matter
• Amorphous topological matter: theory and experiment
• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Symmetry-Protected Topological Phases in a Rydberg Glass
• Topological photonic alloy
• Fractionalization and topology in amorphous electronic solids
• Topological Random Fractals
• Topological Anderson amorphous insulator
• 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
• Quantum walks on random lattices: Diffusion, localization and the absence of parametric quantum speed-up
• Topological diffusive metal in amorphous transition metal monosilicides
• Band alignment effect in the topological photonic alloy
• Quantum Hall effect and Landau levels without spatial long-range correlations
• A tale of two localizations: coexistence of flat bands and Anderson localization in a photonics-inspired amorphous system
• Percolation Transition in a Topological Phase
• Floquet Amorphous Topological Orders in a One-dimensional Rydberg Glass
• Quantum Hall criticality in an amorphous Chern insulator
• Three-Dimensional Quantum Hall Effect in Topological Amorphous Metals
• Topological band insulators without translational symmetry
• Non-self-averaging topological Anderson insulator
• Entanglement signatures of a percolating quantum system