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

TL;DR

This paper develops a theory of critical transport in amorphous Chern insulators, revealing nonuniversal critical behavior that differs from traditional quantum Hall transitions, highlighting unique phenomena in amorphous topological systems.

Contribution

It introduces a new framework for understanding criticality in amorphous topological insulators, showing it extends beyond existing universal scaling paradigms.

Findings

Critical exponents are nonuniversal.

Critical conductance distributions are nonuniversal.

Criticality arises from a combination of geometric and Anderson localization transitions.

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.