Topological Random Fractals

TL;DR

This paper introduces topological electronic states on random fractal lattices, demonstrating their robust properties and distinct critical behavior, expanding the understanding of topological phases in complex disordered systems.

Contribution

It presents the first study of topological states on random fractals, showing they support quantized conductance and form a new thermodynamic phase of matter.

Findings

Support for quantized conductance in topological random fractals

Existence of a robust mobility gap in these systems

Distinct critical properties from classical class D systems

Abstract

We introduce the notion of topological electronic states on random lattices in non-integer dimensions. By considering a class $D$ model on critical percolation clusters embedded in two dimensions, we demonstrate that these topological random fractals exhibit a robust mobility gap, support quantized conductance and represent a well-defined thermodynamic phase of matter. The finite-size scaling analysis further suggests that the critical properties are not consistent with the class $D$ systems in two dimensions. Our results establish topological random fractals as the most complex systems known to support nontrivial band topology with their distinct unique properties.