Structural Disorder Induced Second-order Topological Insulators in Three Dimensions

TL;DR

This paper predicts and demonstrates the existence of second-order topological insulators in amorphous systems without crystalline symmetry, showing that disorder can induce such phases and revealing their key properties.

Contribution

It introduces the concept of amorphous second-order topological insulators and shows disorder can induce topological phases in non-crystalline materials.

Findings

Existence of second-order topological insulators in amorphous systems.

Disorder can induce topological phases from trivial states.

Presence of hinge states and quantized conductance in amorphous phases.

Abstract

Higher-order topological insulators are established as topological crystalline insulators protected by crystalline symmetries. One celebrated example is the second-order topological insulator in three dimensions that hosts chiral hinge modes protected by crystalline symmetries. Since amorphous solids are ubiquitous, it is important to ask whether such a second-order topological insulator can exist in an amorphous system without any spatial order. Here we predict the existence of a secondorder topological insulating phase in an amorphous system without any crystalline symmetry. Such a topological phase manifests in the winding number of the quadrupole moment, the quantized longitudinal conductance and the hinge states. Furthermore, in stark contrast to the viewpoint that structural disorder should be detrimental to the higher-order topological phase, we remarkably find that structural disorder can induce a second-order topological insulator from a topologically trivial phase in a regular geometry. We finally demonstrate the existence of a second-order topological phase in amorphous systems with time-reversal symmetry.