Amorphous topological phases protected by continuous rotation symmetry

TL;DR

This paper introduces amorphous topological phases protected by continuous rotation symmetry, demonstrating their robustness against boundary misalignment and local disorder, and classifying these phases through systematic models and topological invariants.

Contribution

It reveals that amorphous topological materials can host protected surface states under continuous rotation symmetry, overcoming limitations of crystalline reflection symmetry.

Findings

Edge states remain protected from localization despite disorder

Systematic classification of amorphous topological phases in 2D

Construction of models and calculation of topological invariants

Abstract

Protection of topological surface states by reflection symmetry breaks down when the boundary of the sample is misaligned with one of the high symmetry planes of the crystal. We demonstrate that this limitation is removed in amorphous topological materials, where the Hamiltonian is invariant on average under reflection over any axis due to continuous rotation symmetry. While the local disorder caused by the amorphous structure weakens the topological protection, we demonstrate that the edge remains protected from localization. In order to classify such phases we perform a systematic search over all the possible symmetry classes in two dimensions and construct the example models realizing each of the proposed topological phases. Finally, we compute the topological invariant of these phases as an integral along a meridian of the spherical Brillouin zone of an amorphous Hamiltonian.