Topological phases of amorphous matter

TL;DR

This paper reviews recent advances in understanding topological phases in amorphous materials, highlighting new theoretical and experimental tools that do not rely on crystal symmetries, expanding the classification of phases of matter.

Contribution

It summarizes how topological phases can emerge in amorphous systems and discusses new methods for their characterization without translational symmetry.

Findings

Topological states can exist in amorphous systems without crystal symmetry.

New tools have been developed for theoretical and experimental characterization.

Amorphous topological phases could lead to novel technological applications.

Abstract

Topological phases of matter are often understood and predicted with the help of crystal symmetries, although they don't rely on them to exist. In this chapter we review how topological phases have been recently shown to emerge in amorphous systems. We summarize the properties of topological states and discuss how disposing of translational invariance has motivated the surge of new tools to characterize topological states in amorphous systems, both theoretically and experimentally. The ubiquity of amorphous systems combined with the robustness of topology has the potential to bring new fundamental understanding in our classification of phases of matter, and inspire new technological developments.