# Higher-order topological insulators in amorphous solids

## TL;DR

This paper demonstrates that higher-order topological insulator phases can exist in amorphous solids with a crystalline boundary, expanding the understanding of topological phases beyond crystalline materials.

## Contribution

It introduces the concept of amorphous higher-order topological insulators and shows their stability under certain conditions, even without local crystalline symmetry.

## Key findings

- Corner states persist in amorphous systems with crystalline boundaries.
- Corner states dissolve as disorder percolates to edges, leading to trivial insulators.
- Topological phases can exist in amorphous materials with boundary constraints.

## Abstract

We identify the possibility of realizing higher order topological (HOT) phases in noncrystalline or amorphous materials. Starting from two and three dimensional crystalline HOT insulators, accommodating topological corner states, we gradually enhance structural randomness in the system. Within a parameter regime, as long as amorphousness is confined by outer crystalline boundary, the system continues to host corner states, yielding amorphous HOT insulators. However, as structural disorder percolates to the edges, corner states start to dissolve into amorphous bulk, and ultimately the system becomes a trivial insulator when amorphousness plagues the entire system. These outcomes are further substantiated by computing the quadrupolar (octupolar) moment in two (three) dimensions. Therefore, HOT phases can be realized in amorphous solids, when wrapped by a thin (lithographically grown, for example) crystalline layer. Our findings suggest that crystalline topological phases can be realized even in the absence of local crystalline symmetry.