Higher Order Topological Insulators in Amorphous Solids

We identify the possibility of realizing higher order topological (HOT) phases in noncrystalline or amorphous materials. Specifically, 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, realizing an amorphous HOT insulator. However, as structural disorder percolates to the edges, corner states start to dissolve into amorphous bulk, and ultimately the system becomes a trivial insulator (devoid of corner modes), when amorphousness plagues the entire system. These outcomes are further substantiated from the scaling of the quadrupolar (octupolar) moment in two (three) dimensions with the scrambling radius. Therefore, HOT phases can be realized in amorphous solids, when wrapped by a thin crystalline layer.