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.
Highlights
INTRODUCTIONAn nth order topological phase supports boundary states of codimension dc = n, with corner (dc = d) and hinge (dc = d − 1) modes standing as its prime representatives [15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37]
D-dimensional topological systems support gapless boundary modes of codimension one [1,2,3]
We here establish that higher order topological (HOT) phases can be realized even when the crystalline symmetry is absent in the bulk of the system
Summary
An nth order topological phase supports boundary states of codimension dc = n, with corner (dc = d) and hinge (dc = d − 1) modes standing as its prime representatives [15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37]. When (a) amorphousness is confined within the interior of the system and (b) the scale of structural disorder is smaller than the band gap, the corner states remain sharp and we realize a second-order amorphous HOTI, see Fig. 2. We investigate the stability of such corner states in an amorphous system, lacking the C4 symmetry
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