Abstract
The tenfold classification of topological phases enumerates all strong topological phases for both clean and disordered systems. These strong topological phases are connected to the existence of robust edge states. However, in addition to the strong topological phases in the tenfold classification, there exist weak topological phases whose properties under disorder are less well understood. It is unknown if the weak topological indices can be generalized for arbitrary disorder, and the physical signatures of these indices is not known. In this paper, we study disordered models of the two dimensional weak AIII insulator. We demonstrate that the weak invariants can be defined at arbitrary disorder, and that these invariants are connected to the presence or absence of bound charge at dislocation sites.
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