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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.
Using an explicit 1-dimensional model, we provide direct evidence that the one-dimensional topological phases from the AIII and BDI symmetry classes follow a $mathbb Z$-classification, even in the strong disorder regime when the Fermi level is embedd
The traditional concept of phase transitions has, in recent years, been widened in a number of interesting ways. The concept of a topological phase transition separating phases with a different ground state topology, rather than phases of different s
Topological magnon insulators are the bosonic analogs of electronic topological insulators. They are manifested in magnetic materials with topologically nontrivial magnon bands as realized experimentally in a quasi-two-dimensional (quasi-2D) kagome f
We have studied the magnetic-field-driven quantum phase transitions in Josephson junction arrays with a large coordination number. The characteristic energies were extracted in both the superconducting and insulating phases by integrating the current
The effect of strong disorder on chiral-symmetric 3-dimensional lattice models is investigated via analytical and numerical methods. The phase diagrams of the models are computed using the non-commutative winding number, as functions of disorder stre