Disordered topological crystalline insulators

Topological phases are known for their robustness to local perturbations and for hosting extended states that evade the localization expected in low dimensional systems. Such states exist both on boundaries and in the bulk at the transitions between topological phases. This effect is epitomized in two-dimensions by the plateau transition of Chern bands dividing regions of different Chern numbers, either by varying energy or disorder strength. In the absence of a Chern invariant, crystalline symmetry may still protect the topology of two-dimensional systems. In this case, the topology may be fragile, which means that it is not robust to the mixing with trivial bands. In this talk, we explore the impact of disorder in two-dimensional topological systems protected by crystalline symmetry, the structure of their impurity states, and the possibility for the existence of delocalized states in the bulk.