Agenda

Résumé : The imposition of crystalline symmetries is known to lead to a rich variety of insulating and superconducting topological phases. These include higher-order topological phases and obstructed atomic limits. We classify such topological crystalline phases (TCPs) in the presence of disorder that preserves the crystalline symmetry on average. We find that, while clean TCPs evade a general bulk-boundary principle, disordered TCPs admit a complete bulk-boundary correspondence. While the boundary signatures of most disordered TCPs are similar to their clean counterparts, the addition of disorder to certain TCPs results in higher-order statistical topological phases, in which zero-energy hinge states have critical wavefunction statistics, while remaining protected from Anderson localization.