Selective bulk-boundary correspondence in higher-order topological insulators with anticommuting mirror and chiral symmetries

We investigate higher-order topological insulators protected by chiral and mirror symmetries. Using models in the BDI class, which include the prototypical topological quadrupole insulator, we show that breaking mirror symmetries that anticommute with the chiral operator leads to edge-selective bulk-boundary correspondence, with gap closings and bound states appearing only at a subset of boundaries of the same orientation. We define a new edge-sensitive topological invariant, distinguishing this mechanism from previous reports of non-topological edge-selection effects.