Disorder and phase diagrams of higher-order topological insulators

In this work, we study the disorder effects on bulk-boundary correspondence of two-dimensional higher-order topological insulators (HOTIs). We concentrate two cases: (i) bulk-corner correspondence, (ii) edge-corner correspondence. For case, demonstrate existence mobility gaps and clarify related invariant that characterizes gap. Furthermore, find that, while system preserves in presence disorder, corner states are protected by gap instead bulk show edge band HOTIs no longer closed simultaneously. Therefore, a rich phase diagram is obtained, including various disorder-induced transition processes. Notably, from non-trivial to trivial realized, distinguishing other states. Our results deepen understanding enrich transitions disordered HOTIs.