Bulk-boundary correspondence in disordered higher-order topological insulators

TL;DR

This paper investigates how disorder affects the bulk-boundary correspondence in two-dimensional higher-order topological insulators, revealing disorder-induced phase transitions and the role of mobility gaps in protecting corner states.

Contribution

It provides a detailed analysis of disorder effects on HOTIs, introducing the concept of mobility gap protection and mapping out a rich phase diagram with disorder-induced phase transitions.

Findings

Corner states protected by mobility gap, not bulk gap

Disorder induces phase transitions, including from non-trivial to trivial phases

Bulk and edge gaps do not close simultaneously under disorder

Abstract

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