Successive phase transition in higher-order topological Anderson insulators

Disorder, traditionally believed to hinder the propagation of waves, has recently been shown to prompt the occurrence of topological phase transitions. For example, when disorder strength continuously increases and surpasses a certain critical value, a transition from topologically trivial to nontrivial insulating phases can occur. However, in the nontrivial phase region, it remains unclear whether a finer phase diagram can be further classified by varying disorder strengths. Here, we present a successive topological phase transition driven by the disorder strength in a higher-order topological insulator with long-range couplings. As the disorder strength gradually increases, the real-space topological invariant of the system undergoes a consecutive change from 0 to 4, accompanied by a stepped increase in the number of boundary-localized corner states. Our work opens a pathway for utilizing disorder to induce phase transitions among different higher-order topological insulators.