Title: Successive Phase Transition in Higher-order Topological Anderson Insulators

Abstract: 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 certain critical value, a phase transition from topologically trivial to nontrivial insulating phases occurs. However, in the parameter domain of the nontrivial phase, whether there exists a finer phase diagram that can be further classified by different disorder strengths is still unclear. 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 strength of the disorder gradually increases, the real-space topological invariant of the system undergoes a consecutive change from 0 to 4, accompanied by the stepped increase in the number of boundary-localized corner states. Our work opens an avenue for utilizing disorder to induce phase transitions among different higher-order topological insulators.