  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.
