Third-order topological insulator induced by disorder

We have found the first instance of a third-order topological Anderson insulator (TOTAI). This disorder-induced topological phase is gapped and characterized by a quantized octupole moment and topologically protected corner states, as revealed by a detailed numerically exact analysis. We also find that the disorder-induced transition into the TOTAI phase can be analytically captured with remarkable accuracy using the self-consistent Born approximation. For a larger disorder strength, the TOTAI undergoes a transition to a trivial diffusive metal that in turn becomes an Anderson insulator at even larger disorder. Our findings show that disorder can induce third-order topological phases in three dimensions, therefore extending the class of known higher-order topological Anderson insulators.