Disordered intrinsic higher-order topological insulators

Higher order topological insulators are a novel phase of matter in which topologically protected modes appear at corners or hinges rather than surfaces. Unlike conventional topological insulators, higher-order topological insulators can be protected by either a bulk gap or a Wannier gap. Here, we study disordered models of higher-order topological insulators whose topological modes are protected by internal symmetries and a Wannier gap. Like conventional topological insulators, we find that the topological modes are stable against weak disorder. However, we also find that increasing disorder leads to a transition to a trivial state without the mobility gap closing, in striking contrast to the case of conventional disordered topological insulators, in which topological transitions only occur at mobility gap closings. Instead, the topological transition occurs during a real-space Wannier gap closing.