Phase diagram of amorphous quantum spin Hall insulators

In light of recent progress in the study of amorphous topological phases, we investigate the effects of structural disorder on the topological properties of a two-dimensional quantum spin Hall insulator modeled by the Bernevig-Hughes-Zhang Hamiltonian. Using a real-space formulation of the Z2 invariant for Dirac-type Hamiltonian, we map out the phase diagram as a function of disorder strength and the mass parameter. Our results reveal that under the influence of structural disorder, a system can either undergo a phase transition from a topologically non-trivial to a topologically trivial phase or from a trivial to non-trivial phase. Remarkably, in certain parameter regimes, the system exhibits a re-entrant behaviour: a topologically non-trivial phase in the perfect lattice undergoes a transition to a trivial state under the influence of weak disorder but re-emerges as the disorder strength is further increased. We corroborate these findings through analysis of the bulk-boundary correspondence and transport calculations.