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 ${\mathbb{Z}}_2$ invariant for a 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 nontrivial to a topologically trivial ($\mathrm{N}\to \mathrm{T}$) phase or from a trivial to nontrivial phase ($\mathrm{T}\to \mathrm{N}$). Remarkably, in certain parameter regimes, the system exhibits a re-entrant behavior: A topologically nontrivial 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 ($\mathrm{N}\to \mathrm{T}\to \mathrm{N}$). We corroborate these findings through analysis of the bulk-boundary correspondence and transport calculations.

Close

PrevNext

View figure in article

• Phase diagrams
• Quantum spin Hall effect
• Disordered systems
• Topological insulators