Topological anderson insulator in type-II hyperbolic lattice

Abstract The discovery of hyperbolic lattices has provided an unprecedented platform to extend topological phases of matter from Euclidean to non-Euclidean spaces. However, to date, most studies on hyperbolic topological states have been limited to type-I hyperbolic lattices, with few reports on type-II configurations. Inspired by the recent experimental realization of topological Anderson insulators and the study of non-Euclidean lattices, we investigate the impact of disorder on a type-II hyperbolic quantum spin Hall insulator (QSHI). Our study demonstrates that the helical edge states of the QSHI phase are robust against weak disorder. Most notably, we find that disorder can induce a phase transition from a trivial phase to a QSHI phase, as confirmed by numerical results based on the real-space spin Bott index B . Finally, by calculating the quantized conductance G and real-space density distributions, we identify this disorder-induced phase as a type-II hyperbolic topological Anderson insulator (HTAI).