Tunable cornerlike states in topological type-II hyperbolic lattices
Phys. Rev. B 113, 205301 – Published 1 May, 2026
DOI: https://doi.org/10.1103/p26g-wscd
Abstract
Type-II hyperbolic lattices constitute a new class of hyperbolic structures that are projected onto the Poincaré ring and possess both an inner and an outer boundary. In this work we reveal the higher-order topological phases in type-II hyperbolic lattices, characterized by the generalized quadrupole moment. Unlike the type-I hyperbolic lattices where zero-energy cornerlike states exist on a single boundary, the higher-order topological phases in type-II hyperbolic lattices possess zero-energy cornerlike states localized on both the inner and outer boundaries. These findings are verified within both the modified Bernevig-Hughes-Zhang model and the Benalcazar-Bernevig-Hughes model. Furthermore, we demonstrate that the higher-order topological phase remains robust against weak disorder in type-II hyperbolic lattices. Our work provides a route for realizing and controlling higher-order topological states in type-II hyperbolic lattices.
