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arXiv · 2601.06963

Tunable cornerlike states in topological type-II hyperbolic lattices

Zheng-Rong Liu·Tan Peng·Xiang Liu·Xiao-Xia Yi·Chun-Bo Hua·Rui Chen·Bin Zhou
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Abstract

Type-II hyperbolic lattices constitute a new class of hyperbolic structures that are projected onto the Poincar\'{e} 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.

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Zheng-Rong Liu, Tan Peng, Xiang Liu, Xiao-Xia Yi, Chun-Bo Hua, Rui Chen, Bin Zhou. 2026-01-11. Tunable cornerlike states in topological type-II hyperbolic lattices. https://doi.org/10.1103/p26g-wscd

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