Tunable cornerlike states in topological type-II hyperbolic lattices

TL;DR

This paper uncovers higher-order topological phases with zero-energy cornerlike states on both boundaries in type-II hyperbolic lattices, verified through models and robust against weak disorder.

Contribution

It reveals the existence of higher-order topological phases with cornerlike states on both boundaries in type-II hyperbolic lattices, expanding the understanding of topological states in hyperbolic structures.

Findings

Zero-energy cornerlike states exist on both inner and outer boundaries.

Higher-order topological phases are verified in two models.

The topological phase is robust against weak disorder.

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.