Dynamic transfer of chiral edge states in topological type-II hyperbolic lattices

The discovery of hyperbolic lattice, a discretized regularization of non-Euclidean space with constant negative curvature, has provided an unprecedented platform to extend topological phases of matter from Euclidean to non-Euclidean spaces. To date, however, all previous hyperbolic topological states are limited to conventional type-I hyperbolic lattice with a single edge, leaving the dynamic transfer of hyperbolic topological states between different edges completely unresolved. Here, by extending the hyperbolic topological physics from the conventional type-I hyperbolic lattices to the newfangled type-II hyperbolic lattices, we report the type-II hyperbolic Chern insulator featuring outer and inner chiral edge states and demonstrate their dynamic transfer across the bulk to the opposite edge via two distinct mechanisms: anti-parity-time phase transition and Landau-Zener single-band pumping. Our work lays the foundation for further exploring the dynamic evolution of hyperbolic topological effects, with the final goal of inspiring applications leveraging dynamic manipulations of the hyperbolic topological states.