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Hyperbolic tessellation5/17/2023 ![]() ![]() Since the pioneering discovery of the integer quantum Hall effect in 1980 7, a large number of fascinating quantum phases with distinct topological properties have been successively proposed. Our findings suggest a useful platform to study topological phases beyond Euclidean space, and may have potential applications in the field of high-efficient topological devices, such as topological lasers, with enhanced edge responses.Įxploring novel topological phases of matter is one of the most fascinating research areas in physics 1, 2, 3, 4, 5, 6. These novel topological states are observed in designed hyperbolic circuit networks by measuring site-resolved impedance responses and dynamics of voltage packets. Furthermore, we show that the fractal-like midgap higher-order zero modes appear in deformed hyperbolic lattices, and the number of zero modes increases exponentially with the lattice size. ![]() Based on the extended Haldane model, the boundary-dominated first-order Chern edge state with a nontrivial real-space Chern number is achieved. Here, we demonstrate both in theory and experiment that exotic topological states can exist in engineered hyperbolic lattices with unique properties compared to their Euclidean counterparts. Recently, the experimental realization of the hyperbolic lattice, which is the regular tessellation in non-Euclidean space with a constant negative curvature, has attracted much attention. To date, most of the established topological states have been employed in Euclidean systems. The discovery of novel topological states has served as a major branch in physics and material sciences. ![]()
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