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Topological Hyperbolic Lattices

Cited 38 time in Web of Science Cited 40 time in Scopus

Yu, Sunkyu; Piao, Xianji; Park, Namkyoo

Issue Date
American Physical Society
Physical Review Letters, Vol.125 No.5, p. 053901
Non-Euclidean geometry, discovered by negating Euclid's parallel postulate, has been of considerable interest in mathematics and related fields for the description of geographical coordinates, Internet infrastructures, and the general theory of relativity. Notably, an infinite number of regular tessellations in hyperbolic geometry-hyperbolic lattices-are expected to extend Euclidean Bravais lattices and the consequent wave phenomena to non-Euclidean geometry. However, topological states of matter in hyperbolic lattices have yet to be reported. Here we investigate topological phenomena in hyperbolic geometry, exploring how the quantized curvature and edge dominance of the geometry affect topological phases. We report a recipe for the construction of a Euclidean photonic platform that inherits the topological band properties of a hyperbolic lattice under a uniform, pseudospin-dependent magnetic field, realizing a non-Euclidean analog of the quantum spin Hall effect. For hyperbolic lattices with different quantized curvatures, we examine the topological protection of helical edge states and generalize Hofstadter's butterfly, by employing two empirical parameters that measure the edge confinement and defect immunity. We demonstrate that the proposed platforms exhibit the unique spectral-magnetic sensitivity of topological immunity in highly curved hyperbolic planes. Our approach is applicable to general non-Euclidean geometry and enables the exploitation of infinite lattice degrees of freedom for band theory.
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  • College of Engineering
  • Department of Electrical and Computer Engineering
Research Area Disordered, Open-System Wave Mechanics, Photonic AI Systems, Photonic Neuromorphic Devices, 광학 뉴로모픽 소자, 광학 인공지능 시스템, 무질서, 열린계 파동역학


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