Hyperbolic lattices in circuit quantum electrodynamics | Nature
2019年7月3日 · We present numerical simulations of hyperbolic analogues of the kagome lattice that show unusual densities of states in which a macroscopic number of degenerate eigenstates comprise a...
Phys. Rev. B 105, 125118 (2022) - Crystallography of hyperbolic …
2022年3月15日 · Motivated by recent insights into hyperbolic band theory, we initiate a crystallography of hyperbolic lattices. We show that many hyperbolic lattices feature a hidden crystal structure characterized by unit cells, hyperbolic Bravais lattices, and …
[2105.01087] Crystallography of Hyperbolic Lattices - arXiv.org
2021年5月3日 · Motivated by recent insights into hyperbolic band theory, we initiate a crystallography of hyperbolic lattices. We show that many hyperbolic lattices feature a hidden crystal structure characterized by unit cells, hyperbolic Bravais lattices, and …
Motivated by recent insights into hyperbolic band theory, we initiate a crystallography of hyperbolic lattices. We show that many hyperbolic lattices feature a hidden crystal structure characterized by unit cells, hyperbolic Bravais lattices, and associated symmetry groups.
Phys. Rev. Lett. 125, 053901 (2020) - Topological Hyperbolic Lattices
2020年7月29日 · 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.
Observation of novel topological states in hyperbolic lattices
2022年5月26日 · To illustrate the hyperbolic lattice in the Poincaré disk, we introduce the Schläfli notation {p, q}, which represents a tessellation of the plane by p-sided regular polygons with the ...
Higher-order topological hyperbolic lattices - Physical Review …
2023年5月15日 · A hyperbolic lattice allows for any -fold rotational symmetry, in stark contrast to a two-dimensional crystalline material, where only 2-fold, 3-fold, 4-fold, or 6-fold rotational symmetry is permitted. This unique feature motivates us to ask whether the enriched rotational symmetry in a hyperbolic lattice can lead to any new topological phases ...
Anomalous and Chern topological waves in hyperbolic networks
2024年3月14日 · In this work, we design and demonstrate experimentally a topological hyperbolic lattice in a non-reciprocal scattering wave network, establishing unidirectional channels to induce new and...
Directions in hyperbolic lattices - De Gruyter
2018年7月1日 · It is well known that the orbit of a lattice in hyperbolic n-space is uniformly distributed when projected radially onto the unit sphere. In the present work, we consider the fine-scale statistics of the projected lattice points, and express the limit distributions in terms of random hyperbolic lattices.
Hyperbolic matter in electrical circuits with tunable complex …
2023年2月4日 · In tabletop experiments, negatively curved spaces can be simulated with hyperbolic lattices. Here we introduce and experimentally realize hyperbolic matter as a paradigm for topological states...