Hyperbolic Topological Band Insulators

Abstract

Recently, hyperbolic lattices that tile the negatively curved hyperbolic plane emerged as a new paradigm of synthetic matter, and their energy levels were characterized by a band structure in a four- (or higher-)dimensional momentum space. To explore the uncharted topological aspects arising in hyperbolic band theory, we here introduce elementary models of hyperbolic topological band insulators: the hyperbolic Haldane model and the hyperbolic Kane-Mele model; both obtained by replacing the hexagonal cells of their Euclidean counterparts by octagons. Their non-trivial topology is revealed by computing topological invariants in both position and momentum space. The bulk-boundary correspondence is evidenced by comparing bulk and boundary density of states, by modelling propagation of edge excitations, and by their robustness against disorder.

main text (4 pages incl. 5 figures and 1 table) + references + supplementary material (24 pages incl. 13 figures and 2 tables)

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Cited by in corpus (37)

• Hyperbolic Matter in Electrical Circuits with Tunable Complex Phases
• Hyperbolic band topology with non-trivial second Chern numbers
• Chern insulator in a hyperbolic lattice
• Higher-order topological insulators in hyperbolic lattices
• Higher-order Topological Hyperbolic Lattices
• Hybrid skin-topological effect induced by eight-site cells and arbitrary adjustment of the localization of topological edge states
• Non-Abelian hyperbolic band theory from supercells
• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Density of states of tight-binding models in the hyperbolic plane
• Symmetry and topology of hyperbolic Haldane models
• Hybrid higher-order skin-topological effect in hyperbolic lattices
• Anderson localization transition in disordered hyperbolic lattices
• Hyperbolic non-Abelian semimetal
• Simulating Holographic Conformal Field Theories on Hyperbolic Lattices
• Converging Periodic Boundary Conditions and Detection of Topological Gaps on Regular Hyperbolic Tessellations
• Engineering topological states and quantum-inspired information processing using classical circuits
• Colloquium: Synthetic quantum matter in non-standard geometries
• Topological linear response of hyperbolic Chern insulators
• Hyperbolic Fractional Chern insulators
• Anderson transition and mobility edges on hyperbolic lattices with randomly connected boundaries
• Hyperbolic lattices and two-dimensional Yang-Mills theory
• Kitaev model on Hurwitz hyperbolic tilings: A non-Abelian gapped chiral spin liquid
• Hyperbolic Spin Liquids
• Non-Hermitian Skin Effect Along Hyperbolic Geodesics
• Chiral Gapless Spin Liquid in Hyperbolic Space
• Hubbard and Heisenberg models on hyperbolic lattices: Metal-insulator transitions, global antiferromagnetism, and enhanced boundary fluctuations
• Geometrically frustrated self-assembly of hyperbolic crystals from icosahedral nanoparticles
• Quantum geometric tensors from sub-bundle geometry
• Uncovering Exceptional Contours in non-Hermitian Hyperbolic Matter
• Hyperbolic Continuous Topological Transition in Real Space
• Tunable cornerlike states in topological type-II hyperbolic lattices
• Tessellation codes: encoded quantum gates by geometric rotation
• Entanglement scaling behaviors of free fermions on hyperbolic lattices
• Topological states and flat bands in exactly solvable decorated Cayley trees
• Discrete holography and density of states in the crossover from hyperbolic to Euclidean lattices
• Hofstadter's Butterfly in AdS${}_3$ Black Holes
• Temperature-Dependent Collective Excitations in a Three-Dimensional Dirac System ZrTe${}_5$