Hyperbolic band topology with non-trivial second Chern numbers

Abstract

Topological band theory establishes a standardized framework for classifying different types of topological matters. Recent investigations have shown that hyperbolic lattices in non-Euclidean space can also be characterized by hyperbolic Bloch theorem. This theory promotes the investigation of hyperbolic band topology, where hyperbolic topological band insulators protected by first Chern numbers have been proposed. Here, we report a new finding on the construction of hyperbolic topological band insulators with a vanished first Chern number but a non-trivial second Chern number. Our model possesses the non-abelian translational symmetry of {8,8} hyperbolic tiling. By engineering intercell couplings and onsite potentials of sublattices in each unit cell, the non-trivial bandgaps with quantized second Chern numbers can appear. In experiments, we fabricate two types of finite hyperbolic circuit networks with periodic boundary conditions and partially open boundary conditions to detect hyperbolic topological band insulators. Our work suggests a new way to engineer hyperbolic topological states with higher-order topological invariants.

References in corpus (8)

• Topological Acoustics
• Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
• Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
• Topological properties of linear circuit lattices
• Observation of novel topological states in hyperbolic lattices
• Hyperbolic Matter in Electrical Circuits with Tunable Complex Phases
• Hyperbolic Topological Band Insulators
• Band theory and boundary modes of high-dimensional representations of infinite hyperbolic lattices

Cited by in corpus (28)

• Non-Abelian inverse Anderson transitions
• Non-Abelian hyperbolic band theory from supercells
• 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
• Observation of Large-Number Corner Modes in $\mathbb{Z}$-class Higher-Order Topolectrical Circuits
• Converging Periodic Boundary Conditions and Detection of Topological Gaps on Regular Hyperbolic Tessellations
• A brief review of hybrid skin-topological effect
• Engineering topological states and quantum-inspired information processing using classical circuits
• Topological linear response of hyperbolic Chern insulators
• Colloquium: Synthetic quantum matter in non-standard geometries
• Hyperbolic Fractional Chern insulators
• Observation of Impurity-Induced Scale-Free Localization in a Disordered Non-Hermitian Electrical Circuit
• Anderson transition and mobility edges on hyperbolic lattices with randomly connected boundaries
• Hyperbolic lattices and two-dimensional Yang-Mills theory
• Hyperbolic Spin Liquids
• Non-Hermitian Skin Effect Along Hyperbolic Geodesics
• Eigenmodes of the Laplacian on Hyperbolic Lattices
• Four-dimensional Floquet topological insulator with an emergent second Chern number
• Flow of unitary matrices: Real-space winding numbers in one and three dimensions
• Localization renormalization and quantum Hall systems
• Hyperbolic Continuous Topological Transition in Real Space
• Real-space representation of the second Chern number
• Tunable cornerlike states in topological type-II hyperbolic lattices
• Discrete holography and density of states in the crossover from hyperbolic to Euclidean lattices
• Temperature-Dependent Collective Excitations in a Three-Dimensional Dirac System ZrTe${}_5$