Hyperbolic Matter in Electrical Circuits with Tunable Complex Phases

Abstract

Curved spaces play a fundamental role in many areas of modern physics, from cosmological length scales to subatomic structures related to quantum information and quantum gravity. 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 through topolectrical circuit networks relying on a complex-phase circuit element. The experiment is based on hyperbolic band theory that we confirm here in an unprecedented numerical survey of finite hyperbolic lattices. We implement hyperbolic graphene as an example of topologically nontrivial hyperbolic matter. Our work sets the stage to realize more complex forms of hyperbolic matter to challenge our established theories of physics in curved space, while the tunable complex-phase element developed here can be a key ingredient for future experimental simulation of various Hamiltonians with topological ground states.

6 pages + methods + supplementary information

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• Chiral tunneling and the Klein paradox in graphene
• Photovoltaic Hall effect in graphene
• Microwave photonics with superconducting quantum circuits
• Fiber-optical analogue of the event horizon
• Topological nodal line semimetals
• Topological properties of linear circuit lattices
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• Hyperbolic Topological Band Insulators
• Chern insulator in a hyperbolic lattice
• Universality of Hofstadter butterflies on hyperbolic lattices
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Cited by in corpus (40)

• Hyperbolic band topology with non-trivial second Chern numbers
• Non-Abelian inverse Anderson transitions
• Higher-order topological insulators in hyperbolic lattices
• Higher-order Topological Hyperbolic Lattices
• Non-Abelian hyperbolic band theory from supercells
• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Symmetry and topology of hyperbolic Haldane models
• Density of states of tight-binding models in the hyperbolic plane
• 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
• Aperiodic spin chains at the boundary of hyperbolic tilings
• Engineering non-Hermitian Second Order Topological Insulator in Quasicrystals
• 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
• Magnetic Flux Response of Non-Hermitian Topological Phases
• Eigenmodes of the Laplacian on Hyperbolic Lattices
• Hyperbolic Spin Liquids
• Non-Hermitian Skin Effect Along Hyperbolic Geodesics
• Kitaev model on Hurwitz hyperbolic tilings: A non-Abelian gapped chiral spin liquid
• Four-dimensional Floquet topological insulator with an emergent second Chern number
• Chiral Gapless Spin Liquid in Hyperbolic Space
• Hubbard and Heisenberg models on hyperbolic lattices: Metal-insulator transitions, global antiferromagnetism, and enhanced boundary fluctuations
• Wormhole-induced effective coupling in SYK chains
• Random-Flux-Induced Transition Sequence between Weak and Strong Topological Phases with Anisotropic Localization Properties
• Unveiling Non-Hermitian Spectral Topology in Hyperbolic Lattices with Non-Abelian Translation Symmetry
• Uncovering Exceptional Contours in non-Hermitian Hyperbolic Matter
• Quantum geometric tensors from sub-bundle geometry
• Tessellation codes: encoded quantum gates by geometric rotation
• Tunable cornerlike states in topological type-II hyperbolic lattices
• Qubits on programmable geometries with a trapped-ion quantum processor
• Hofstadter's Butterfly in AdS${}_3$ Black Holes
• Discrete holography and density of states in the crossover from hyperbolic to Euclidean lattices