Circuit Implementation of a Four-Dimensional Topological Insulator

Abstract

The classification of topological insulators predicts the existence of high-dimensional topological phases that cannot occur in real materials, as these are limited to three or fewer spatial dimensions. We use electric circuits to experimentally implement a four-dimensional (4D) topological lattice. The lattice dimensionality is established by circuit connections, and not by mapping to a lower-dimensional system. On the lattice's three-dimensional surface, we observe topological surface states that are associated with a nonzero second Chern number but vanishing first Chern numbers. The 4D lattice belongs to symmetry class AI, which refers to time-reversal-invariant and spinless systems with no special spatial symmetry. Class AI is topologically trivial in one to three spatial dimensions, so 4D is the lowest possible dimension for achieving a topological insulator in this class. This work paves the way to the use of electric circuits for exploring high-dimensional topological models.

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Cited by in corpus (71)

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• Experimental Observation of Higher-Order Topological Anderson Insulators
• Topological defect engineering and PT-symmetry in non-Hermitian electrical circuits
• Topolectric circuits: Theory and construction
• Observation of novel topological states in hyperbolic lattices
• Topological insulators and semimetals in classical magnetic systems
• Non-abelian gauge fields in circuit systems
• Hyperbolic band topology with non-trivial second Chern numbers
• Observation of Antichiral Edge States in a Circuit Lattice
• Ideal type-II Weyl points in topological circuits
• Realization of a Hopf insulator in circuit systems
• Non-Abelian inverse Anderson transitions
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• A comprehensive review on developments of synthetic dimensions
• Zoology of non-Hermitian spectra and their graph topology
• Higher-order topological states mediated by long-range coupling in $D_4$-symmetric lattices
• Demonstration of acoustic high-order Stiefel-Whitney semimetal in bilayer graphene sonic crystals
• Experimental observation of non-Hermitian higher-order skin interface states in topological electric circuits
• Symmetry and topology of hyperbolic Haldane models
• Custodial chiral symmetry in a Su-Schrieffer-Heeger electrical circuit with memory
• Experimental realization of two-dimensional weak topological insulators
• Second Chern crystals in four-dimensional synthetic translation space with inherently nontrivial topology
• Four-dimensional semimetals with tensor monopoles: From surface states to topological responses
• Impedance responses and size-dependent resonances in topolectrical circuits via the method of images
• Observation of Large-Number Corner Modes in $\mathbb{Z}$-class Higher-Order Topolectrical Circuits
• Realization of an atomic quantum Hall system in four dimensions
• Observation of higher-order topological states on a quantum computer
• Non-Abelian tensor Berry connections in multi-band topological systems
• Dissipative analog of four-dimensional quantum Hall physics
• Observation of inverse Anderson transitions in Aharonov-Bohm topolectrical circuits
• Anomalous fractal scaling in two-dimensional electric networks
• Cooper-pair transistor as a minimal topological quantum circuit
• Observation of flat-band localization and topological edge states induced by effective strong interactions in electrical circuit networks
• Four-dimensional topological lattices through connectivity
• Revealing Chern number from quantum metric
• Exploring topological phase transition andWeyl physics in five dimensions with electric circuits
• Non-Hermitian Dirac cones with valley-dependent lifetimes
• Moiré circuits: engineering magic-angle behaviors
• Engineering topological states and quantum-inspired information processing using classical circuits
• Topolectrical-circuit realization of quadrupolar surface semimetals
• Colloquium: Synthetic quantum matter in non-standard geometries
• Revealing the boundary Weyl physics of the four-dimensional Hall effect via phason engineering in metamaterials
• Superfluid Vortices in Four Spatial Dimensions
• Two-point spectroscopy of Fibonacci topoelectrical circuits
• Zeros of Green Functions in Topological Insulators
• Electric circuit emulation of topological transitions driven by quantum statistics
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• Four-dimensional Floquet topological insulator with an emergent second Chern number
• $SO(5)$ Landau Model and 4D Quantum Hall Effect in The $SO(4)$ Monopole Background
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• Topological Insulators with Hybrid-order Boundary States
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• Tensor Theory for Higher Dimensional Chern Insulators with Large Chern Numbers
• Evaluation of real-space second Chern number using the kernel polynomial method
• Topological Phases in Non-Hermitian Nonlinear-Eigenvalue Systems
• Liouville Fock state lattices and potential simulators
• Higher-dimensional magnetic Skyrmions
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• Compact localized currents in flat bands with broken time-reversal symmetry
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