4D spinless topological insulator in a periodic electric circuit

Abstract

According to the mathematical classification of topological band structures, there exist a number of fascinating topological states in dimensions larger than three with exotic boundary phenomena and interesting topological responses. While these topological states are not accessible in condensed matter systems, recent works have shown that synthetic systems, such as photonic crystals or electric circuits, can realize higher-dimensional band structures. Here, we argue that the 4D spinless topological insulator, due to its symmetry properties, is particularly well suited to be implemented in these synthetic systems. We explicitly construct a 2D electric circuit lattice, whose resonance frequency spectrum simulate the 4D spinless topological insulator. We perform detailed numerical calculations of the circuit lattice and show that the resonance frequency spectrum exhibit pairs of 3D Weyl boundary states, a hallmark of the nontrivial topology. These pairs of 3D Weyl states with the same chirality are protected by classical time-reversal symmetry that squares to $+1$, which is inherent in the proposed circuit lattice. We also discuss how the simulated 4D topological band structure can be observed in experiments.

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• Non-abelian gauge fields in circuit systems
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• Square-root higher-order Weyl semimetals
• ${\mathbb{Z}}_2$-projective translational symmetry protected topological phases
• Observation of Antichiral Edge States in a Circuit Lattice
• Switching spinless and spinful topological phases with projective $PT$ symmetry
• Brillouin Klein Bottle From Artificial Gauge Fields
• Observation of symmetry protected zero modes in topolectrical circuits
• Ideal type-II Weyl points in topological circuits
• Realization of a Hopf insulator in circuit systems
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• Classification of time-reversal-invariant crystals with gauge structures
• Experimental observation of non-Hermitian higher-order skin interface states in topological electric circuits
• Second Chern crystals in four-dimensional synthetic translation space with inherently nontrivial topology
• General Theory of Momentum-Space Nonsymmorphic Symmetry
• Symmetry-enforced topological band crossings in orthorhombic crystals: Classification and materials discovery
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• Four-dimensional topological lattices through connectivity
• Revealing Chern number from quantum metric
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• Moiré circuits: engineering magic-angle behaviors
• Generalization of Benalcazar-Bernevig-Hughes model to arbitrary dimensions
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• Colloquium: Synthetic quantum matter in non-standard geometries
• Superfluid Vortices in Four Spatial Dimensions
• Engineering second-order nodal-line semimetals by breaking $\mathcal{P}\mathcal{T}$ symmetry and periodic driving
• Observation of non-local impedance response in a passive electrical circuit
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• A semiclassical treatment of spinor topological effects in driven, inhomogeneous insulators under external electromagnetic fields
• Exact Solutions of D-dimensional Klein-Gordon Oscillator with Snyder-de Sitter Algebra
• Four-dimensional Floquet topological insulator with an emergent second Chern number
• Topological Insulators with Hybrid-order Boundary States
• Upper bound of a band complex
• Takagi topological insulator with odd $\mathcal{P}\mathcal{T}$ pairs of corner states
• Quantum Transports in Two-Dimensions with Long Range Hopping: Shielding, Localization and the Extended Isolated State
• Second Euler number in four dimensional synthetic matter
• Unconventional hybrid-order topological insulators
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• Takagi Topological Insulator on the Honeycomb Lattice
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• Brillouin Platycosms and Topological Phases
• Projective Spacetime Symmetry of Spacetime Crystals
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• Exact solutions of Kondo problems in higher-order fermions
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