Topolectrical circuit realization of topological corner modes

Abstract

Quantized electric quadrupole insulators have recently been proposed as novel quantum states of matter in two spatial dimensions. Gapped otherwise, they can feature zero-dimensional topological corner mid-gap states protected by the bulk spectral gap, reflection symmetries and a spectral symmetry. Here we introduce a topolectrical circuit design for realizing such corner modes experimentally and report measurements in which the modes appear as topological boundary resonances in the corner impedance profile of the circuit. Whereas the quantized bulk quadrupole moment of an electronic crystal does not have a direct analogue in the classical topolectrical-circuit framework, the corner modes inherit the identical form from the quantum case. Due to the flexibility and tunability of electrical circuits, they are an ideal platform for studying the reflection symmetry-protected character of corner modes in detail. Our work therefore establishes an instance where topolectrical circuitry is employed to bridge the gap between quantum theoretical modelling and the experimental realization of topological band structures.

12 pages, 7 figures

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• Dirac cones and higher-order topology in quasi-continuous media
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• Dynamical signatures of point-gap Weyl semimetal
• Existence of a negative next-nearest-neighbor coupling in evanescently coupled dielectric waveguides
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• A General Method to Design Acoustic Higher-Order Topological Insulators
• Electrical analogue of one-dimensional and quasi-one-dimensional Aubry-André-Harper lattices
• Third-order topological insulator induced by disorder
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• Two-dimensional non-Hermitian topological phases induced by asymmetric hopping in a one-dimensional superlattice
• Dynamical Detection of Topological Spectral Density
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• Evolution of spectral topology in one-dimensional long-range nonreciprocal lattices
• Exceptional Non-Hermitian Phases in Disordered Quantum Wires
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• Corner Charge Fluctuation as an Observable for Quantum Geometry and Entanglement in Two-dimensional Insulators
• Multiple higher-order topological phases with even and odd pairs of zero-energy corner modes in a $C_3$ symmetry broken model
• Topological quantum transition driven by charge-phonon coupling in higher-order topological insulators
• Hinge Modes and Surface States in Second-Order Topological Three-Dimensional Quantum Hall Systems induced by Charge Density Modulation
• Time-reversal invariant finite-size topology
• Generation of twisted magnons via spin-to-orbital angular momentum conversion
• Terahertz Magnetospectroscopy of Cyclotron Resonances from Topological Surface States in Thick Films of Cd${}_x$Hg${}_{1-x}$Te
• Time evolution of Majorana corner modes in Floquet second-order topological superconductor
• Thermodynamic electric quadrupole moments of nematic phases from first-principles calculation
• Network model for higher-order topological phases
• Mesoscopic transport signatures of disorder-induced non-Hermitian phases
• Protection of all nondefective twofold degeneracies by anti-unitary symmetries in non-Hermitian systems
• Qubit-photon corner states in all dimensions
• Electric Circuit Realizations of Fracton Physics
• Out of equilibrium chiral higher order topological insulator on a $\pi$-flux square lattice
• Simulating Floquet topological phases in static systems
• Wannier Topology and Quadrupole Moments for a generalized Benalcazar-Bernevig-Hughes Model
• Periodic Clifford symmetry algebras on flux lattices
• Dynamically Induced Exceptional Phases in Quenched Interacting Semimetals
• Third-order topological insulator in three-dimensional lattice of magnetic vortices
• Quantum Monte Carlo study of topological phases on a spin analogue of Benalcazar-Bernevig-Hughes model
• Experimental observation of edge-dependent quantum pseudospin Hall effect
• Multi-Dimensional Quantum Walks: a Playground of Dirac and Schrödinger Particles
• Rotoinversion-symmetric bulk-hinge correspondence and its applications to higher-order Weyl semimetals
• Higher-order topological phase of interacting photon pairs
• Revealing the spatial nature of sublattice symmetry
• Supersymmetry on the lattice: Geometry, Topology, and Flat Bands
• Higher-order topological insulator in a modified Haldane-Hubbard model
• Observation of Flat Frequency Bands at Open Edges and Antiphase Boundary Seams in Topological Mechanical Metamaterials
• Floquet higher-order topological phases in momentum space
• Wannier band transitions in disordered $\pi$-flux ladders
• Versatile Control of Nonlinear Topological States in Non-Hermitian Systems
• Universal quantum gates, artificial neurons and pattern recognition simulated by \textit{LC} resonators
• A semiclassical treatment of spinor topological effects in driven, inhomogeneous insulators under external electromagnetic fields
• Parity-time symmetric systems with memory
• Realizing Corner States in Artificial Crystals Based on Topological Spin Textures
• Crystalline-electromagnetic responses of higher order topological semimetals
• Non-Hermitian Quantum Fractals
• Nonlinear topological phase diagram in dimerized sine-Gordon model
• Ground state topology of a four-terminal superconducting double quantum dot
• Topological Wannier cycles for the bulk and edges
• Effect of local Coulomb interaction on Majorana corner modes: weak and strong correlation limits
• Switchable Non-Hermitian Skin Effect in Bogoliubov Modes
• Topological Classical Systems with Generalized Chiral Symmetry
• Implementing non-Abelian Hatano-Nelson model in electric circuits
• Observing the nodal-line conversion determined by the relative homotopy
• Spin-Dependent High-Order Topological Insulator and Two Types of Distinct Corner Modes in Monolayer FeSe/GdClO Heterostructure
• Thermodynamics of a Higher-Order Topological Insulator
• Topological Modes Protected by Chiral and Two-Fold Rotational Symmetry in a Spring-Mass Model with a Lieb Lattice Structure
• Fractional second-order topological insulator from a three-dimensional coupled-wires construction
• Electric polarization and its quantization in one-dimensional non-Hermitian chains
• Creation of electrical knots and observation of DNA topology
• Remote control of spin polarization of topological corner states
• Floquet topological insulators with hybrid edges
• Emergent metallicity at the grain boundaries of higher-order topological insulators
• Higher-order topology in twisted multilayer systems: a review
• Engineering rich two-dimensional higher-order topological phases by flux and periodic driving
• A topological classification of molecules and chemical reactions with a perplectic structure
• Upper bound of a band complex
• Memristive Ising Circuits
• Hierarchical Topological States in Thermal Diffusive Networks
• Non-reciprocity is necessary for robust dimensional reduction and strong responses in stochastic topological systems
• Fermionic tensor networks for higher order topological insulators from charge pumping
• Second-order topological insulator in a coinless discrete-time quantum walk
• Higher-order topology and corner triplon excitations in two-dimensional quantum spin-dimer models
• Takagi topological insulator with odd $\mathcal{P}\mathcal{T}$ pairs of corner states
• Boundary-driven many-body phase transitions in a non-Hermitian disordered fermionic chain
• Topological Corner States in Bilayer and Trilayer Systems with Vertically Stacked Topological Heterostructures
• Projective symmetry determined topology in flux Su-Schrieffer-Heeger model
• Topological electronic states in holey graphyne
• Magnetic impurities along the edge of a quantum spin Hall insulator: Realizing a one-dimensional AIII insulator
• Family of third-order topological insulators from Su-Schrieffer-Heeger stacking
• Higher-order topological superconductor phases in a multilayer system
• Observation of edge solitons and transitions between them in a trimer circuit lattice
• Magnetless Circulators Based on Synthetic Angular-Momentum Bias: Recent Advances and Applications
• Effects of first- and second-order topological phases on equilibrium crystal shapes
• Encyclopedia of emergent particles in three-dimensional crystals
• Distinguishing trivial and topological quadrupolar insulators by Wannier-Stark ladders
• Topological reflection matrix
• Second-order topology and supersymmetry in two-dimensional topological insulators
• Additive rule of real and reciprocal space topologies at disclinations
• Mixed higher-order topology and nodal and nodeless flat band topological phases in a superconducting multiorbital model
• Symmetry induced selective excitation of topological states in SSH waveguide arrays
• Second-order topological insulator in periodically driven lattice
• Majorana corner states in square and Kagome quantum spin liquids
• Bulk-boundary correspondence in topological systems with the momentum dependent energy shift
• Recipe for higher-order topology on the triangular lattice
• External control of qubit-photon interaction and multi-qubit reset in a dissipative quantum network
• Time-reversal invariant topological skyrmion phases
• Higher-order topology in honeycomb lattice with Y-Kekulé distortions
• Topological characteristics of gap closing points in nonlinear Weyl semimetals
• Higher-Order Topological Systems and Their Sub-Symmetry-Protected Topology
• Tunable corner states in topological insulators with long-range hoppings and diverse shapes
• Projective Spacetime Symmetry of Spacetime Crystals
• Tunable symmetry-protected higher-order topological states with fermionic atoms in bilayer optical lattices
• Brillouin Platycosms and Topological Phases
• Synthetic plasmonic lattice formation through invariant frequency comb excitation in graphene structures
• Realization of a three-dimensional quantum Hall effect in a Zeeman-induced second order topological insulator on a torus
• Mirror-symmetry protected higher-order topological zero-frequency boundary and corner modes in Maxwell lattices
• Topological Micro-Electro-Mechanical Systems
• Topological parafermion corner states in clock-symmetric non-Hermitian second-order topological insulator
• Reentrant quantum spin Hall effect in the presence of an exchange field
• Topological Computation by non-Abelian Braiding in Classical Metamaterials
• Takagi Topological Insulator on the Honeycomb Lattice
• Perfectly localized Majorana corner modes in fermionic lattices
• Observation of Embedded Topology in a Trivial Bulk via Projective Crystal Symmetry
• Quasiperiodic Quadrupole Insulators
• Chiral topological phases in designed mechanical networks
• Exploring Thouless Pumping in the Generalized Creutz Model: A Graphical Method and Modulation Schemes
• Spin separation and filtering assisted by topological corner states in the Kekulé lattice
• Nonlinear quadrupole topological insulators
• Arboreal Obstructed Atomic Insulating and Metallic Phases of Fermions
• Unveiling Topological Hinge States in the Higher-Order Topological Insulator WTe${}_2$ Based on the Fractional Josephson Effect
• Experimental observation of phase transitions of a deformed Dicke model using a reconfigurable, bi-parametric electronic platform
• Tunable cornerlike states in topological type-II hyperbolic lattices
• Obstructed Atomic Insulators and Superfluids of Fermions Coupled to ${\mathbb{Z}}_2$ Gauge Fields
• Electric circuit analog of Landau-Zener tunneling using time-varying elements
• Nonlinearity-induced corner states in a kagome lattice
• Nonlinear dynamical topological phases in Cooper-pair box array
• Fractional chiral second-order topological insulator from a three-dimensional array of coupled wires
• Gapless States Localized along a Staircase Edge in Second-Order Topological Insulators
• Extended Haldane model -- a modern gateway to topological insulators
• Anomalous gapped boundaries between surface topological orders in higher-order topological insulators and superconductors with inversion symmetry
• Fragile dislocation modes in obstructed atomic topological phases
• Quantum-vacuum-protected topological edge polaritons
• Topological defects in a double-mirror quadrupole insulator displace diverging charge
• Topological Photonics on a Small Scale
• Crystalline Weyl semimetal phase in Quantum Spin Hall systems under magnetic fields
• Asymmetric real topology of conduction and valence bands
• Hinge modes of three-dimensional Euler insulators
• Higher-order topological insulator in cubic semiconductor quantum wells
• Projected branes as platforms for crystalline, superconducting, and higher-order topological phases
• Magnetic-Field Tunable Möbius and Higher-Order Topological Insulators in Three-Dimensional Layered Octagonal Quasicrystals
• Interacting many-body non-Hermitian systems as Markov chains
• Graphyne as a second-order and real Chern topological insulator in two dimensions
• Three-dimensional higher-order topological insulator protected by cubic symmetry
• Line defects in infinite networks of resistors
• One-dimensional topology and topolectrics of nonsymmorphic Kramers degenerate systems
• Multiterminal Josephson junctions with tunable topological properties
• Arbitrary Control of Non-Hermitian Skin Modes via Disorder and An Electric Field
• Higher-order topological quantum paramagnets
• Topological states and flat bands in exactly solvable decorated Cayley trees
• Non-Hermitian physics and topological phenomena in convective thermal metamaterials
• Observing complementary Lucas sequences using non-Hermitian zero modes
• Engineering the Bogoliubov Modes through Geometry and Interaction: From Collective Edge Modes to Flat-band Excitations
• Anti-higher-order Weyl semimetal
• Wilson loop invariants and bulk-boundary correspondence in higher-order topological insulators with two anticommuting mirror symmetries
• Proposal for realizing and probing topological crystalline insulators in optical lattices
• Dynamics of 2D topological quadrupole insulator and Chern insulator induced by real-space topological changes
• Application of Jordan Decomposition to Non-Hermitian Lattice Models with Spectrally-Isolated Lower Dimensional States
• Nonlinear Anderson localization in Toda lattices
• Non-Hermitian Higher-Order Dirac Semimetals
• Non-Hermitian Higher-Order Weyl Semimetals
• Triply-degenerate point in three-dimensional spinless systems