Observation of symmetry protected zero modes in topolectrical circuits

Abstract

Higher-order topological insulators are a new class of topological phases of matter, originally conceived for electrons in solids. It has been suggested that ${\mathbb{Z}}_N$ Berry phase (Berry phase quantized into $2\pi /N$) is a useful tool to characterize the symmetry protected topological states, while the experimental evidence is still elusive. Recently, topolectrical circuits have emerged as a simple yet very powerful platform for studying topological physics that are challenging to realize in condensed matter systems. Here, we present the first experimental observation of second-order corner states characterized by ${\mathbb{Z}}_3$ Berry phase in topolectrical circuits. We demonstrate theoretically and experimentally that the localized second-order topological states are protected by a generalized chiral symmetry of tripartite lattices, and they are pinned to "zero energy". By introducing extra capacitors within sublattices in the circuit, we are able to examine the robustness of the zero modes against both chiral-symmetry conserving and breaking disturbances. Our work paves the way for testing exotic topological band theory by electrical-circuit experiments.

arXiv comment6 pages, 5 figures, accepted by Phys. Rev. Research as a Rapid Communication

References in corpus (42)

• Quantized Electric Multipole Insulators
• Higher-Order Topological Insulators
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Topolectrical circuit realization of topological corner modes
• Reflection symmetric second-order topological insulators and superconductors
• Observation of a phononic quadrupole topological insulator
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Acoustic higher-order topological insulator on a Kagome lattice
• Demonstration of a quantized microwave quadrupole insulator with topologically protected corner states
• Quantization of fractional corner charge in $C_n$-symmetric higher-order topological crystalline insulators
• Topolectrical circuits
• Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals
• Direct observation of corner states in second-order topological photonic crystal slabs
• Topological protection of photonic mid-gap cavity modes
• Photonic quadrupole topological phases
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Second-order photonic topological insulator with corner states
• Observation of second-order topological insulators in sonic crystals
• Corner states of light in photonic waveguides
• Second-order topological insulators and superconductors with an order-two crystalline symmetry
• Elastic higher-order topological insulator with topologically protected corner states
• Photonic crystal nanocavity based on a topological corner state
• Robust zero-energy modes in an electronic higher-order topological insulator: the dimerized Kagome lattice
• Realization of an acoustic third-order topological insulator
• Higher-Order Topological Insulators in Quasicrystals
• A fractional corner anomaly reveals higher-order topology
• Observation of Quadrupole Transitions and Edge Mode Topology in an LC network
• Non-linear second-order topological insulators
• Bound states in the continuum of higher-order topological insulators
• Higher-order topological electric circuits and topological corner resonance on the breathing Kagome and pyrochlore lattices
• Topolectrical-circuit octupole insulator with topologically protected corner states
• Band structure engineering and reconstruction in electric circuit networks
• Probing the Berry Curvature and Fermi Arcs of a Weyl Circuit
• 4D spinless topological insulator in a periodic electric circuit
• Higher-order Topological Mott Insulators
• Topological Anderson Insulator in electric circuits
• ${\mathbb{Z}}_Q$ Berry Phase for Higher-Order Symmetry-Protected Topological Phases
• Splitting the hinge mode of higher-order topological insulators
• Higher-order topological solitonic insulators
• $Z_N$ Berry Phases in Symmetry Protected Topological Phases
• Chern insulators for electromagnetic waves in electrical circuit networks

Cited by in corpus (27)

• Classical higher-order topological insulators
• Topolectric circuits: Theory and construction
• Realization of the square-root higher-order topological insulator in electric circuits
• Topological insulators and semimetals in classical magnetic systems
• Square-root higher-order Weyl semimetals
• Observation of Antichiral Edge States in a Circuit Lattice
• Realization of quasicrystalline quadrupole topological insulators in electrical circuits
• Exact Higher-order Bulk-boundary Correspondence of Corner-localized States
• Experimental observation of non-Hermitian higher-order skin interface states in topological electric circuits
• Corner modes of the breathing kagome lattice: origin and robustness
• Higher-order topological phases in crystalline and non-crystalline systems: a review
• A Higher-Order Topological Insulator Phase in a Modulated Haldane Model
• Custodial chiral symmetry in a Su-Schrieffer-Heeger electrical circuit with memory
• Experimental realization of two-dimensional weak topological insulators
• Observation of Large-Number Corner Modes in $\mathbb{Z}$-class Higher-Order Topolectrical Circuits
• Bulk-boundary correspondence in disordered higher-order topological insulators
• Anomalous fractal scaling in two-dimensional electric networks
• Competition of non-Hermitian skin effect and topological localization of corner states observed in circuits
• Observation of type-III corner states induced by long-range interactions
• Strongly Nonlinear Topological Phases of Cascaded Topoelectrical Circuits
• Engineering topological states and quantum-inspired information processing using classical circuits
• Competition of First-Order and Second-Order Topology on the Honeycomb Lattice
• Nonlinear Corner States in Topologically Nontrivial Kagome Lattice
• Third-order topological insulator in three-dimensional lattice of magnetic vortices
• Experimental observation of edge-dependent quantum pseudospin Hall effect
• Multiple topological corner states in the continuum of extended kagome lattice
• One-dimensional topology and topolectrics of nonsymmorphic Kramers degenerate systems