System size dependent topological zero modes in coupled topolectrical chains

Abstract

In this paper, we demonstrate the emergence and disappearance of topological zero modes (TZMs) in a coupled topolectrical (TE) circuit lattice. Specifically, we consider non-Hermitian TE chains in which TZMs do not occur in the individual uncoupled chains, but emerge when these chains are coupled by inter-chain capacitors. The coupled system hosts TZMs which show size-dependent behaviours and vanish beyond a certain critical size. In addition, the emergence or disappearance of the TZMs in the open boundary condition (OBC) spectra for a given size of the coupled system can be controlled by modulating the signs of its inverse decay length. Analytically, trivial and non-trivial phases of the coupled system can be distinguished by the differing ranks of their corresponding Laplacian matrix. The TE circuit framework enables the physical detection of the TZMs via electrical impedance measurements. Our work establishes the conditions for inducing TZMs and modulating their behavior in coupled TE chains.

arXiv comment9 Pages, 5 Figures

References in corpus (49)

• Edge states and topological invariants of non-Hermitian systems
• Imaging topological edge states in silicon photonics
• Topological phases of non-Hermitian systems
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Origin of Non-Hermitian Skin Effects
• Non-Bloch Band Theory of Non-Hermitian Systems
• Topolectrical circuit realization of topological corner modes
• Lasing in topological edge states of a 1D lattice
• Observation of bulk boundary correspondence breakdown in topolectrical circuits
• Observation of non-Hermitian bulk-boundary correspondence in quantum dynamics
• Anatomy of skin modes and topology in non-Hermitian systems
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Probing topological invariants in the bulk of a non-Hermitian optical system
• Topological Origin of Zero-Energy Edge States in Particle-Hole Symmetric Systems
• Non-Hermitian skin effect and chiral damping in open quantum systems
• Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Critical non-Hermitian Skin Effect
• Reciprocal skin effect and its realization in a topolectrical circuit
• Probing non-Hermitian Skin Effect and non-Bloch Phase Transitions
• Higher-order non-Hermitian skin effect
• Chiral voltage propagation in a self-calibrated topolectrical Chern circuit
• Topological Zero-Energy Modes in Gapless Commensurate Aubry-André-Harper Models
• Topology-Induced Spontaneous Non-reciprocal Pumping in Cold-Atom Systems with Loss
• Robust zero-energy modes in an electronic higher-order topological insulator: the dimerized Kagome lattice
• Magnetic Proximity Effect as a Pathway to Spintronic Applications of Topological Insulators
• Experimental Observation of Higher-Order Topological Anderson Insulators
• Topological defect engineering and PT-symmetry in non-Hermitian electrical circuits
• Dimensional Crossover of Topological Edge States in Su-Schrieffer-Heeger Model
• Lattice models with exactly solvable topological hinge and corner states
• Impurity induced scale-free localization
• Simulating hyperbolic space on a circuit board
• Non-Hermitian Floquet topological phases: Exceptional points, coalescent edge modes, and the skin effect
• Second-order Dirac superconductors and magnetic field induced Majorana hinge modes
• Helical damping and anomalous critical non-Hermitian skin effect
• Active topolectrical circuits
• Analysis of the Robustness of Conventional and Topologically Protected Edge States in Phononic Crystal Plates
• Nonreciprocal response theory of nonhermitian mechanical metamaterials: response phase transition from the skin effect of zero modes
• Coupling between Exciton-Polariton Corner Modes through Edge States
• Non-Hermitian Floquet topological superconductors with multiple Majorana edge modes
• Anomalous topological edge states in non-Hermitian piezophononic media
• Quantized classical response from spectral winding topology
• Non-Hermitian Pseudo-Gaps
• The boundaries and twist defects of the color code and their applications to topological quantum computation
• Designing non-Hermitian real spectra through electrostatics
• Holographic duality between $(2+1)$-d quantum anomalous Hall state and $(3+1)$-d topological insulators
• Non-Hermitian Model for Asymmetrical Tunneling
• Scaling rule in critical non-Hermitian skin effect

Cited by in corpus (7)

• Topological Non-Hermitian skin effect
• Dimensional transmutation from non-Hermiticity
• Universal competitive spectral scaling from the critical non-Hermitian skin effect
• Impedance responses and size-dependent resonances in topolectrical circuits via the method of images
• Competition of non-Hermitian skin effect and topological localization of corner states observed in circuits
• Engineering topological states and quantum-inspired information processing using classical circuits
• Protected chaos in a topological lattice