Observation of cnoidal wave localization in non-linear topolectric circuits

Abstract

We observe a localized cnoidal (LCn) state in an electric circuit network. Its formation derives from the interplay of non-linearity and the topology inherent to a Su-Schrieffer-Heeger (SSH) chain of inductors. Varicap diodes act as voltage-dependent capacitors, and create a non-linear on-site potential. For a sinusoidal voltage excitation around midgap frequency, we show that the voltage response in the non-linear SSH circuit follows the Korteweg-de Vries equation. The topological SSH boundary state which relates to a midgap impedance peak in the linearized limit is distorted into the LCn state in the non-linear regime, where the cnoidal eccentricity decreases from edge to bulk.

References in corpus (21)

• Topological Insulators
• Topological insulators and superconductors
• Topological Photonics
• Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
• Topolectrical circuit realization of topological corner modes
• Observation of phononic helical edge states in a mechanical 'topological insulator'
• Topolectrical circuits
• Time Reversal Invariant Topologically Insulating Circuits
• Topological Sound
• Topological properties of linear circuit lattices
• Chiral voltage propagation in a self-calibrated topolectrical Chern circuit
• Self-induced topological transitions and edge states supported by nonlinear staggered potentials
• Band structure engineering and reconstruction in electric circuit networks
• Probing the Berry Curvature and Fermi Arcs of a Weyl Circuit
• Boundary-obstructed topological phases
• Topologically Enhanced Harmonic Generation in a Nonlinear Transmission Line Metamaterial
• Active topolectrical circuits
• Another Exact Ground State of a 2D Quantum Antiferromagnet
• Chaotic behaviour of the solutions to a perturbed Korteweg-de Vries equation
• Topological Toda lattice and nonlinear bulk-edge correspondence
• Self-localized topological states in three dimensions

Cited by in corpus (18)

• Topological Non-Hermitian skin effect
• Dimensional transmutation from non-Hermiticity
• Non-Abelian inverse Anderson transitions
• Zoology of non-Hermitian spectra and their graph topology
• Simulating Holographic Conformal Field Theories on Hyperbolic Lattices
• Impedance responses and size-dependent resonances in topolectrical circuits via the method of images
• Skin modes in a nonlinear Hatano-Nelson model
• Nonlinear Topological Mechanics in Elliptically Geared Isostatic Metamaterials
• Anomalous fractal scaling in two-dimensional electric networks
• Percolation-induced PT symmetry breaking
• Kinked linear response from non-Hermitian cold-atom pumping
• Engineering topological states and quantum-inspired information processing using classical circuits
• Observation of non-local impedance response in a passive electrical circuit
• Non-reciprocal breathing solitons
• Protected chaos in a topological lattice
• Observation of edge solitons and transitions between them in a trimer circuit lattice
• Topological Phases in Non-Hermitian Nonlinear-Eigenvalue Systems
• Dark solitons in nonlinear Su-Schrieffer-Heeger lattices