Active topolectrical circuits

Abstract

The transfer of topological concepts from the quantum world to classical mechanical and electronic systems has opened fundamentally new approaches to protected information transmission and wave guidance. A particularly promising technology are recently discovered topolectrical circuits that achieve robust electric signal transduction by mimicking edge currents in quantum Hall systems. In parallel, modern active matter research has shown how autonomous units driven by internal energy reservoirs can spontaneously self-organize into collective coherent dynamics. Here, we unify key ideas from these two previously disparate fields to develop design principles for active topolectrical circuits (ATCs) that can self-excite topologically protected global signal patterns. Realizing autonomous active units through nonlinear Chua diode circuits, we theoretically predict and experimentally confirm the emergence of self-organized protected edge oscillations in one- and two-dimensional ATCs. The close agreement between theory, simulations and experiments implies that nonlinear ATCs provide a robust and versatile platform for developing high-dimensional autonomous electrical circuits with topologically protected functionalities.

arXiv comment10 pages, 4 figures, includes supplementary material. This version adds 2D experiments

References in corpus (41)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Topological Insulators in Three Dimensions
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Topological invariants of time-reversal-invariant band structures
• Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials
• Topological Acoustics
• Active Brownian Particles. From Individual to Collective Stochastic Dynamics
• Topolectrical circuit realization of topological corner modes
• 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
• Topological Boundary Modes in Isostatic Lattices
• Topological mechanics of gyroscopic metamaterials
• Topolectrical circuits
• Topological nature of nonlinear optical effects in solids
• Topological protection of photonic mid-gap cavity modes
• Topological active matter
• Time Reversal Invariant Topologically Insulating Circuits
• Topological properties of linear circuit lattices
• Chiral voltage propagation in a self-calibrated topolectrical Chern circuit
• Nonlinear conduction via solitons in a topological mechanical insulator
• Robust zero-energy modes in an electronic higher-order topological insulator: the dimerized Kagome lattice
• Observation of a higher-order topological bound state in the continuum
• 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
• Band structure engineering and reconstruction in electric circuit networks
• Observation and control of nonlinear electromagnetic topological edge states
• Topologically Enhanced Harmonic Generation in a Nonlinear Transmission Line Metamaterial
• Topologically protected modes in non-equilibrium stochastic systems
• Imaging Coulomb Islands in a Quantum Hall Interferometer
• Inverse Design of Discrete Mechanical Metamaterials
• Topological phase transition in coupled rock-paper-scissor cycles
• Autonomous actuation of zero modes in mechanical networks far from equilibrium
• Stochastic cycle selection in active flow networks
• Topological Phenomena in Classical Optical Networks
• Transmission Line Model for Materials with Spin-Momentum Locking
• Mode selection in compressible active flow networks
• Observation of Bulk Polarization Transitions and Higher-Order Embedded Topological Eigenstates for Sound
• Spectral Design of Active Mechanical and Electrical Metamaterials

Cited by in corpus (54)

• Topological active matter
• Topological Non-Hermitian skin effect
• Topological defect engineering and PT-symmetry in non-Hermitian electrical circuits
• Non-Hermitian band topology and skin modes in active elastic media
• Topological framework for directional amplification in driven-dissipative cavity arrays
• Simulating hyperbolic space on a circuit board
• Hyperbolic Matter in Electrical Circuits with Tunable Complex Phases
• Dimensional transmutation from non-Hermiticity
• Non-Abelian inverse Anderson transitions
• Observation of cnoidal wave localization in non-linear topolectric circuits
• Real-Time Steering of Curved Sound Beams in a Feedback-based Topological Acoustic Metamaterial
• Nonlinearity-induced transition in nonlinear Su-Schrieffer-Heeger model and nonlinear higher-order topological system
• Restoration of the non-Hermitian bulk-boundary correspondence via topological amplification
• Topological synchronization of quantum van der Pol oscillators
• Topological synchronization of coupled nonlinear oscillators
• Simulating Holographic Conformal Field Theories on Hyperbolic Lattices
• Cyclotron quantization and mirror-time transition on nonreciprocal lattices
• System size dependent topological zero modes in coupled topolectrical chains
• Experimental realization of two-dimensional weak topological insulators
• Transition from topological to chaos in the nonlinear Su-Schrieffer-Heeger model
• Impedance responses and size-dependent resonances in topolectrical circuits via the method of images
• Breitenlohner-Freedman bound on hyperbolic tilings
• Observation of Large-Number Corner Modes in $\mathbb{Z}$-class Higher-Order Topolectrical Circuits
• Topological edge solitons and their stability in a nonlinear Su-Schrieffer-Heeger model
• Collective vibrations of confined levitating droplets
• Nonlinear Topological Mechanics in Elliptically Geared Isostatic Metamaterials
• Anomalous fractal scaling in two-dimensional electric networks
• Collective vibrations of a hydrodynamic active lattice
• Engineering topological states and quantum-inspired information processing using classical circuits
• Quench dynamics and bulk-edge correspondence in nonlinear mechanical systems
• Two-point spectroscopy of Fibonacci topoelectrical circuits
• Electric circuit emulation of topological transitions driven by quantum statistics
• Protection of all nondefective twofold degeneracies by anti-unitary symmetries in non-Hermitian systems
• Protected chaos in a topological lattice
• Electric Circuit Realizations of Fracton Physics
• Active Control Approach to Temporal Acoustic Cloaking
• Memristive Ising Circuits
• Bloch Oscillations, Landau-Zener Transition, and Topological Phase Evolution in a Pendula Array
• Real-time-controlled artificial quiet channel for acoustic cloaking under varying detection conditions
• Observation of edge solitons and transitions between them in a trimer circuit lattice
• Topological split-ring resonator based metamaterials with $\mathcal{P}\mathcal{T}$ symmetry relying on gain and loss
• Optimal synchronisation to a limit cycle
• Hermitian and non-Hermitian topology in active matter
• Chiral topological phases in designed mechanical networks
• Multifractal statistics of non-Hermitian skin effect on the Cayley tree
• Solving the Kinetic Ising Model with Non-Reciprocity
• Topological edge states in all-dielectric square-lattice arrays of bianisotropic microwave resonators
• Spectral Design of Active Mechanical and Electrical Metamaterials
• Electric circuit analog of Landau-Zener tunneling using time-varying elements
• Topological Phases in Non-Hermitian Nonlinear-Eigenvalue Systems
• Nonlinear dynamical topological phases in Cooper-pair box array
• Nonlinear Anderson localization in Toda lattices
• Crystalline Weyl semimetal phase in Quantum Spin Hall systems under magnetic fields
• Correspondence between non-Hermitian topology and directional amplification in the presence of disorder