Non-Newtonian Topological Mechanical Metamaterials Using Feedback Control

Abstract

We introduce a method to design topological mechanical metamaterials that are not constrained by Newtonian dynamics. The unit cells in a mechanical lattice are subjected to active feedback forces that are processed through autonomous controllers, pre-programmed to generate the desired local response in real-time. As an example, we focus on the quantum Haldane model, which is a two-band system with directional complex coupling terms, violating Newton's third law. We demonstrate that the required topological phase, characterized by chiral edge modes, can be achieved in an analogous mechanical system only with closed-loop control. We then show that our approach enables to realize, for the first time, a modified version of the Haldane model in a mechanical metamaterial. Here, the complex-valued couplings are polarized in a way that modes on opposite edges of a lattice propagate in the same direction, and are balanced by counter-propagating diffusive bulk modes. The proposed method is general and flexible, and could be used to realize arbitrary lattice parameters, such as non-local or nonlinear couplings, time dependent potentials, non-Hermitian dynamics, and more, on a single platform.

arXiv comment4+ pages, plus supplemental material

References in corpus (31)

• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Topological Photonics
• Photonic Floquet Topological Insulators
• Imaging topological edge states in silicon photonics
• Acoustic topological insulator and robust one-way sound transport
• Observation of phononic helical edge states in a mechanical 'topological insulator'
• Observation of bulk boundary correspondence breakdown in topolectrical circuits
• Topological Phononic Crystals with One-Way Elastic Edge Waves
• Anatomy of skin modes and topology in non-Hermitian systems
• Topological mechanics of gyroscopic metamaterials
• Topologically protected elastic waves in phononic metamaterials
• Floquet Topological Insulators for Sound
• Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial
• Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide
• Non-reciprocal robotic metamaterials
• Topologically protected acoustic helical edge states and interface states in strongly coupled metamaterial ring lattices
• Valley-Polarized Quantum Anomalous-Hall Effects in Silicene
• Edge waves in plates with resonators: An elastic analogue of the quantum valley Hall effect
• Chiral voltage propagation in a self-calibrated topolectrical Chern circuit
• Topological Origin of Equatorial Waves
• Non-Hermitian band topology and skin modes in active elastic media
• Subwavelength and directional control of flexural waves in zone-folding induced topological plates
• Antichiral edge states in a modified Haldane nanoribbon
• Dynamics and topology of non-Hermitian elastic lattices with non-local feedback control interactions
• Experimental Realization of a Reconfigurable Electroacoustic Topological Insulator
• Anti-chiral edge states in an exciton polariton strip
• Floquet topological system based on frequency-modulated classical coupled harmonic oscillators
• Anti-chiral edge states in Heisenberg ferromagnet on a honeycomb lattice
• Topologically protected pseudospins in 2D spring-mass system
• Strain tuned topology in the Haldane and the modified Haldane models

Cited by in corpus (14)

• Topological active matter
• Acoustic non-Hermitian skin effect from twisted winding topology
• Realization of active metamaterials with odd micropolar elasticity
• Real-Time Steering of Curved Sound Beams in a Feedback-based Topological Acoustic Metamaterial
• Non-Hermitian elastic waveguides with piezoelectric feedback actuation: non-reciprocal bands and skin modes
• Insensitive edge solitons in a non-Hermitian topological lattice
• Synthetic Mechanical Lattices with Synthetic Interactions
• 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
• Emergent clustering due to quorum sensing interactions in active matter
• Combinatorial Design of Floppy Modes and Frustrated Loops in Metamaterials
• Mechanical activity and odd elasticity of passive, 2D chiral metamaterials
• Metal-Insulator Coexistence and Gap-Crossing Domain-Wall Modes in an Aubry-André Model with Nonlocal Hopping
• Phase space analysis of nonlinear wave propagation in a bistable mechanical metamaterial with a defect