Nonreciprocal response theory of nonhermitian mechanical metamaterials: response phase transition from the skin effect of zero modes

Abstract

Nonreciprocal nonhermitian systems provide an unconventional localization mechanism of topological zero modes via the nonhermitian skin effect. While fundamental theoretical characterizations of this effect involve the biorthogonal system of right and left eigenmodes, the recent demonstration of this effect for a zero mode in a robotic metamaterial (Ghatak et al., arXiv:1907.11619) is based on the direct experimental observation of the conventional right eigenvectors. Here I show that such nonreciprocal mechanical metamaterials reveal their underlying biorthogonality in the directly observable response of the system to external excitation. Applied to the ground-breaking experiment, this nonreciprocal response theory predicts that the zero-mode skin effect goes along an extended phase where the system is highly sensitive to physical perturbations, leading to a diverging response in the limit of a large system.

5 pages, 3 figures

References in corpus (4)

• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Reciprocal skin effect and its realization in a topolectrical circuit
• Nonlinear conduction via solitons in a topological mechanical insulator
• Hidden Chern number in one-dimensional non-Hermitian chiral-symmetric systems

Cited by in corpus (65)

• Exceptional Topology of Non-Hermitian Systems
• Topological Origin of Non-Hermitian Skin Effects
• Critical non-Hermitian Skin Effect
• Non-Hermitian Topological Sensors
• Topological active matter
• Higher-order non-Hermitian skin effect
• Topological Non-Hermitian skin effect
• Exponentially-enhanced quantum sensing with non-Hermitian lattice dynamics
• Non-Bloch band theory of non-Hermitian Hamiltonians in the symplectic class
• Skin effect and winding number in disordered non-Hermitian systems
• Impurity induced scale-free localization
• Unraveling non-Hermitian pumping: emergent spectral singularities and anomalous responses
• Many-body topology of non-Hermitian systems
• Topological Field Theory of Non-Hermitian Systems
• Geometric Response and Disclination-Induced Skin Effects in Non-Hermitian Systems
• Non-equilibrium stationary states of quantum non-Hermitian lattice models
• Many-Body Topological and Skin States without Open Boundaries
• Liouvillian Skin Effect in an Exactly Solvable Model
• Non-Hermitian skin clusters from strong interactions
• Exceptional Bound States and negative Entanglement Entropy
• Anomalous Skin Effects in Disordered Systems with a Single non-Hermitian Impurity
• Exceptional Spin Liquids from Couplings to the Environment
• Non-Hermitian Topological Metamaterials with Odd Elasticity
• Free-Fermionic Topological Quantum Sensors
• Zoology of non-Hermitian spectra and their graph topology
• Linear response theory of open systems with exceptional points
• Sensitivity of non-Hermitian systems
• Berry connection induced anomalous wave-packet dynamics in non-Hermitian systems
• Non-Hermitian Aubry-André model with Power-Law Hopping
• Homotopy, Symmetry, and Non-Hermitian Band Topology
• Bulk-boundary correspondence in point-gap topological phases
• Petermann factors and phase rigidities near exceptional points
• Response strengths of open systems at exceptional points
• System size dependent topological zero modes in coupled topolectrical chains
• Compatibility of transport effects in non-Hermitian nonreciprocal systems
• The non-Hermitian skin effect: A perspective
• Critical non-Hermitian topology induced quantum sensing
• Filling up complex spectral regions through non-Hermitian disordered chains
• Non-Hermitian extended midgap states and bound states in the continuum
• State-dependent Topological Invariants and Anomalous Bulk-Boundary Correspondence in non-Hermitian Topological Systems
• Uniform response theory of non-Hermitian systems: Non-Hermitian physics beyond the exceptional point
• Moving along an exceptional surface towards a higher-order exceptional point
• Quantum metric dependent anomalous velocity in systems subject to complex electric fields
• Fundamental constraints on the observability of non-Hermitian effects in passive systems
• Transport effects in non-Hermitian nonreciprocal systems: General approach
• Complete absorption of topologically protected waves
• Non-Hermitian skin effect and lasing of absorbing open-boundary modes in photonic crystals
• Non-Hermitian physics of levitated nanoparticle array
• Anomalous Hall effect from a non-Hermitian viewpoint
• Geometric contribution to adiabatic amplification in non-Hermitian systems
• Quantum Sensing with Driven-Dissipative Su-Schrieffer-Heeger Lattices
• Multicritical quantum sensors driven by symmetry-breaking
• Generalized Petermann factor of non-Hermitian systems at exceptional points
• Topological directed amplification
• Optical non-Hermitian skin effect in two-dimensional uniform media
• Renormalization approach to the analysis and design of Hermitian and non-Hermitian interfaces
• Hermitian and non-Hermitian topology in active matter
• Fragmented exceptional points and their bulk and edge realizations in lattice models
• Non-Hermitian Hopf insulators
• Exceptionally deficient topological square-root insulators
• Topological photonics in nanoscaled systems with far field radiation and polarization singularities
• Non-Hermitian magnetic moment
• Covariant formulation of the Berry connection in non-Hermitian systems
• Exploring Nonreciprocal Noise Transfer under Onsager-Casimir Symmetry in Synthetic-Field Optomechanics
• Hall conductance of a non-Hermitian two-band system with k-dependent decay rates