Non-Hermitian band topology and skin modes in active elastic media

Abstract

Solids built out of active components can exhibit non-reciprocal elastic coefficients that give rise to non-Hermitian wave phenomena. Here, we investigate non-Hermitian effects present at the boundary of two-dimensional active elastic media obeying two general assumptions: their microscopic forces conserve linear momentum and arise only from static deformations. Using continuum equations, we demonstrate the existence of the non-Hermitian skin effect in which the boundary hosts an extensive number of localized modes. Furthermore, lattice models reveal non-Hermitian topological transitions mediated by exceptional rings driven by the activity level of individual bonds.

arXiv commentThree figures with supplementary information

References in corpus (65)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Edge states and topological invariants of non-Hermitian systems
• Exceptional Topology of Non-Hermitian Systems
• Localization transitions in non-Hermitian quantum mechanics
• Topological phases of non-Hermitian systems
• The physics of exceptional points
• Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
• Symmetry and Topology in Non-Hermitian Physics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Band Theory for Non-Hermitian Hamiltonians
• Non-Hermitian Chern bands
• Observation of bulk boundary correspondence breakdown in topolectrical circuits
• Non-Hermitian Boundary Modes
• Topological Phononic Crystals with One-Way Elastic Edge Waves
• Anatomy of skin modes and topology in non-Hermitian systems
• Topological Boundary Modes in Isostatic Lattices
• Topological mechanics of gyroscopic metamaterials
• Non-reciprocal robotic metamaterials
• Classification of Exceptional Points and Non-Hermitian Topological Semimetals
• Reciprocal skin effect and its realization in a topolectrical circuit
• Non-Hermitian Quantum Sensing: Fundamental Limits and Non-Reciprocal Approaches
• Topological modes bound to dislocations in mechanical metamaterials
• New topological invariants in non-Hermitian systems
• Odd viscosity in chiral active fluids
• Odd elasticity
• Amorphous topological insulators constructed from random point sets
• Nonlinear conduction via solitons in a topological mechanical insulator
• Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics
• Exceptional rings in two-dimensional correlated systems with chiral symmetry
• Symmetry-protected nodal phases in non-Hermitian systems
• Selective buckling via states of self-stress in topological metamaterials
• Topological exceptional surfaces in non-Hermitian systems with parity-time and parity-particle-hole symmetries
• Isostaticity, auxetic response, surface modes, and conformal invariance in twisted kagome lattices
• Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
• Topological mechanics of origami and kirigami
• Non-Hermitian systems and topology: A transfer-matrix perspective
• Transformable topological mechanical metamaterials
• An Introduction to Topological Insulators
• Phonons in a one-dimensional microfluidic crystal
• Exceptional Surfaces in PT-Symmetric Photonic Systems
• Spatiotemporal order and emergent edge currents in active spinner materials
• Mechanical Weyl Modes in Topological Maxwell Lattices
• Perspective on topological states of non-Hermitian lattices
• Unraveling non-Hermitian pumping: emergent spectral singularities and anomalous responses
• Mirror skin effect and its electric circuit simulation
• Exceptional rings protected by emergent symmetry for mechanical systems
• Dynamics and topology of non-Hermitian elastic lattices with non-local feedback control interactions
• Active topolectrical circuits
• Non-Hermitian dynamics without dissipation in quantum systems
• Anomalous Hydrodynamics of Two-Dimensional Vortex Fluid
• Heat transport in model jammed solids
• Geometric classification of non-Hermitian topological systems through the singularity ring
• Dualities and non-Abelian mechanics
• Geared topological metamaterials with tunable mechanical stability
• Topological phases and nonreciprocal edge states in non-Hermitian Floquet Insulators
• A Classification of Non-Hermitian Random Matrices
• Parity-time symmetry breaking in magnetic systems
• Universality classes of topological phase transitions with higher-order band crossing
• Anomalous Topological Active Matter
• Non-Hermitian Topological Metamaterials with Odd Elasticity
• Topological Phase Transition Independent of System Non-Hermiticity
• Tunable Band Topology in Gyroscopic Lattices
• Realization of a Topological Phase Transition in a Gyroscopic Lattice
• Linking scalar elastodynamics and non-Hermitian quantum mechanics
• The free surface of a colloidal chiral fluid: waves and instabilities from odd stress and Hall viscosity

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• Exponentially-enhanced Quantum Non-Hermitian Sensing via Optimized Coherent Drive
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