Non-Hermitian Topological Metamaterials with Odd Elasticity

TL;DR

This paper explores non-Hermitian topological mechanics in 1D and 2D lattices with odd elasticity, revealing unique effects like exponential localization of elastic waves and complex eigenfrequencies of topological modes.

Contribution

It introduces a framework for non-Hermitian topological mechanics with odd elasticity, extending the non-Hermitian skin effect to 2D lattices and defining a Berry phase for such systems.

Findings

Bulk elastic waves localize exponentially in 2D lattices.

Topological modes have complex eigenfrequencies due to broken $\\mathcal{PT}$-symmetry.

Localized modes are sensitive to perturbations.

Abstract

We establish non-Hermitian topological mechanics in one dimensional (1D) and two dimensional (2D) lattices consisting of mass points connected by meta-beams that lead to odd elasticity. Extended from the "non-Hermitian skin effect" in 1D systems, we demonstrate this effect in 2D lattices in which bulk elastic waves exponentially localize in both lattice directions. We clarify a proper definition of Berry phase in non-Hermitian systems, with which we characterize the lattice topology and show the emergence of topological modes on lattice boundaries. The eigenfrequencies of topological modes are complex due to the breaking of $\mathcal{PT}$-symmetry and the excitations could exponentially grow in time in the damped regime. Besides the bulk modes, additional localized modes arise in the bulk band and they are easily affected by perturbations. These distinguishing features may manifest themselves in various active materials and biological systems.