Non-Hermitian topological metamaterials with odd elasticity

Abstract

We establish non-Hermitian topological mechanics in one-dimensional (1D) and 2D lattices consisting of mass points connected by metabeams 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 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.

Non-Hermitian topological coupler for elastic waves

“…On the other hand, non-Hermiticity is another concept extended from quantum condensed matters to classical wave regimes, which refers to the gain and loss contrast of an active system or the loss contrast in a totally passive system [27]. Non-Hermiticity focuses on the system sensitivity in terms of the material gain or loss, and it can manipulate wave propagation as proposed in the optical [28][29][30], acoustic [31,32], and elastic systems [33]. With increasing non-Hermiticity, the system will evolve from the so-called PTsymmetric phase into PT-broken phase by going through an exceptional point, where multiple eigenstates (and eigenvalues) coalesce [34].…”

Realization of active metamaterials with odd micropolar elasticity

“…In this case u a represents geometric deformations and M ab represents the stiffness matrix containing all of the material's elastic moduli. We refer to the antisymmetric components M ab À M ba À Á =2 as odd elasticity 27,[30][31][32] . A material displaying odd elasticity must violate Maxwell-Betti reciprocity, though it needs not rely on external sources of linear or angular momentum.…”

Disorder-driven Phase Transitions of Second-order Non-Hermitian Skin Effects

“…Introduction -The unique physical behaviors of non-Hermitian mechanics appear in various open systems such as optics [1][2][3][4][5], electrical circuits [6][7][8][9], mechanical systems [10][11][12][13][14], open quantum systems [15][16][17], and correlated quantum systems with a finite lifetime [18][19][20][21][22][23]. The non-Hermitian skin effect(NHSE) is an exotic example of non-Hermitian mechanics, in which the bulk mode shows a dramatic difference depending on the boundary condition [24][25][26][27][28][29].…”