Hermitian and non-hermitian topological edge states in one-dimensional perturbative elastic metamaterials

Abstract

Topological edge states, identified by topological invariants, have been widely investigated in classical wave systems over the past decades due to their intriguing features such as robustness against defects. Most previous studies in this field have so far focused on their Hermitian Hamiltonians characterized by real-valued eigenfrequencies and orthogonal eigenvectors, while the intrinsically lossy nature of classical wave systems has inspired explorations towards their non-Hermitian counterparts for more realistic experimental investigations and practical applications. Here, we present and experimentally demonstrate a type of elastic metamaterials that can be described by the Su–Schrieffer–Heeger (SSH) model to realize topological edge states in elastic wave system under Hermitian or non-Hermitian modulation. The elastic metamaterials are one-dimensional tight-binding chains consisting of square plates (corresponding to mass points) connected by thin beams (corresponding to rigid bonds). For the hypothetically Hermitian case, alternating hopping strengths contribute to dimerization which gives rise to topologically non-trivial and trivial band gaps as well as the associated topological edge states. For the non-Hermitian case, when uneven absorptive dampings are applied to the double-sized unit cell, topological edge states can still be obtained even though the hopping strengths are identical. These results extend the topological physics in elastic wave systems beyond the conventional Hermiticity assumption and could offer greater possibilities for related elastic functional devices.