Abstract
We investigate non-Hermitian elastic lattices characterized by non-local feedback interactions. In one-dimensional lattices, proportional feedback produces non-reciprocity associated with complex dispersion relations characterized by gain and loss in opposite propagation directions. For non-local controls, such non-reciprocity occurs over multiple frequency bands characterized by opposite non-reciprocal behavior. The dispersion topology is investigated with focus on winding numbers and non-Hermitian skin effect, which manifests itself through bulk modes localized at the boundaries of finite lattices. In two-dimensional lattices, non-reciprocity is associated with directional wave amplification. Moreover, the combination of skin effect in two directions produces modes that are localized at the corners of finite two-dimensional lattices. Our results describe fundamental properties of non-Hermitian elastic lattices, and suggest new possibilities for the design of meta materials with novel functionalities related to selective wave filtering, amplification and localization. The considered non-local lattices also provide a platform for the investigation of topological phases of non-Hermitian systems.
Highlights
Metamaterials and phononic crystals are periodic structures designed to manipulate acoustic and elastic waves [1, 2]
Recent breakthroughs in topological insulators in solid state physics [8] and photonics [9] have motivated the search for topology-based functionalities in mechanical and acoustic metamaterials
Aligned with recent findings in quantum lattices [53], our results show that eigenfrequencies belonging to regions with ν < 0 define bulk modes localized at the left boundary (Fig. 4(c)), while ν > 0 values produce localization at the right boundary (Fig. 4(f))
Summary
Metamaterials and phononic crystals are periodic structures designed to manipulate acoustic and elastic waves [1, 2]. Feedback control has been pursued to establish non-reciprocal interactions in a mechanical metamaterial that emulates the non-Hermitian Su-Schrieffer-Heeger (SSH) model [43] Such setting was used to experimentally demonstrate the existence of zero-frequency edge states in the non-Hermitian topological phase, and to realize unidirectional wave amplification [44]. Motivated by these notable contributions, we here investigate a family of 1D and 2D elastic lattices with non-local, proportional feedback interactions and explore a series of unconventional phenomena stemming from their non-Hermiticity. We summarize the main results of the work and outline future research directions
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