Refraction of flexural wave in the valley topological interface

Abstract

The transport behavior of valley kink states has attracted significant research interest due to its potential prospects in energy harvesting vibration mitigation and elastic wave imaging In this work we extensively investigate the topological refraction in valley elastic topological insulators (TIs) when the topological edge states (TES) transport from the interface termination into the bare plate We show that the refraction pattern (negative or positive refraction) depends on the type of valleys from which the edge state is projected and the refraction angles can be tuned by the Dirac frequency Thus we can realize the conversion of the refracted wave into the evanescent wave resulting in no refraction beams in the bare plate which provides a new perspective for vibration isolation and mitigation We then construct a new layered TI by alternately arranging two unit cells with opposite topological phases The dispersion relation of the layered TI shows a negative band and a positive band in the bulk band gap corresponding to two different edge modes In the edge states the wave energy would transfer toward the negative (positive) direction of the wave vector along the interface when an incident wave couples to this TI resulting in a negative (positive) shift parallel to the interface We selectively achieve negative (positive) refraction by exciting only one desired edge mode In particular the presence of the impedance mismatch between the layered TIs and the bare plate leads to the relatively low energy amplitude of the refracted beam Our research results provide new insights into manipulating the refraction wave in plates and facilitate potential applications in vibration mitigation beam splitting and negative refraction images