Elastic Topological Insulator via the Valley Hall Effect with Distorted Hexagonal Holes

Abstract

Topological insulators have been studied extensively owing to its distinguished characteristics, which generates the edge state in which wave can propagate without backscattering. This work proposes a phononic crystal with distorted hexagonal holes, as an elastic topological insulator for in-plane wave based on the analogues of valley hall effect. First, the existence of a nontrivial valley topological phase on the phononic crystal is revealed by Bloch wave functions, Bloch frequencies at the valley, and numerically calculated valley Chem numbers, respectively. Then, a topologically protected edge state is generated on the boundary of two phononic crystals with different topological phases. Its topological protection property is confirmed on the band diagram by a supercell method utilizing the revealed valley topological phases. Finally, the nature of the edge state, which is topologically protected against sharp angles, is observed directly through a full field simulation.