Valley Hall Elastic Edge States in Locally Resonant Metamaterials.

Wenbo Fang,Yuyang Chen,Chunyu Han,Yijie Liu

doi:10.3390/ma15041491

Abstract

This paper presents a locally resonant metamaterial periodically rearranged as a local resonator, that is hexagonal holes arranged in a thin plate replace the elastic local resonator to achieve the quantum valley Hall effect. Due to the symmetry in the primitive hexagonal lattice, one Dirac point emerges at high symmetry points in the Brillouin zone in the sub-wavelength area. Rotating the beam element of the resonator can break the spatial inversion symmetry to lift the Dirac degeneracy and form a new bandgap. Thus, the band inversion is discovered by computing the relationship between the associated bandgap and the rotational parameter. We also confirmed this result by analyzing the vortex chirality and calculating the Chern number. We can discover two kinds of edge states in the projected band obtained by computing the supercell composed of different topological microstructures. Finally, the propagation behavior in various heterostructures at low frequencies was analyzed. It is shown that these valley Hall elastic insulators can guide elastic waves along sharp interfaces and are immune to backscattering from defects or disorder. By utilizing elastic resonators, a simple reconfigurable topological elastic metamaterial is realized in the sub-wavelength area.

Highlights

Elastic metamaterials are designed to control and manipulate the propagation behavior of elastic waves
Researchers have shifted their focus to the elastic wave analogue of the quantum spin Hall effect (QSHE), which is able to retain the time-reversal symmetry
We proposed a locally resonant metamaterial that periodically rearranges its local resonator by replacing the hexagonal hole in a thin plate to achieve the quantum valley Hall effect

Summary

Introduction

Elastic metamaterials are designed to control and manipulate the propagation behavior of elastic waves. Researchers have shifted their focus to the elastic wave analogue of the quantum spin Hall effect (QSHE), which is able to retain the time-reversal symmetry While these QSHE systems are passive in the conventional sense, the doubly degenerate Dirac cone generated by zone folding [22,23,24] or accidental degeneracy [24,25,26,27,28] is required for the establishment of two pseudospin states. The QVHE system only requires the formation of a single Dirac degeneracy in the dispersion relation This Dirac point can be lifted by employing the passive method to form a new bandgap, which can develop the TPES for valley-dependent properties at high symmetry points in the Brillouin region [32,33,34]. It is shown that the topologically protected edge state may sustain wave transport in the valley topology

Numerical Model of the Locally Resonant Metamaterial

Topological Phase

Valley Topology Edge States

Conclusions