Valley Anisotropy and Valley Topological States in Elastic Metamaterials*

Valley, as a new degree of freedom, has emerged as an efficient way in manipulating waves in electronics, photonics and phononics. We present the valley anisotropy by introducing asymmetrical metamaterials made of hard spiral and soft materials. We study the phononic band structure and valley pseudospin in these spiral elastic metamaterials. By numerical calculations, we show the deviated Berry curvature and valley Chern number. The adjustment of the geometrical parameters in the spirals allows an extreme tunability of the Berry curvature and valley Chern number, resulting in the topological transition. We exploit the adjustment of the geometrical parameters to demonstrate the formation of valley topological states unprecedented in conventional topological platforms. Lastly, we present the topologically protected transport of elastic waves in our anisotropic topological elastic metamaterials.