Topological phononic crystals

Valley phononic crystals (VPCs) and Weyl phononic crystals (WPCs) are two typical types of topological phononic crystals. The valleys are the pair of energy extrema at two inequivalent corners of the reduced Brillouin zone of the 2-D hexagonal materials. The valley pseudospin, as new degree of freedom in addition to charge and spin, may provide a great alternative to be used in information encoding and processing. VPCs are 2-D acoustic or elastic artificial materials with valleys, and chiral valley states and robust valley edge transport, can be exhibited in either the acoustic or elastic VPCs. Weyl semimetals are materials in which the electrons have linear dispersions in all directions while are doubly degenerate at single points, called the Weyl points, near the Fermi surface in 3-D momentum space. Weyl points also exist in 3-D phononic crystals for acoustic or elastic waves, referred to as WPCs. The surface arc states in the WPC, not only manifest the normal refraction, but also the negative refraction when turning from one surface to another. In either case, they are immune against reflection. Topological phononic crystals extend topological physics from microscopic scales to macroscopic scales, which may accelerate the practical application of the topological physics.