Spin-1 Weyl point and surface arc state in a chiral phononic crystal

The $\mathrm{spin}\ensuremath{-}1$ Weyl point is formed by three bands touching at a single point in three-dimensional (3D) momentum space, with two of the bands showing conelike dispersion while the third band is flat. Such a triply degenerate point carries a higher topological charge $\ifmmode\pm\else\textpm\fi{}2$ and can be described by a three-band Hamiltonian. We first propose a tight-binding model of a 3D Lieb lattice with chiral interlayer coupling to form the spin-1 Weyl point. Then we design a chiral phononic crystal that carries these $\mathrm{spin}\ensuremath{-}1$ Weyl points and special straight-type acoustic Fermi arcs. We also demonstrate computationally the robust propagation of topologically protected surface states that can travel around a corner or defect without reflection. Our results pave the way to the manipulation of acoustic waves in 3D structures, and they provide a platform for exploring energy transport properties in 3D $\mathrm{spin}\ensuremath{-}1$ Weyl systems.