Ideal type-II Weyl phases and surface states for elastic waves in three-dimensional solid phononic crystals

The study of Weyl semimetals (WSs) has been attracting widely attention due to the fact that the Weyl point (WP) and associated topological invariants enable WSs to exhibit a variety of unusual properties, including robust surface wave and chiral anomaly. However, for the elastic analogue of ideal type-II WS, having the strongly tilted cone dispersion and conical Fermi surface, its realization still remains elusive. Here, we show an elastic type-II WS in three-dimensional (3D) solid phononic crystals (PnCs) with the broken spatial inversion symmetry. The ideal type-II WPs with opposite topological charges (+/- 1), opened Fermi-arc-like surface states and associated robust transport for 3D elastic wave are demonstrated. Furthermore, we reveal the phase transition between the elastic type-II WSs and two valley topological insulators (TIs). At the domain wall of two 3D PnCs with different valley topological phase, the Fermi-circle-like surface states are obtained. Our research provides a platform for the exploration of Weyl physics on a macroscopic mechanical structure.