Ideal type-II Weyl phonons in wurtzite CuI

Weyl materials exhibiting topologically nontrivial touching points in band dispersion pave the way to exotic transport phenomena and novel electronic devices. Here, we demonstrate the signature of an ideal type-II Weyl phase in phonon dispersion of solids through first-principles investigations. Type-II phononic Weyl phase is manifested in noncentrosymmetric wurtzite CuI by six pairs of Weyl points (WPs) in the ${k}_z=0.0$ plane. On the iodine-terminated surface of the crystal, very clean surface arcs are readily detectable. Each pair of WPs connected by open surface arcs is well separated by a large distance of $0.26\phantom{\rule{0.16em}{0ex}}{\AA{}}^{\ensuremath{-}1}$. The opposite chirality of WPs with quantized Berry curvature produces Weyl phonon Hall effect, in analogy to valley Hall effect of electrons. Such ideal type-II Weyl phase is readily observable in experiment, providing a unique platform to study novel thermal transport properties distinct from type-I Weyl phase.