Coexistent three-component and two-component Weyl phonons in TiS, ZrSe, and HfTe

Abstract

In analogy to various fermions of electrons in topological semimetals, topological mechanical states with two type of bosons, Dirac and Weyl bosons, were reported in some macroscopic systems of kHz frequency and those with a type of doubly-Weyl phonons in atomic vibrational framework of THz frequency of solid crystals were recently predicted. However, to date no three-component bosons of phonon has been reported. Here, through first-principles calculations, we have reported that the phonon spectra of the WC-type TiS, ZrSe, and HfTe commonly host the unique triply degenerate nodal points (TDNPs) and single two-component Weyl points (WPs) in THz frequency. Quasiparticle excitations near TDNPs of phonons are three-component bosons, beyond the conventional and known classifications of Dirac, Weyl and doubly-Weyl phonons. {Moreover, we have found that both TiS and ZrSe have five pairs of type-I Weyl phonons and a pair of type-II Weyl phonons, whereas HfTe only has four pairs of type-I Weyl phonons. They carry non-zero topological charges. On the (10$\bar{1}$0) crystal surfaces, we observe topological protected surface arc states connecting two WPs with opposite charges, which host modes that propagate nearly in one direction on the surface.