Three-component bosons in TiS, ZrSe and HfTe

Abstract: Topological semimetals with several types of three-dimensional (3D) fermion of electrons, such as Dirac fermions, Weyl fermions, Dirac nodal lines and triply degenerate nodal points have been theoretically predicted and then experimentally discovered in the electronic structures of a series of solid crystals. In analogy of various typical fermions, topological mechanical states with two type of bosons, Dirac and Weyl bosons, were also experimentally reported in some macroscopic systems of kHz frequency and with a type of doubly-Weyl phonons in atomic vibrational framework of THz frequency of solid crystal was also recently predicted. However, to date no triply degenerate nodal point of phonon beyond the conventional Dirac, Weyl and doubly-Weyl phonons has been reported. Here, through first-principles calculations, we have reported on the prediction that the WC-type TiS, ZrSe, and HfTe commonly host the unique triply degenerate nodal point of phonon in THz frequency due to the occurrence of the phonon band inversion between the doubly degenerate planar vibrational mode and the singlet vertical vibrational mode at the boundary A point of the bulk Brillouin zone. Quasiparticle excitations near this triply degenerate nodal point of phonons are three-component bosons, different from the known classifications. The underlying mechanism can be attributed to the leading role of the comparable atomic masses of constituent elements in compounds in competition with the interatomic interaction. Additionally, the electronic structures in their bulk crystals exhibit the coexisted triply degenerate nodal point and Weyl fermions. The novel coexistence of three-component bosons, three-component fermions and Weyl fermions in these materials thus suggest an enriched platform for studying the interplay between different types of fermions and bosons.