  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.
