  Weyl points are often believed to appear in pairs with opposite chirality. In
this work, we show by first-principles calculations and symmetry analysis that
single Weyl phonons with linear dispersion and double Weyl phonons with
quadratic dispersion are simultaneously present between two specific phonon
branches in realistic materials with trigonal or hexagonal lattices. These
phonon Weyl points are guaranteed to locate at high-symmetry points due to the
screw rotational symmetry, forming a unique triangular Weyl complex. In sharp
contrast to conventional Weyl systems with surface arcs terminated at the
projections of a pair of Weyl points with opposite chirality, the phonon
surface arcs of the unconventional triangular Weyl complex connect the
projections of one double Weyl point and two single Weyl points. Importantly,
the phonon surface arcs originating from the triangular Weyl complex are
extremely long and span the entire surface Brillouin-zone. Furthermore, there
are only nontrivial phonon surface states across the iso-frequency surface,
which facilitates their detection in experiments and further applications. Our
work not only offers the promising triangular phonon Weyl complex but also
provides guidance for exploring triangular Weyl bosons in both phononic and
photonic systems.
