  In the search for stable topological semimetals with clean band profiles, we
have screened all the 3$d$ metal-intercalated transition-metal dichalcogenides
(3dI-TMDCs) by performing hybrid-functional-based ab initio calculations. Two
classes of topological materials featuring twelve Weyl nodes in the $k_z=0$
plane (without spin-orbit interactions) are identified: (a)
time-reversal-breaking Weyl semimetals VT$_3$X$_6$ (ferromagnetic) and (b)
spinless Weyl semimetals MnT$_3$X$_6$ (nonmagnetic), where T=Nb, Ta; X=S, Se.
VNb$_3$S$_6$, prototypical of class (a), is half-metallic with only two bands
crossing at the Fermi level to form Weyl nodes. MnNb$_3$S$_6$ in the
nonmagnetic phase is essentially a spinless version of VNb$_3$S$_6$ featuring
an equally clean and simple band profile. Although the space group symmetry
(P6$_3$22) implies that the degeneracy between the two bands is lifted for $k$
away from the Weyl nodes, the gap remains extremely small ($\ll$ 0.1 meV) along
a loop connecting the Weyl nodes. This quasi-nodal-line degeneracy is explained
in terms of the quasi-mirror symmetry of the lattice, induced by the in-plane
twofold rotation axes, and the specific orbital nature of the bands. 3dI-TMDCs
are chemically and thermally stable stoichiometric compounds containing no
toxic elements and are a viable platform for the study of topological
condensed-matter physics.

Strongly Correlated Electrons