  Monolayers of transition-metal dichalcogenides (TMDs) are two-dimensional
materials whose low energy sector consists of two inequivalent valleys. The
valence bands have a large spin splitting due to strong spin-orbit coupling.
Furthermore the spin is polarized up in one valley and down in the other (in
directions perpendicular to the two-dimensional crystal). We focus on lightly
hole-doped systems where the Fermi surface consists of two disconnected circles
with opposite spins. For both proximity induced and intrinsic local attractive
interaction induced superconductivity, a fully gapped intervalley pairing state
is favored in this system, which is an equal superposition of the singlet and
the m=0 triplet for the lack of centrosymmetry. We show that a
ferromagnetically ordered magnetic-adatom chain placed on a monolayer TMD
superconductor provides a platform to realize one-dimensional topological
superconducting state characterized by the presence of Majorana zero modes at
its ends. We obtain the topological phase diagram and show that the topological
superconducting phase is affected not only by the adatom spacing and the
direction of the magnetic moment, but also by the orientation of the chain
relative to the crystal.
