  In monolayer transition metal dichalcogenides (TMDs), electrons in opposite
$K$ valleys are subject to opposite effective Zeeman fields, which are referred
to as Ising spin-orbit coupling (SOC) fields. The Ising SOC, originated from
in-plane mirror symmetry breaking pins the electron spins in out-of-plane
directions, and results in the newly discovered Ising superconducting states
with strongly enhanced upper critical fields. In this work, we show that the
Ising SOC generates equal-spin triplet Cooper pairs with spin polarization in
the in-plane directions. Importantly, the spin-triplet Cooper pairs can induce
superconducting pairings in a half-metal wire placed on top of the TMD and
result in a topological superconductor with Majorana end states. Direct ways to
detect equal-spin triplet Cooper pairs and the differences between Ising
superconductors and Rashba superconductors are discussed.
