  The few-layer transition metal dichalcogenides (TMDs) have been recently
suggested as a platform for controlled unconventional superconductivity. We
study the manifestations of unconventional triplet pairing in the density of
states of a disordered TMD based monolayer. The conventional singlet pairing
attraction is assumed to be the dominant pairing interaction. We map the phase
diagrams of disordered Ising superconductors in the plane of temperature and
the in-plane magnetic field. The latter suppresses singlet and promote triplet
correlations. The triplet order parameters of a trivial (non-trivial) symmetry
compete (cooperate) with the singlet order parameter which gives rise to a rich
phase diagram. We locate the model-dependent phase boundaries and compute the
order parameters in each of the distinct phases. With this information, we
obtain the density of states by solving the Gorkov equation. The triplet
components of the order parameters may change an apparent width of the density
of states by significantly increasing the critical field. The triplet
components of the order parameters lead to the density of states broadening
significantly exceeding the broadening induced by magnetic field and disorder
in the singlet superconductor.
