  The presence of a non-centrosymmetric crystal structure and in-plane mirror
symmetry allows an Ising spin-orbit coupling to form in some two-dimensional
materials. Examples include transition metal dichalcogenide superconductors
like monolayer NbSe$_2$, MoS$_2$, TaS$_2$, and PbTe$_2$, where a nontrivial
nature of the superconducting state is currently being explored. In this study,
we develop a microscopic formalism for Ising superconductors that captures the
superconducting instability arising from a momentum-dependent spin- and
charge-fluctuation-mediated pairing interaction. We apply our pairing model to
the electronic structure of monolayer NbSe$_2$, where first-principles
calculations reveal the presence of strong paramagnetic fluctuations. Our
calculations provide a quantitative measure of the mixing between the even- and
odd-parity superconducting states and its variation with Coulomb interaction.
Further, numerical analysis in the presence of an external Zeeman field reveals
the role of Ising spin-orbit coupling and mixing of odd-parity superconducting
state in influencing the low-temperature enhancement of the critical magnetic
field.
