Robust parity-mixed superconductivity in disordered monolayer transition metal dichalcogenides

Monolayer NbSe$_2$ is a nodal topological Ising superconductor at magnetic in-plane fields exceeding the Pauli limit, with nodal points strictly on high symmetry lines in the Brillouin zone. Here, we use a combined numerical and group-theoretical approach in real-space to characterize the unconventional superconducting state in monolayer transition metal dichalcogenides. Even with a conventional pairing interaction, the superconducting state is intrinsically parity-mixed and robust against on-site disorder. The interplay between the Zeeman magnetic field, strong spin-orbit interaction, and electronic orbital content confer the unique superconducting and topological properties. The discussion also extends to strongly hole-doped MoS$_2$ and its relatives.