We address the parity-mixed superconductivity in a locally noncentrosymmetric multilayer system (Rashba), and in monolayer transition metal dichalcogenides (Ising). For the Rashba system, we investigate the magnetic field dependence of an ideal superconducting vortex lattice in the parity-mixed pair-density wave phase of multilayer superconductors within a circular cell Ginzburg-Landau approach. In multilayer systems, due to local inversion symmetry breaking, a Rashba spin-orbit coupling is induced at the outer layers. This combined with a perpendicular paramagnetic limiting magnetic field stabilizes a staggered layer dependent pair-density wave phase in the superconducting singlet channel. The motivating guiding question is: what is the minimal necessary Maki value for the appearance of the pair-density wave phase of a superconducting trilayer system. On the other hand, Ising materials like monolayer NbSe2 are nodal topological superconductors at magnetic in-plane fields exceeding the Pauli limit, with nodal points strictly on high symmetry lines in the Brillouin zone. 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.

https://journals.aps.org/prb/abstract/10.1103/PhysRevB.97.144508

https://journals.aps.org/prb/abstract/10.1103/PhysRevB.98.144518