Finite-momentum pairing in superconducting monolayer NbSe₂

The nature of the so-called Ising superconducting state in non-centrosymmetric monolayer transition metal dichalcogenides remains a subject of intense debate. Here, we study the possibility of finite-momentum pairing within a low-energy interacting microscopic electronic model for monolayer 1H-NbSe₂. We find that, in the presence of both Rashba and Ising spin-orbit coupling (SOC), a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like state is expected to emerge for sufficiently strong in-plane fields. For special orientations of the magnetic field, this FFLO state displays topological Bogolyubov Fermi surfaces or nodes depending on the center-of-mass momentum of the Cooper pairs, protected by a crystalline mirror symmetry. We also show that out of the eight symmetry-allowed interactions involving the low-energy fermions in this model, four of them favor a pair-density wave (PDW) state involving momentum transfer K that may have a helical or chiral character. We investigate the stability and topology of these PDW states and their competition with the uniform superconducting phase in the presence of trigonal warping and mismatch between the K/K’ and the Γ pockets.