Crystalline nodal topological superconductivity and Bogolyubov Fermi surfaces in monolayer NbSe₂

We present a microscopic calculation of the phase diagram of the Ising superconductor NbSe2 in the presence of both in-plane magnetic field and Rashba spin-orbit coupling (SOC). Repulsive interactions lead to two distinct instabilities, in singlet and triplet interaction channels. While we recover the previously predicted nodal topological superconducting state in the absence of Rashba SOC at large magnetic field with six pairs of nodes along Γ-M lines, a finite Rashba SOC breaks the symmetry that protects these nodes and therefore generally lifts them, resulting in a topologically trivial phase. There is an exception when the field is applied along one of the three Γ-K lines, however. In that case, a single mirror symmetry remains that can protect two pairs of nodes out of the original six, resulting in a crystalline topological superconducting phase. Depending on the Cooper pairs' center-of-mass momentum, this superconducting state displays either Bogolyubov Fermi surfaces or point nodes. Moreover, a chiral topological superconducting phase with a Chern number of 6 is realized in the regime of large Rashba SOC and dominant triplet interactions, spontaneously breaking time-reversal symmetry.