Crystalline Nodal Topological Superconductivity and Bogolyubov Fermi Surfaces in Monolayer NbSe$_2$.

We present a microscopic calculation of the phase diagram of the Ising superconductor NbSe$_2$ in presence of both in-plane magnetic field and Rashba spin-orbit coupling. Repulsive interactions lead to two distinct instabilities, in singlet- and triplet- interaction channels. In the regime of large fields, the topological character of the superconducting state depends strongly on the magnetic field direction. When the field is applied along one of the three $\Gamma$-$K$ lines, a crystalline topological superconducting phase is stabilized, whereas for other field directions the pairing state is topologically trivial. 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 Chern number of 6 is realized in the regime of large Rashba and dominant triplet interactions, spontaneously breaking time-reversal symmetry.