Crystalline nodal topological superconductivity in monolayer NbSe$_{2}$

We present a microscopic calculation of the phase diagram of the Ising superconductor NbSe$_{2}$ in the presence of both in-plane magnetic fields 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 nodal topological superconducting phase is stabilized, whereas for other field directions the pairing state is topologically trivial. In the regime of large Rashba and dominant triplet interactions, a chiral topological superconducting phase emerges, in which time-reversal symmetry is spontaneously broken and the system acquires a Chern number of $\pm 6$.