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

## TL;DR

This paper investigates the phase diagram of monolayer NbSe$_2$ under magnetic fields and Rashba SOC, revealing crystalline topological superconductivity with Bogolyubov Fermi surfaces and chiral phases with high Chern numbers.

## Contribution

It uncovers how Rashba SOC and magnetic field orientation influence topological phases, including crystalline and chiral superconducting states, in NbSe$_2$.

## Key findings

- Rashba SOC lifts nodes except along specific symmetry lines.
- Crystalline topological phase protected by mirror symmetry.
- Chiral phase with Chern number 6 at strong SOC and triplet interactions.

## Abstract

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 (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 \(\Gamma\)-\(M\) 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 $\Gamma$-$K$ 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 \emph{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 Chern number of 6 is realized in the regime of large Rashba SOC and dominant triplet interactions, spontaneously breaking time-reversal symmetry.