The Upper Critical Field of Bilayer NbSe2

We report on the fate of the superconducting state of bilayer NbSe$_2$ in a large parallel magnetic field. Due to strong spin-orbit coupling, the system exhibits an an out-of-plane polarization of electron spins in each valley, which leads to an enhanced upper critical field $H_{c2}^{||}$ as compared to that expected from the Pauli limit $H_p$ [1]. We explore the behavior of $H_{c2}^{||}(T)$ in the low temperature limit, down to $T = 0.3$K (approximately $0.06T_c$), and we find a maximum upper critical field of 28 T which is >3 times the Pauli limit. We find that the measured $H_{c2}^{||}(T)$ deviates significantly from the standard pair-breaking theory as $T \rightarrow 0$, and we compare our results to recent observations of Ising superconductivity in NbSe$_2$ [1] and in ionic-liquid-gated MoS$_2$ [2], as well as to calculations of $H_{c2}$ based on realistic band structure of NbSe$_2$. References: [1] Xi et al. arXiv:1507.08731 (2015) [2] Saito et al. arXiv:1506.04146 (2015)