Low-temperature anomaly and anisotropy of critical magnetic fields in transition-metal dichalcogenide superconductors

We clarify why spin-singlet superconductivity persists in monolayer transition-metal dichalcogenides even in high magnetic fields beyond the Pauli limit. The phenomenon called Ising protection is caused by two magnetically active potentials: a Zeeman field and an Ising spin-orbit interaction. These potentials induce two spin-triplet pairing correlations in a spin-singlet superconductor. One belonging to odd-frequency symmetry class arises solely from a Zeeman field and always makes the superconducting state unstable. The other belonging to even-frequency symmetry class arises from the interaction between the two magnetic potentials and eliminates the instability caused by odd-frequency pairs. The presence or absence of such even-frequency spin-triplet pairs explains the anisotropy of the Ising protection. The analytical expression of the superfluid weight enables us to conclude that induced even-frequency spin-triplet Cooper pairs support spin-singlet superconductivity in high Zeeman fields.