Unconventional Superconductivity in Bilayer Transition Metal Dichalcogenides

Bilayer transition metal dichalcogenides (TMDs) belong to a class of materials with two unique features, the coupled spin-valley-layer degrees of freedom and the crystal structure that is globally centrosymmetric but locally noncentrosymmetric. In this Letter, we will show that the combination of these two features can lead to a rich phase diagram for unconventional superconductivity, including intralayer and interlayer singlet pairings and interlayer triplet pairings, in bilayer superconducting TMDs. In particular, we predict that the inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov state can exist in bilayer TMDs under an in-plane magnetic field. We also discuss the experimental relevance of our results and possible experimental signatures.