Orbital effect induced finite-momentum pairing and Josephson vortex lattice melting in layered Ising superconductors

The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is a fascinating superconducting phase characterized by a spatially modulated order parameter that occurs in unconventional superconductors under strong magnetic fields. In this study, we explore the impact of in-plane magnetic fields on the superconducting state in layered Ising superconductors. Our findings reveal the emergence of an orbital-effect-induced finite-momentum pairing state, which is coupled to Josephson vortices and is fundamentally different from the FFLO state. Notably, recent experiments have revealed an unexpected first-order phase transition in bulk Ising superconductors. Our theoretical analysis demonstrates that this phase transition is primarily driven by the melting of a Josephson vortex lattice. Furthermore, our calculations for both the in-plane upper critical field and the melting line are in excellent agreement with the experimental data. These results not only advance the understanding of novel field-induced phases in layered Ising superconductors, but also pave the way for controlling these exotic states through magnetic field manipulation.