Orbital-FFLO State and Josephson Vortex Lattice Melting in Layered Ising Superconductors

This study explores the impact of in-plane magnetic fields on the superconducting state in layered Ising superconductors, resulting in the emergence of the orbital Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state coupled with Josephson vortices. Recent experiments have revealed an unexpected first-order phase transition in these superconductors under strong in-plane magnetic fields. Our theoretical analysis demonstrates that this phase transition is primarily driven by the formation and subsequent melting of a Josephson vortex lattice within the superconducting layers. As the magnetic field increases, the vortex lattice undergoes a transition from a solid to a liquid state, triggering the observed first-order phase transition. We calculate both the melting line and the in-plane critical field in the phase diagram, showing strong agreement with experimental results.