Orbital Fulde-Ferrell-Larkin-Ovchinnikov state in an Ising superconductor

In superconductors possessing both time and inversion symmetries, the Zeeman effect of an external magnetic field can break the time-reversal symmetry, forming a conventional Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state characterized by Cooper pairings with finite momentum(1,2). In superconductors lacking (local) inversion symmetry, the Zeeman effect may still act as the underlying mechanism of FFLO states by interacting with spin-orbit coupling (SOC). Specifically, the interplay between the Zeeman effect and Rashba SOC can lead to the formation of more accessible Rashba FFLO states that cover broader regions in the phase diagram(3-5). However, when the Zeeman effect is suppressed because of spin locking in the presence of Ising-type SOC, the conventional FFLO scenarios are no longer effective. Instead, an unconventional FFLO state is formed by coupling the orbital effect of magnetic fields with SOC, providing an alternative mechanism in superconductors with broken inversion symmetries(6-8). Here we report the discovery of such an orbital FFLO state in the multilayer Ising superconductor 2H-NbSe2. Transport measurements show that the translational and rotational symmetries are broken in the orbital FFLO state, providing the hallmark signatures of finite-momentum Cooper pairings. We establish the entire orbital FFLO phase diagram, consisting of a normal metal, a uniform Ising superconducting phase and a six-fold orbital FFLO state. This study highlights an alternative route to achieving finite-momentum superconductivity and provides a universal mechanism to preparing orbital FFLO states in similar materials with broken inversion symmetries.