Enhancing of the in-plane FFLO-state critical temperature in heterostructures by the orbital effect of the magnetic field

It is well-known that the orbital effect of the magnetic field suppresses superconducting $T_c$. We show that for a system, which is in the Larkin–Ovchinnikov–Fulde–Ferrell (FFLO) state at zero external magnetic field, the orbital effect of an applied magnetic field can lead to the enhancement of the critical temperature higher than $T_c$ at zero field. We concentrate on two systems, where the in-plane FFLO-state was predicted recently. These are equilibrium $S/F$ bilayers and $S/N$ bilayers under nonequilibrium quasiparticle distribution. However, it is suggested that such an effect can take place for any plane superconducting system, which is in the in-plane FFLO-state (or is close enough to it) at zero applied field.