Inhomogeneous superconducting states and umklapp processes in ferromagnet/superconductor nanostructures

Abstract We derive a new boundary-value problem (BVP) for the ferromagnetic metal/superconductor (FM/S) nanostructures, where superconductivity is a superposition of the BCS pairing with zero total momentum in the S layers and the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) pairing with nonzero 3D coherent momentum k in the FM layers. It is shown that the processes of mutual transformation between BCS and FFLO pairs at the FM/S boundary are the umklapp processes during which coherent pair momentum k becomes confined in the FM layer. We originally investigate the interplay between the BCS and 3D FFLO states in the pure FM/S bilayers. This competition leads to a partial compensation of the exchange field paramagnetic effect.