Modelling the electric field effect in superconducting films

We present a phenomenological model of periodic ferroelectric-superconductor (FE-S) heterostructures containing two alternating ferroelectric and superconducting layers. The interaction at the FE-S contacts is described as a coupling of the local carrier density of the superconductor with the spontaneous ferroelectric polarization near the FE-S interface. For the stronger coupling, we find a stable symmetric domain-type phase exhibiting the ferroelectric domain structure. With a further increase of the coupling energy, we obtain the complete suppression of the superconducting state in the S-film. The behavior of the system is discussed for different thicknesses of the S-films.