Electronic instabilities at paraelectric and superconducting interface: A mean field approach*

We examine the modified electronic states at the interface between superconducting and ferro(para)-electric films. We find that the coupling of a classical fluctuating paraelectric $P$ and superconducting $\psi$ order parameters can significantly modify these orders at the interface. Using a Ginzburg-Landau formalism, we show that linear and quadratic terms of the electric polarization produce instabilities in $\psi$ at the interface, where the linear interaction produces a modulation of the order parameters and create an interface-induced ferroelectric polarization within the paraelectric bulk state. We will discuss implications of this work for the experiments on the epitaxial oxide films.