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Induced polarization at a paraelectric/superconducting interface

We examine the modified electronic states at the interface between superconducting and ferro(para)-electric heterostructures. We find that electric polarization $P$ and superconducting $ψ$ order parameters can be significantly modified due to coupling through linear terms brought about by explicit symmetry breaking at the interface. Using an effective action and a Ginzburg-Landau formalism, we show that an interaction term linear in the electric polarization will modify the superconducting order parameter $ψ$ at the interface. This also produces modulation of a ferroelectric polarization. It is shown that a paraelectric-superconductor interaction will produce an interface-induced ferroelectric polarization.