Theory of coexistence of superconductivity and ferroelectricity

An investigation of the coexistence and competition of ferroelectricity and superconductivity is reported. We show that the starting Hamiltonian of a previous study by Birman and Weger [Phys. Rev. B 64, 174503 (2001)] can be exactly diagonalized. The result differs significantly from mean-field theory. A Hamiltonian with a different realization of the coupling between ferroelectricity and superconductivity is proposed. We report the results for mean-field theory applied to this Hamiltonian. We find that the order parameters are strongly affected by this coupling. The "Matthias conjecture" that each of these order parameters tends to suppress the other is supported by our results.