Theory of coexistence of superconductivity and ferroelectricity: A dynamical symmetry model

We propose and investigate a model for the coexistence of superconductivity (SC) and ferroelectricity (FE) based on the dynamical symmetries su(2) for the (pseudospin) SC sector h(4) for the (displaced oscillator) FE sector and su(2) ⊗ h(4) for the composite system. We assume a minimal symmetry-allowed coupling and simplify the Hamiltonian using a double mean-field approximation. A variational coherent-state trial wave function is used for the ground state: the energy and the relevant order parameters for SC and FE are obtained. For positive sign of the SC-FE coupling coefficient, a nonzero value of either order parameter can suppress the other one (FE polarization suppresses SC and vice versa). This gives some support to the "Matthias' conjecture," that SC and FE tend to be mutually exclusive. For such a ferroelectric superconductor we predict that (a) the SC gap Δ (and T_c) will increase with increasing applied pressure when pressure quenches FE, as in many ferroelectrics, and (b) the FE polarization →P will increase with increasing applied magnetic field up to H_c, which is equivalent to the prediction of a new type of magnetoelectric effect in a coexistent SC-FE material. Some discussion will be given of possible relation of these results to the cuprate superconductors.