Electrostatically induced phase transitions in superconducting complex oxides

We describe quantum phase transitions in superconducting complex oxides which could be tuned by electrostatic charge transfer. Using a simple model for the superconductivity of a thin film or surface of a bulk copper oxide, we show that tuning the carrier density may allow the visitation of several superconducting phases with different pairing symmetries such as extended $s$- $(se)$, $d$- and $(se \pm id)$-wave. We construct a universal phase diagram for single-band superconductors with $se$- and d-wave components of the order parameter based on symmetry considerations alone. For a specific model with nearest neighbor attraction, we obtain the phase diagram in the interaction versus filling factor space showing the boundaries of the possible phases. Finally, we calculate the superfluid density and penetration depth as characteristic properties of each phase.