Valence Fluctuation Driven Non-Fermi LIquid Behavior and Unconventional Superconductivity in Pressurized CeCu_{2}Si_{2}

I study an Extended Periodic Anderson Model (EPAM) with non-local hybridisation, $V_{fc}$, and a coulomb interaction, $U_{fc}$, between localised $f$ electrons and wide band conduction ($c$) electrons. Within DMFT, a quantum phase transition (QPT) driven by soft $f$-valence fluctuations, accompanied by a discontinuous jump in the Fermi volume, is found as $V_{fc}$ is tuned across a critical value. Near the associated QCP, an unconventional superconductive instability, driven by these extended, singular valence fluctuations, naturally emerges. {\it All} these phenomena are representative of observations in pressurised $CeCu_{2}Si_{2}$.