NMR study of the Superconducting gap variation near the Mott transition in Cs$_{3}$C$_{60}$

Former extensive studies of superconductivity in the \textit{A}$_{3}$C$_{60}$ compounds, where \textit{A} is an alkali, have led to consider that Bardeen Cooper Schrieffer (BCS) electron-phonon pairing prevails in those compounds, though the incidence of electronic Coulomb repulsion has been highly debated. The discovery of two isomeric fulleride compounds Cs$_{3}$C$_{60}$ which exhibit a transition with pressure from a Mott insulator (MI) to a superconducting (SC) state clearly re-opens that question. Using pressure ($p$) as a single control parameter of the C$_{60}$ balls lattice spacing, one can now study the progressive evolution of the SC properties when the electronic correlations are increased towards the critical pressure $p_{c}$ of the Mott transition. We have used $^{13}$C and $^{133}$Cs NMR measurements on the cubic phase A15-Cs$_{3}$C$_{60}$ just above $p_{c}=5.0(3)$ kbar, where the SC transition temperature $T_{c}$ displays a dome shape with decreasing cell volume. From the $T$ dependence below $T_{c}$ of the nuclear spin lattice relaxation rate $(T_{1})^{-1}$ we determine the electronic excitations in the SC state, that is $2\Delta$, the SC gap value. We find that $2\Delta$ increases with decreasing $p$ towards $p_{c}$, where $T_{c}$ decreases on the SC dome, so that $2\Delta /k_{B}T_{c}$ increases regularly upon approaching the Mott transition. These results bring clear evidence that the increasing correlations near the Mott transition are not significantly detrimental to SC. They rather suggest that repulsive electron interactions might even reinforce elecron-phonon SC, being then partly responsible for the large $T_{c}$ values, as proposed by theoretical models taking the electronic correlations as a key ingredient.