  Despite almost 40 years of research, the origin of heavy-fermion
superconductivity is still strongly debated. Especially, the pressure-induced
enhancement of superconductivity in CeCu$_2$Si$_2$ away from the magnetic
breakdown is not sufficiently taken into consideration. As recently reported in
CeCu$_2$Si$_2$ and several related compounds, optimal superconductivity occurs
at the pressure of a valence crossover, which arises from a virtual critical
end point at negative temperature $T_{\rm cr}$. In this context, we did a
meticulous analysis of a vast set of top-quality high-pressure electrical
resistivity data of several Ce-based heavy fermion compounds. The key novelty
is the salient correlation between the superconducting transition temperature
$T_{\rm c}$ and the valence instability parameter $T_{\rm cr}$, which is in
line with theory of enhanced valence fluctuations. Moreover, it is found that,
in the pressure region of superconductivity, electrical resistivity is governed
by the valence crossover, which most often manifests in scaling behavior. We
develop the new idea that the optimum superconducting $T_{\rm c}$ of a given
sample is mainly controlled by the compound's $T_{\rm cr}$ and limited by
non-magnetic disorder. In this regard, the present study provides compelling
evidence for the crucial role of critical valence fluctuations in the formation
of Cooper pairs in Ce-based heavy fermion superconductors besides the
contribution of spin fluctuations near magnetic quantum critical points, and
corroborates a plausible superconducting mechanism in strongly correlated
electron systems in general.
