Why there is a difference between optimal doping for maximal and critical doping for highest in cuprate superconductors?

A long-standing puzzle is why there is a difference between the optimal doping δ optimal ≈ 0.15 for the maximal superconducting (SC) transition temperature T c and the critical doping δ critical ≈ 0.19 for the highest superfluid density ρ s in cuprate superconductors? This puzzle is calling for an explanation. Within the kinetic energy driven SC mechanism, it is shown that except the quasiparticle coherence, ρ s is dominated by the bare pair gap, while T c is set by the effective pair gap. By calculation of the ratio of the effective and the bare pair gaps, it is shown that the coupling strength decreases with increasing doping. This doping dependence of the coupling strength induces a shift from the critical doping for the maximal value of the bare pair gap parameter to the optimal doping for the maximal value of the effective pair gap parameter, which leads to a difference between the optimal doping for the maximal T c and the critical doping for the highest ρ s .