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

Author-Highlights
• We show why there is a difference between the optimal doping and critical doping.
• TcTc is set by the effective pair gap and quasiparticle coherence in cuprate superconductors.
• The superfluid density is dominated by the bare pair gap and quasiparticle coherence.
• The coupling strength decreases with increasing doping.

A long-standing puzzle is why there is a difference between the optimal doping  δoptimal≈0.15δoptimal≈0.15 for the maximal superconducting (SC) transition temperature TcTc and the critical doping  δcritical≈0.19δcritical≈0.19 for the highest superfluid density ρsρs 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, ρsρs is dominated by the bare   pair gap, while TcTc 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 TcTc and the critical doping for the highest ρsρs.