Hole density dependence of the critical temperature and coupling constant in the cuprate superconductors

A bond valence sum (BVS) analysis was performed for the p-type cuprate superconductors. The superconducting critical temperature T(c) versus in-plane Cu-O BVS correlation for copper is grouped into classes and subclasses. Only within a class or subclass for which the nonelectronic effect is constant does the variation of the in-plane Cu-O BVS reflect the corresponding change in the hole density n(H) of the CuO(2) layers. This study strongly suggests that the T(c) for every class or subclass of the superconductors is an inverted parabolic function of n(H), and so is the coupling constant lambda for Cooper pair formation.