On the relation between (maximum) critical temperature and c-axis layered structure in cuprates

In this paper, we continue, from Physica A 289 (2001) 165, the analysis of the relation between maximum critical temperatures of the oxygen-doped high-temperature superconducting cuprates Hg(n),Tl2(n) and Bi2(n) and the number n of CuO2 layers per molecular unit, on the basis of a model of indirect-exchange pairing between conduction electrons (quasiparticles) via oxygen anions as the origin of Cooper-pair formation, previously used in numerous applications. A separability property of the coupling strength essentially simplifies the analysis. Numerical results are presented for the Hg(n) series with n=1–7. Since the equation determining these maximum TC's, as a function of n, cannot be solved directly, we take a detour via an associated series obtained formally from the oxygen-doped systems by subsequent selective cation doping. Relations between the two series then enable conclusions to be drawn concerning the dependence on n of maximum critical temperatures for the oxygen-doped systems. It is found conclusively, in agreement with experiment, that TC(n) reaches a maximum at n=3, deviating qualitatively from an asymptotic n-dependence as proposed in many earlier analyses. We also elucidate the cause of the deviating behavior of the cuprate series Tl1(n), i.e., nominally Tl1Ba2Can−1CunO2n+3, where the maximum occurs at n=4, in the framework of indirect-exchange pairing.