On the relation between (maximum) critical temperature and c-axis layered structure in cuprates. (I). Evaluation of existing analyses

The present paper is the first part of an analysis aimed at an explanation of the observed relation between maximum critical temperature TC(n) and number n of CuO2 layers, per molecular unit, in the three cuprate series Tl2(n), Bi2(n) and Hg(n). We scrutinize relevant models proposed in the literature based on (A) Anderson et al.ʹs interlayer tunneling (ILT) approach, (B) the Lawrence–Doniach (LD) version of Ginzburg–Landau (GL) phenomenology of phase transitions, (C) a recent scenario for high-temperature superconductivity proposed by Leggett, and (D) the effect of different doping of non-equivalent CuO2 layers (n 3). It is established that models A–C inevitably lead to an asymptotically increasing TC(n) with the number of layers, in contrast with the observed pronounced maximum at n=3. Regarding the effect of differently doped non-equivalent CuO2 layers, the available analyses lead to results which are either non-committal, inapplicable, or highly speculative.