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

Abstract

The present paper is the first part of an analysis aimed at an explanation of the observed relation between maximum critical temperature T C ( n) and number n of CuO 2 layers, per molecular unit, in the three cuprate series Tl 2( n), Bi 2( n) and Hg( n). We scrutinize relevant models proposed in the literature based on (A) Anderson et al.'s 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 CuO 2 layers ( n⩾3). It is established that models A–C inevitably lead to an asymptotically increasing T C ( n) with the number of layers, in contrast with the observed pronounced maximum at n=3. Regarding the effect of differently doped non-equivalent CuO 2 layers, the available analyses lead to results which are either non-committal, inapplicable, or highly speculative.