Effects of interlayer interactions on the critical temperature of high-Tccompounds

Abstract

We show that the dependence of $T_c$ on the number of layers in the unit cell of high-$T_c$ Thallium compounds is quantitatively explained within the BCS framework, irrespective of the precise mechanism responsible for pairing. The intraplanar pairing is augmented by a weak interplanar scattering of the pair, thereby enhancing the $T_c$ of layered compounds without increasing either the density of states or the number of carriers per ${\mathrm{CuO}}_2$ plane. The origin of the interplanar coupling is investigated and implications of the present model to other high-$T_c$ materials (bismuth and yttrium compounds) are discussed.