Superconducting order parameter symmetry in multilayer cuprates

We classify the allowed order parameter symmetries in multilayer cuprates and discuss their physical consequences, with emphasis on Josephson tunneling and impurity scattering. Our solutions to the gap equation are based on highly nonspecific forms for the inter- and intraplane pairing interactions in order to arrive at the most general conclusions. Within this framework, the bilayer (N=2) case is discussed in detail with reference to Y-Ba-Cu-O (YBCO) and Bi-Sr-Ca-Cu-O (BSCCO) and the related Landau-Ginzburg free energy functional. Particular attention is paid to the role of small orthorhombic distortions as would derive from the chains in YBCO and from superlattice effects in BSCCO, which give rise to a rich and complex behavior of the multilayer order parameter. This order parameter has N components associated with each of the N bands or layers. Moreover, these components have specific phase relationships. In the orthorhombic bilayer case the (s,-s) state is of special interest, since for a wide range of phase space, this state exhibits π phase shifts in corner Josephson junction experiments. In addition, its transition temperature is found to be insensitive to nonmagnetic interplane disorder, as would be present at the rare earth site in YBCO, for example. Of particular interest, also, are the role of van Hove singularities which are seen to stabilize states with ${\mathit{d}}_{{\mathit{x}}^2\mathrm{-}{\mathit{y}}^2}$-like symmetry (as well as nodeless s states) and to elongate the gap functions along the four van Hove points, thereby leading to a substantial region of gaplessness. We find that for these rather general models of the pairing interaction the ${\mathit{d}}_{{\mathit{x}}^2\mathrm{-}{\mathit{y}}^2}$-like states are the most stable solutions in a large region of parameter space. In this way, they should not be specifically associated with a spin fluctuation driven pairing mechanism. © 1996 The American Physical Society.