INTRALAYER AND INTERLAYER SPIN-SINGLET PAIRING AND ENERGY-GAP FUNCTIONS WITH DIFFERENT POSSIBLE SYMMETRIES IN HIGH-T-C LAYERED SUPERCONDUCTORS

Anisotropy and the wave-vector dependence of the energy gap function d etermine many important properties of a superconductor. Stal ting from fist principles, we present here a complete analysis of possible symm etries of the superconducting gap function E-g(k) at the Fermi surface in high-T-c layered superconductors with either a simple orthorhombic or a tetragonal unit cell. This is done within the framework of Gorko v's mean-held theory of superconductivity in the so-called ''layer rep resentation'' introduced by us earlier. For N conducting cuprate layer s. J = 1,2,...,N, in each unit cell, the spin-singlet order parameters Delta(JJ')(k) can be expanded in terms of possible basis functions of all the irreducible representations relevant to layered crystals, whi ch are obtained here. In layered materials, the symmetry is restricted to the translational lattice periodicity in the direction perpendicul ar to the layers and the residual point group and translational symmet ries for the two-dimensional unit cell in each layer of the three-dime nsional unit cell. We derive an exact general relation to determine di fferent branches of the energy gap function E-g(k) at the Fermi surfac e in terms of Delta(JJ')(k), which include both intralayer and interla yer order parameters. For N = 2, we also obtain an exact expression fo r quasiparticle energies E-p(k), p = 1,2. in the superconducting state in the presence of intralayer and complex interlayer order parameters as well as complex tunneling matrix elements between the two layers i n the unit cell, which need not be equivalent. The form of the possibl e basis functions are also listed in terms of cylindrical coordinates k(t),phi,k(z) to take advantage of the orthogonality of functions with respect to phi integrations. In layered materials, with open Fermi su rfaces in the k(z) direction, there is orthogonality of basis function s with respect to k(z) also (-pi less than or equal to k(z)d less than or equal to pi). Our results show that in orthorhombic systems, plana r d(kx2-ky2)-like (B-1g) and d(kxky)-like (B-2g) symmetries are always mixed, respectively, with the planar s-wave-like (A(1g)) and A(2g)-li ke symmetries of the corresponding tetragonal system. There is also th e possibility of a weak modulation of E-g(k) as a function of k(z)(sim ilar to cos k(z)d). In addition, in the presence of interlayer pairing s which may or may not have the same symmetry as the intralayer order parameters, even in tetragonal systems the nodes of the d(kz2-ky2)-lik e intralayer gap function will be shifted. In view of this, some sugge stions for analyzing experimental data are also presented.