Journal of Low Temperature Physics, Vol. 99, Nos. 3/4, 1995 Electrodynamic Response in Cuprate Superconductors M. J. Graf and M. Palumbo Physikalisches Institut, Universit?it Bayreuth, D-95440 Bayreuth, Germany We present results from a microscopic theory of the electrodynamic response (Bile) in high-To superconductors for an array of coupled superconducting layers. In this model each layer is described by a two-dimensional Fermi liquid, and interlayer coupling is mediated by thermally activated incoherent scattering processes. We discuss the surface resistance in the c-direction and show that a d-state symmetry of the order parameter leads to an anomalous T-dependence at frequencies below Ao, and imposes rather stringent conditions on the interlayer coupling. PACS numbers: 7~.20.Mn, 74.80.Dm, 7~.25.Fy, 7~.ZS.Nf, 7~.72.-h An unresolved problem in high-To cuprate superconductors is the symmetry of the order parameter. Many experiments can be explained by the d-wave pai- ring model of superconductivity, e.g., anomalous temperature dependences of the penetration depths and NMR relaxation rates, an apparent gapless behavior, and Josephson interference experiments3 On the other hand, measurements of the tun- neling supercurrents in the c-direction seem to contradict the d-wave model, 2 since this model would lead to a vanishing losephson current along the c-axis. We are interested in the linear response of a homogeneous, layered supercon- ductor to a weak, electric field polarized in the c-direction, E~ = -~O~Az(t). We perform our calculations within the model of incoherently coupled two-dimensional Fermi liquids (interlayer diffusion model). 3,4 In this model, the in-plane conducti- vity is of the usual Fermi liquid type, while the c-axis conductivity originates from incoherent scattering processes, i.e. we neglect coherent propagation along the c- axis. The in-plane conductivity therefore possesses the usual Drude behavior in the normal state, with a d.c. value ~l[ c< 7]f for weak interlayer coupling, whereas the c-axis conductivity is of a diffusive nature, ~• ~ r~ 1, and is suppressed at low temperatures. For simplicity, we assume a cylindrical Fermi surface. The in-plane scatte- ring is taken to be isotropic and is parameterized by a pair breaking parameter, c~ = h/27rkBTcoT]l , and a normalized cross-section, 6~, ranging from 0 (Born limit) to 1 (unitarity limit). 5 Elastic in-plane scattering is formulated in the t-matrix approximation. In this way, the self-energy covers impurity scattering, including 283 0022-2291/95/0500-0283507.50/0 9 1995 Plenum Publishing Corporation