Universal c-axis conductivity of high-$T_c$ oxides in the superconducting state

Abstract

The anisotropy in the temperature dependence of the in-plane and c-axis conductivities of high-T_c cuprates in the superconducting state is shown to be consistent with a strong in-plane momentum dependence of both the quasiparticle scattering rate and the interlayer hopping integral. Applying the cold spot scattering model recently proposed by Ioffe and Millis (Phys. Rev. B {\bf 58}, 11631 (1998)) to the superconducting state, we find that the c-axis conductivity varies approximately as T^3 in an intermediate temperature regime, in good agreement with the experimental result for optimally doped YBa_2Cu_3O_{7-x} and Bi_2Sr_2CaCu_2O_{8+x}.