Thermal conductivity of superconductingBi2Sr2CaCu2O8andYBa2Cu3O7−y

Allen et al. [Phys. Rev. B 49, 9073 (1994)] have considered the thermal conductivity in a metallic superconductor ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_8$ and an insulating parent ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{YCu}}_2$ ${\mathrm{O}}_8$. Allen et al. have stressed that the theory of the thermal conductivity of high-${\mathit{T}}_{\mathit{c}}$ superconductors should account for the fact that the peak observed in ${\mathrm{\kappa }}_{\mathit{a}\mathit{b}}$(T) should be more pronounced in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ than in ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_8$. We have performed calculations of the electronic component of the thermal conductivity of such high-${\mathit{T}}_{\mathit{c}}$ compounds using a variational method. We have considered elastic scattering of electrons by impurities as well as elastic and inelastic scattering of electrons by acoustic phonons. We have used a two-dimensional density of states and an anisotropic electron spectrum with a Josephson-like coupling J between the superconducting planes to better describe 2D-like systems. We show the J dependence of the thermal conductivity and conclude that the different behavior of the thermal conductivity in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ and in ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_8$, i.e., the less pronounced peak in ${\mathrm{\kappa }}_{\mathit{a}\mathit{b}}$ in the latter system, should be due mainly to the more pronounced layered structure and is indeed of electronic origin.