In-plane thermal conductivity and Lorenz number in YBa2Cu3O7−y

We make a tentative proposal to extract the electronic contribution to the in-plane thermal conductivity ${\kappa }_{\mathrm{el}}\mathrm{}\left(T\right)\mathrm{}$ of YBa${}_2$Cu${}_3$O${}_{7-y}$ in the normal state. We have measured ${\kappa }_{\mathrm{ab}}\mathrm{}\left(T\right)\mathrm{}$ for single crystals with various oxygen contents $(6.06\mathrm{}<~$ 7$-y$ $<~6.93)$. The systematic study of the oxygen-content dependence of ${\kappa }_{\mathrm{ab}}$ for the insulating phase enables us to estimate the phononic contribution ${\kappa }_{\mathrm{ph}}\mathrm{}\left(T\right)\mathrm{}$ for the metallic phase to some extent. Based on the estimated ${\kappa }_{\mathrm{ph}},$ we examined ${\kappa }_{\mathrm{el}}$ from the view point of whether the Wiedemann-Franz law holds or not. The estimated ${\kappa }_{\mathrm{el}}$ appears to show only a weak $T$ dependence and no significant change at a characteristic temperature $T^{*}$ below which the electrical conductivity ${\sigma }_{\mathrm{ab}}\mathrm{}\left(T\right)\mathrm{}$ is enhanced possibly due to the opening of a spin gap. The difference between ${\kappa }_{\mathrm{el}}$ and ${\sigma }_{\mathrm{ab}}$ suggests the violation of the Wiedemann-Franz law below $T^{*}$. We discussed the ambiguity of our analyses and other possible interpretations of the present result as well as the picture of the charge transport speculated from the above suggestion.