Thermal conductivity of MgB 2 in the superconducting state

We present thermal conductivity measurements on very pure and dense bulk samples, as indicated by residual resistivity values as low as $0.5\ensuremath{\mu}\ensuremath{\Omega}\mathrm{cm}$ and thermal conductivity values higher than 200 W/mK. In the normal state we found that the Wiedemann-Franz law, in its generalized form, works well suggesting that phonons do not contribute to the heat transport. The thermal conductivity in the superconducting state has been analyzed by using a two-gap model. Thanks to the large gap anisotropy we were able to evaluate quantitatively intraband scattering relaxation times of $\ensuremath{\pi}$ and $\ensuremath{\sigma}$ bands, which depend on the disorder in different way; namely, as the disorder increases, it reduces more effectively the relaxation times of $\ensuremath{\pi}$ than that of $\ensuremath{\sigma}$ bands, as suggested by a recent calculation [Mazin et al., Phys. Rev. Lett. 89, 107002 (2002)].