Mechanisms of heat conductivity in high-Tcsuperconductors

A phenomenological approach to the heat conductivity κ in the mixed state of a high-${\mathit{T}}_{\mathit{c}}$ superconductor is proposed, which permits resolution between the electronic and phononic contributions, ${\mathrm{\kappa }}_{\mathrm{el}}$ and ${\mathrm{\kappa }}_{\mathrm{ph}}$. The scattering amplitude for bandlike quasiparticles vs bound states in the vortex cores has been microscopically estimated. The measurements of the in-plane thermal conductivity κ(B,T) of single crystals ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ and ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_8$ have been performed at several temperatures T from 4 to 110 K and magnetic fields B (along the c axis) up to 11 T. From comparison of experimental data with the phenomenologic model, the ratio ${\mathrm{\kappa }}_{\mathrm{el}}$/${\mathrm{\kappa }}_{\mathrm{ph}}$ (at B=0) has been extracted. This analysis shows that only ${\mathrm{\kappa }}_{\mathrm{el}}$ is field sensitive and it is mostly responsible for the maximum of κ vs T, observed at B=0 in both materials.