Thermal conductivity of Mg(B0.94C0.06)2 superconductors: role of carrier and lattice–impurity scattering

Abstract

We use the Kubo model to calculate the lattice contribution to the thermal conductivity (κph) in Mg(B0.94C0.06)2 superconductors. The theory is formulated when heat transfer is limited by the scattering of phonons from defects, grain boundaries, charge carriers and phonons. Later on, the carrier (electron) contribution to the thermal conductivity (κe) is calculated within relaxation time approximation for π and σ band carriers with s-wave symmetry. Such an estimate sets an upper bound on κe and a very small contribution is seen for total heat transfer at room temperature. Both these channels for heat transfer are clubbed and κtot develops a broad peak before falling off at higher temperatures weakly in MgB2. The substitution of 6% carbon-doped MgB2 results in a considerable reduction of κph and κe at low temperatures, in the vicinity as well as above transition temperature. The contribution of carriers towards κ (T) is negligible and is due to the fact that the carriers are condensed and do not carry entropy.