Thermal Conductivity of Superconducting MgB₂

Abstract

Employing the Geilikman-Kresin (GK) theory, we address the experimental data obtained by Bauer et al ., and by Schneider et al ., on the thermal conductivity ( κ ) of superconducting MgB 2 . The two gaps of this compound have qualitatively been understood via the well-known Suhl, Matthias, and Walker’s (SMW) approach to multi gap superconductivity. Since this approach is based on one -phonon exchange mechanism for the formation of Cooper pairs, it cannot give a quantitative account of the values of T c and the multiple gaps that characterize MgB 2 and other high- T c superconductors (SCs). Despite this fact and some rather ambiguous features, it has been pointed out in a recent critical review by Malik and Llano (ML) that the SMW approach provides an im portant clue to deal with an SC the two gaps of which close at the same T c : consider the possibility of the interaction parameters in the theory to be temperature-dependent. Guided by this clue, ML gave a complete summary of parameters that quantitatively account for the T c and the gaps of MgB 2 via the generalized BCS equations (GBCSEs). GBCSEs which we recall, invoke multi-phonon exchange mechanism for the formation of Cooper pairs and multiple Debye temperatures to deal with composite SCs. The parameter-values given in ML are used here to calculate the temperature-dependent gaps, which are an essential input for the GK theory. Notable features of this work are: 1 ) k MgB 2 is calculated for both—the scenario in which the two gaps of MgB 2 close/do not close at the same temperature whence it is found that 2 ) the latter scenario yields result s in better agreement with experiment.