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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 MgB2. The two gaps of this compound have qualitatively been understood via the well-known Suhl, Matthias, and Walker’s (SMW) approach to multigap 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 Tc and the multiple gaps that characterize MgB2 and other high-Tc 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 important clue to deal with an SC the two gaps of which close at the same Tc: consider the possibility of the interaction parameters in the theory to be temperature-dependent. Guided by this clue, ML gave a
Recasting the BCS theory in the larger framework of the Bethe-Salpeter equation, a new equation is derived for the temperature-dependent critical current density jc(T) of an elemental superconductor (SC) directly in terms of the basic parameters of the theory, namely the dimensionless coupling constant [N(0)V], the Debye temperature θD and, additionally, the Fermi energy EF—unlike earlier such equations based on diverse, indirect criteria. Our approach provides an ab initio theoretical justification for one of the latter, text book equations invoked at T = 0 which involves Fermi momentum; additionally, it relates jc with the relevant parameters of the problem at T ≠ 0. Noting that the numerical value of EF of a high-Tc SC is a necessary input for the construction of its Fermi surface—which sheds light on its gap-structure, we also briefly discuss extension of our approach for such SCs.