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 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 complete summary of parameters that quantitatively account for the Tc and the gaps of MgB2 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) kMgB2 is calculated for both—the scenario in which the two gaps of MgB2 close/do not close at the same temperature whence it is found that 2) the latter scenario yields results in better agreement with experiment.
Highlights
Thermal conductivity (κ) of a superconductor (SC) is an important parameter from the point of view of applications; it helps in the theoretical understanding of the superconducting state [1]
We address the experimental data on the thermal conductivity of MgB2 obtained by Bauer (B) et al [7], and by Schneider (S) et al [8], in an approach that supplements the G [4] and the Geilikman and Kresin (GK) [5] equations by the recently derived generalized BCS equations (GBCSEs) [9]
For a detailed discussion of how the SMW approach implies such dependence of the interaction parameters, we refer the reader to [17], where it is noted that the requirement of closure of both the gaps in MgB2 is met by replacing λ1c and λ2c above as follows: λ1c → λ1c (T ) = λ1c + α1T, α1 = 1.7923×10−3 K−1 (8)
Summary
Thermal conductivity (κ) of a superconductor (SC) is an important parameter from the point of view of applications; it helps in the theoretical understanding of the superconducting state [1]. We give an account of GBCSEs and the G and the GK equations which form our framework Since it was reported in [13] that both the gaps of MgB2 close at about 40 K, we consider in Section 3 the experimental data of both the B [7] and the S [8] groups in this scenario (Scenario 1). For a detailed discussion of how the SMW approach implies such dependence of the interaction parameters, we refer the reader to [17], where it is noted that the requirement of closure of both the gaps in MgB2 is met by replacing λ1c and λ2c above as follows: λ1c → λ1c (T ) = λ1c + α1T , α1 = 1.7923×10−3 K−1 (8).
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