A set of generalized-BCS equations (GBCSEs) was recently derived from a temperature-dependent Bethe-Salpeter equation and shown to deal satisfactorily with the experimental data comprising the Tcs and the multiple gap...A set of generalized-BCS equations (GBCSEs) was recently derived from a temperature-dependent Bethe-Salpeter equation and shown to deal satisfactorily with the experimental data comprising the Tcs and the multiple gaps of a variety of high-temperature superconductors (SCs). These equations are formulated in terms of the binding energies W1(T),W2(T),… of Cooper pairs (CPs) bound via one- and more than one-phonon exchange mechanisms;they contain no direct reference to the gap/s of an SC. Applications of these equations so far were based on the observation that for elemental SCs |W01|=△0 at T = 0 inthe limit of the dimensionless BCS interaction parameter λ→0. Here △0 is the zero-temperature gap whence it follows that the binding energy of a CP bound via one-phonon exchanges at T = 0 is 2|W01|. In this note we carry out a detailed comparison between the GBCSE-based W1(T) and the BCS-based energy gap △(T) for all 0≤T≤Tc and realistic, non-vanishingly-small values of λ. Our study is based on the experimental values of Tc Debye temperature , and ?0 of several selected elements including the “bad actors” such as Pb and Hg. It is thus established that the equation for W1(T) provides a viable alternative to the BCS equation for △(T). This suggests the use of, when required, the equation for W2(T) which refers to CPs bound via two-phonon exchanges, for the larger of the two T-dependent gaps of a non-elemental SC. These considerations naturally lead one to the concept of T-dependent interaction parameters in the theory of superconductivity. It is pointed out that such a concept is needed both in the well-known approach of Suhl et al. to multi-gap superconductivity and the approach provided by the GBCSEs. Attention is drawn to diverse fields where T-dependent Hamiltonians have been fruitfully employed in the past.展开更多
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 h...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.展开更多
文摘A set of generalized-BCS equations (GBCSEs) was recently derived from a temperature-dependent Bethe-Salpeter equation and shown to deal satisfactorily with the experimental data comprising the Tcs and the multiple gaps of a variety of high-temperature superconductors (SCs). These equations are formulated in terms of the binding energies W1(T),W2(T),… of Cooper pairs (CPs) bound via one- and more than one-phonon exchange mechanisms;they contain no direct reference to the gap/s of an SC. Applications of these equations so far were based on the observation that for elemental SCs |W01|=△0 at T = 0 inthe limit of the dimensionless BCS interaction parameter λ→0. Here △0 is the zero-temperature gap whence it follows that the binding energy of a CP bound via one-phonon exchanges at T = 0 is 2|W01|. In this note we carry out a detailed comparison between the GBCSE-based W1(T) and the BCS-based energy gap △(T) for all 0≤T≤Tc and realistic, non-vanishingly-small values of λ. Our study is based on the experimental values of Tc Debye temperature , and ?0 of several selected elements including the “bad actors” such as Pb and Hg. It is thus established that the equation for W1(T) provides a viable alternative to the BCS equation for △(T). This suggests the use of, when required, the equation for W2(T) which refers to CPs bound via two-phonon exchanges, for the larger of the two T-dependent gaps of a non-elemental SC. These considerations naturally lead one to the concept of T-dependent interaction parameters in the theory of superconductivity. It is pointed out that such a concept is needed both in the well-known approach of Suhl et al. to multi-gap superconductivity and the approach provided by the GBCSEs. Attention is drawn to diverse fields where T-dependent Hamiltonians have been fruitfully employed in the past.
文摘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.
