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On a New Equation for Critical Current Density Directly in Terms of the BCS Interaction Parameter, Debye Temperature and the Fermi Energy of the Superconductor

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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 *j _{c}*(

*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

*θ*and, additionally, the Fermi energy

_{D}*E*—unlike earlier such equations based on diverse, indirect criteria. Our approach provides an

_{F}*ab initio*theoretical justification for one of the latter, text book equations invoked at

*T*= 0 which involves Fermi momentum; additionally, it relates

*j*with the relevant parameters of the problem at

_{c}*T*≠ 0. Noting that the numerical value of

*E*of a high-

_{F}*T*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.

_{c}

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Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

*World Journal of Condensed Matter Physics*, Vol. 3 No. 2, 2013, pp. 103-110. doi: 10.4236/wjcmp.2013.32017.

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