Abstract
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.
Highlights
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, the Fermi energy EF—unlike earlier such equations based on diverse, indirect criteria
The critical current density of a superconductor (SC) is the maximum current density that it can carry beyond which it loses the characteristic of superconductivity
This suffices for the problem addressed because Pc corresponds to the situation when W = 0; in this limit, it has been shown in [21] that the equation obtained via the negative energy projection operators is identical with the one obtained via the PEPOs; that: 1) Cooper pairs (CPs) formed via electron-electron and hole-hole scatterings make equal contributions to the BS amplitude; and 2) the amplitudes for the formation of CPs corresponding to the mixed energy projection operators are zero
Summary
The critical current density (jc) of a superconductor (SC) is the maximum current density that it can carry beyond which it loses the characteristic of superconductivity. It is an important parameter because greater its value, greater is the practical use to which the SC can be put. 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. SC Type I; wire of radius a in the absence of external field Type I; thin film or wire Type I; thin film or wire
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