Gapless High-Current Superconductivity

Abstract

The idea of gaplessness, already familiar in several areas of superconductivity, is considered in connection with high-current superconductivity. A calculation is made of the critical temperature ${T}_{c}$ at which a normal metal with zero current becomes thermodynamically unstable against decay into a high-current super-conducting phase. It is pointed out that at ${T}_{c}$ all the various suggested forms of high-current electron-electron interaction, both retarded and nonretarded, are equivalent, so that a calculation of ${T}_{c}$ does not suffer from ambiguity of choice of interaction. It is found that a transition temperature exists when the Bardeen, Cooper, and Schrieffer (BCS) parameter $N(0){V}_{0}>~0.43$ [assuming $N(0){V}_{c0}=0.1$]. In fact, for $0.43<N(0){V}_{0}<0.63$, two values of ${T}_{c}$ exist, since at sufficiently low temperatures, the normal phase is thermodynamically stable against high-current superconductivity. When $N(0){V}_{0}=0.43$, ${T}_{c}=\frac{0.259\ensuremath{\hbar}\ensuremath{\omega}}{{k}_{B}}$. At $T=0$, a separate calculation is made of the $N(0){V}_{0}$ required to obtain high-current superconductivity with a finite thermal energy gap $2({\ensuremath{\epsilon}}_{0}\ensuremath{-}{p}_{F}{v}_{0})$. This calculation, using a nonretarded interaction, includes the correction of an algebraic error in the 1959 paper by Parmenter. The result, $N(0){V}_{0}>~0.70$, is in close agreement with the recent work of Hone, who made use of a retarded interaction in calculating that one must have $N(0){V}_{0}>~0.67$ in order to get finite-thermal-gap high-current superconductivity. This suggests that retardation effects are not crucial in determining the occurrence or non-occurrence of high-current superconductivity. It is pointed out that experimental measurements of Morin and Maita have suggested that some transition-metal superconductors have large enough values of $N(0){V}_{0}$ for both the gapless form and the finite-thermal-gap form of high-current superconductivity to occur. Either form, if it exists, will exhibit the same form of electrical instability that is known to occur under exceptional conditions in conventional low-current superconductivity.