Supercurrent flow through an effective double-barrier structure

Supercurrent flow is studied in a structure that in the Ginzburg-Landau regime can be described in terms of an effective double-barrier potential. In the limit of strongly reflecting barriers, the passage of Cooper pairs through such a structure may be viewed as a realization of resonant tunneling with a rigid wave function. For interbarrier distances smaller than d₀={π}{ξ}(T) no current-carrying solutions exist. For distances between d₀ and 2d₀, four solutions exist. The two symmetric solutions obey a current-phase relation of sin({Δ}{Φ}/2), while the two asymmetric solutions satisfy {Δ}{Φ}={π} for all allowed values of the current. As the distance exceeds nd₀, a group of four solutions appears, each containing (n-1) soliton-type oscillations between the barriers. We prove the inexistence of a continuous crossover between the physical solutions of the nonlinear Ginzburg-Landau equation and those of the corresponding linearized Schr\"odinger equation. We also show that under certain conditions a repulsive {δ} function barrier may quantitatively describe a superconductor-normal-superconductor (SNS) structure. We conclude that the critical current of a SNSNS structure vanishes as {}Tc^'-T, where Tc^' is lower than the bulk critical temperature. {} 1996 The American Physical Society.