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 ${\mathit{d}}_0$=πξ(T) no current-carrying solutions exist. For distances between ${\mathit{d}}_0$ and 2${\mathit{d}}_0$, four solutions exist. The two symmetric solutions obey a current-phase relation of sin(ΔΦ/2), while the two asymmetric solutions satisfy ΔΦ=π for all allowed values of the current. As the distance exceeds ${\mathit{nd}}_0$, 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 Schrödinger 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 √${\mathit{T}}_{\mathit{c}}^{\prime }$-T, where ${\mathit{T}}_{\mathit{c}}^{\prime }$ is lower than the bulk critical temperature. © 1996 The American Physical Society.