Supercurrent flow through an effective double barrier structure

TL;DR

This paper investigates supercurrent flow through an effective double barrier in a superconductor, revealing multiple solution regimes, resonant tunneling behavior, and conditions for supercurrent existence, with implications for SNS structures and critical current behavior.

Contribution

It introduces a detailed analysis of supercurrent solutions in a double barrier structure, including solution multiplicity, resonant tunneling, and the impact of barrier separation on supercurrent flow.

Findings

No supercurrent solutions for barrier distances less than πξ(T).

Multiple solutions with distinct current-phase relations exist for certain barrier separations.

Critical current vanishes as the square root of (T'_c - T) in SNSNS structures.

Abstract

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 $d_0=\pi\xi(T)$ no current-carrying solutions exist. For distances between $d_0$ and $2d_0$, four solutions exist. The two symmetric solutions obey a current-phase relation of $\sin(\Delta\varphi/2)$, while the two asymmetric solutions satisfy $\Delta\varphi=\pi$ for all allowed values of the current. As the distance exceeds $nd_0$, a new group of four solutions appears, each contaning $(n-1)$ 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 delta function barrier may quantitatively describe a SNS structure. We are thus able to predict that the critical current of a SNSNS structure vanishes as $\sqrt{T'_c-T}$, where $T'_c$ is lower than the bulk critical temperature.