Proximity-reduced range of internal phase differences in double Josephson junctions with closely spaced interfaces

A substantial influence of the proximity and pair breaking effects on the range of internal phase differences is shown to take place in symmetric double Josephson junctions with closely spaced interfaces and to affect the evolution of the supercurrent $j$ with the changing central lead's length $L$. If the phase difference $\varphi$ between the external leads is controlled and $L$ exceeds a few coherence lengths, the regime of interchanging modes is established. The range of the phase differences across the two individual interfaces is reduced with decreasing $L$, and the states of the higher energy mode are gradually eliminated. With a further decrease of $L$ the regime of interchanging modes is destroyed along with the asymmetric mode. The conventional single junction current-phase relation $j\left(\varphi \right)$ is eventually established and the condensate states' doubling is fully removed at very small $L$.

Figure 1

Schematic diagram of the double junction.

Figure 2

$f_{l/2-0}^2$ as a function of $l$ at $\chi =0$ (left panel) and $\chi =\pi$ (right panel). Solid curves correspond to the energetically preferable states. Left panel: $\chi =0$, $g_{\delta }=0.1$ and (1) $g_{\ell }=0,\left(2\right)g_{\ell }=0.1,\left(3\right)g_{\ell }=0.3$, and (4) $g_{\ell }=0.8$. Right panel: $\chi =\pi$, $g_{\delta }=0.1$ and (1) $g_{\ell }=0,\left(2\right)g_{\ell }=0.03,\left(3\right)g_{\ell }=0.1,\left(4\right)g_{\ell }=0.25,\left(5\right)g_{\ell }=0.5$, and $\left(6\right)g_{\ell }=0.8$.

Figure 3

Critical current as a function of $l$ at $g_{\ell }=0.1$, $g_{\delta }=0.1$. Inset: The quantity $t_{l/2-0}\left(\varphi \right)$ at (1) $l=0.02$, (2) $l=0.1$, (3) $l=0.25$.

Figure 4

Current-phase relations $\tilde{ȷ}\left(\varphi \right)$ taken for $g_{\ell }=0.1$, $g_{\delta }=0.1$ and (1) $l=1$, (2) $l=0.5$, (3) $l=0.38$, (4) $l=0.25$, (5) $l=0.02$.