Switching the sign of Josephson current through Aharonov-Bohm interferometry

The electromagnetostatic Aharonov-Bohm effect is proposed as a tool to realize a fully controllable Josephson $\pi$ junction. Both the sign and the magnitude of the supercurrent can be tuned in a ring-shaped ballistic normal region coupled to superconducting electrodes by varying the magnetic flux and the electric field around suitable values. We provide a theoretical description of the system within the scattering matrix theory and discuss its implementation in a realistic setup.

Figure 1

Scheme of the Aharonov-Bohm Josephson junction. Light gray region indicates the normal metal ring, whereas dark gray denotes the superconducting leads.

Figure 2

(Color online) Sign switching of the Josephson current $J$ for the setup of Fig. 1 with $\mid \Delta \mid =2E_L$, $k_{F}L=60$, and contact transmission $1∕2$ $(\gamma =\pi ∕3)$. (a) $j\left(\chi \right)$ for $\varphi =0$ and $u=0$ (solid), for $\varphi =0$ and $u=0.8\pi$ (dotted), and for $\varphi =0.8\pi$ and $u=0.8\pi$ (dashed); (b) $j(\chi =0)$ vs $\varphi$ for different values of the gate voltage: $u=\pi ∕20$ (dotted), $u=\pi ∕2$ (dashed), and $u=1.2\pi$ (solid); (c) $j(\chi =0)$ vs $u$ for different values of magnetic flux: $\varphi =0$ (solid), $\varphi =0.1\pi$ (dotted), and $\varphi =0.9\pi$ (dashed).

Figure 3

(Color) Dimensionless Josephson current vs $u$ and $\varphi$ for an AB ring with $\mid \Delta \mid =2E_L$, $k_{F}L=60$, $\gamma =\pi ∕3$, and $\chi =0$.