Magnetic Interference Patterns and Vortices in Diffusive SNS Junctions

We study theoretically the electronic and transport properties of a diffusive superconductor-normal metal-superconductor junction in the presence of a perpendicular magnetic field. We show that the field dependence of the critical current crosses over from the well-known Fraunhofer pattern in wide junctions to a monotonic decay when the width of the normal wire is smaller than the magnetic length ${\xi }_H=\sqrt{{\Phi }_0/H}$, where $H$ is the magnetic field and ${\Phi }_0$ the flux quantum. We demonstrate that this behavior is a direct consequence of the magnetic vortex structure appearing in the normal region and predict how this structure is manifested in the local density of states.

Figure 1

Local density of states as a function of the energy in the middle of a wire of length $L=2\xi$ for two values of the magnetic flux. The different curves correspond to different values of the $y$ coordinate. We have assumed perfect transparency for the interfaces and a phase difference $\varphi =0$. In panel (d) we have used thicker lines to highlight the curves where the DOS is equal to the normal state one.

Figure 2

Spatial map of the modulus of the pair correlations, $|F(\mathbf{R})|$, for $L=2\xi$ and $\varphi =0$. The different panels correspond to different values of the width $W$ and the magnetic flux $\Phi$, as indicated in the graphs. $|F(\mathbf{R})|$ has been normalized to its value inside the electrodes, the temperature is $k_{B}T=0.01\Delta$, and perfect transparency was assumed.

Figure 3

Critical current normalized by the zero-field value vs magnetic flux for a wire length $L=8\xi$, perfect transparent interfaces, $k_{B}T=0.01\Delta$, and different values of $W$. The dashed line shows the standard Fraunhofer pattern given by $\sin (\pi \Phi /{\Phi }_0)/(\pi \Phi /{\Phi }_0)$. The inset shows for $W=0.5\xi$ the comparison between the exact result and the approximation used for the narrow-junction limit.