Magnetoresistance of Proximity-Coupled Au Wires

Measurements of the proximity coupled Au wires show a magnetoresistance that is quadratic in the magnetic field $B$ at low field, with a characteristic field scale $B_c$ determined by phase coherent paths which encompass not only the wire, but also the contacts. $B_c$ is essentially temperature independent at low temperatures, indicating that the area of the phase coherent paths is not determined by the superconducting coherence length $L_T$ in the normal metal, which is strongly temperature dependent at low temperatures. We identify the relevant length scale as a combination of the electron phase coherence length $L_{\phi }$ in the normal metal and the coherence length ${\xi }_S$ in the superconductor.