Contribution of weak localization to nonlocal transport at normal metal/superconductor double interfaces

In connection with a recent experiment [Russo , Phys. Rev. Lett. 95, 027002 (2005)], we investigate the effect of weak localization on nonlocal transport in normal metal/insulator/superconductor/insulator/normal metal (NISIN) trilayers, with extended interfaces. The negative weak localization contribution to the crossed resistance can exceed in absolute value the positive elastic cotunneling contribution if the normal metal phase coherence length or the energy are large enough.