Nonlocal transport through multiterminal diffusive superconducting nanostructures

Motivated by recent experiments on nonlocal transport through multiterminal superconducting hybrid structures, we present self-consistent calculations based on quasiclassical Green's functions for the order parameter, currents and voltages in a system consisting of a diffusive superconductor connected to two normal and one superconducting electrodes. We investigate non-equilibrium effects for different biasing conditions corresponding to measurements of the nonlocal conductance and of the nonlocal resistance. It is shown that while the nonlocal conductance does not change its sign, this change might be observed in a nonlocal resistance measurement for certain parameter range. The change of sign of the nonlocal signal takes places at a voltage of the order of the self-consistent gap of the superconducting region. We show that this is not related to the nonlocal Andreev processes but rather to non-equilibrium effects. We finally discuss the case of four terminal measurements and demonstrate that a change of sign in the nonlocal resistance appears when the current injected into the superconductor exceeds a critical value. The connection to the existing experiments is discussed.