Coulomb Effects on Electron Transport and Shot Noise in Hybrid Normal-Superconducting Metallic Structures

We analyze the effect of electron-electron interactions on Andreev current and shot noise in diffusive hybrid structures composed of a normal metal attached to a superconductor via a weakly transmitting interface. We demonstrate that at voltages/temperatures below the Thouless energy of a normal metal Coulomb interaction yields a reduction of both Andreev current and its noise by a constant factor which essentially depends on the system dimensionality. For quasi-1d structures this factor is $\sim N_{\mathrm{C}\mathrm{h}}^{8\mathrm{/}g}$, where $N_{\mathrm{C}\mathrm{h}}$ and $g$ are respectively the number of conducting channels and dimensionless conductance of a normal metal. At voltages above the Thouless energy the interaction correction to Andreev current and shot noise acquires an additional voltage dependence which turns out to be a power-law in the quasi-1d limit.