Circuit influence on electron transport in hybrid superconductor---normal-metal nanostructures

We study the effects of the circuit impedance on transport properties of hybrid structures consisting of a superconductor tunnel-coupled to two normal-metal electrodes. At subgap conditions (i.e. at low voltages and temperatures with respect to the superconducting energy gap) the dominant transport mechanism of Cooper pairs is by Andreev reflection. We derive the analytic expressions for the direct and crossed Andreev current, and the elastic cotunneling current. The results can be used for improving the accuracy of hybrid devices employed in electrical metrology and for noise measurements in quantum information processing.