Full Counting Statistics of Electron Transfer between Superconductors

We present an extension of the Keldysh-Green’s function method, which allows one to calculate the full distribution of transmitted particles through a mesoscopic superconductor. The method is applied to the statistics of supercurrent in short contacts. If the current is carried by Andreev bound states the distribution corresponds to switching between long trains of electrons going in opposite directions. For weak (gapless) superconductors or tunnel junctions we find that at low temperatures the distribution has negative “probabilities.” Accounting for the quantum mechanical nature of the measuring device shows that these negative values can indeed be measured.