Distribution functions and current-current correlations in normal-metal-superconductor heterostructures

We introduce electronlike and holelike distribution functions, which determine the currents and the fluctuation spectra of the currents measured at a normal-conductor-superconductor heterostructure. These distribution functions are expressed with the help of newly defined partial densities of states for heterostructures. Voltage measurements using a weakly coupled contact on such a structure show the absence of a contact resistance to the superconducting reservoir and illustrate how the interface to the superconductor acts as an Andreev mirror. We also discuss the current-current correlations measured at two normal contacts and argue that the appearance of positive correlations is a purely mesoscopic effect, which vanishes in the limit of a large number of channels and in the average over an ensemble.