Current fluctuations in mesoscopic systems with Andreev scattering

Using a scattering theory approach we study the zero-frequency current fluctuations of the normal terminals of a phase-coherent mesoscopic structure with a superconducting region. We find that for devices where the potential of the superconducting region is externally fixed (Fig. 1), the expression for current fluctuations is a. simple generalization of the corresponding expression obtained in Buttiker [Phys Rev. B 46, 12 485 (1992)] for purely normal mesoscopic systems. ln contrast to purely normal mesoscopic systems, we find that the current fluctuations between two different contacts can be positive in these devices. We apply this formula to derive a simple expression for the shot noise in a normal superconducting (NS) junction and study the noise to current ratio both as a function of the applied bias and a potential barrier at the NS interface. For devices with a. floating superconductor (Fig. 2), a self-consistent calculation of the current fluctuations is necessary, and here we derive an approximate formula valid in the small bias limit. We show that two similar devices with identical average currents can exhibit very different fluctuations depending on whether the superconductor is held at a fixed potential or is left floating.