Current noise in biased superconducting weak links

Non-equilibrium current noise of a short quasi–one-dimensional constriction between two superconductors is considered. We derive a general expression for the frequency-dependent current-current correlation function valid for arbitrary temperatures, transparencies, and bias voltages. This formalism is then applied to a single current-carrying quantum mode with perfect transparency, and at zero frequency and temperature. Contrary to a transparent channel separating two normal conductors, a weak link between two superconductors exhibits a finite level of noise. The source of noise is the fractional Andreev scattering of quasi-particles with energies |E| greater than the half-width ${\mit \Delta}$ of the superconducting gap. For high bias voltages, $V \gg {\mit \Delta} /e$, the zero-frequency limit of the noise spectrum, S(0), as well as the excess current $I_{\rm{exc}}$, are twice as large than for a normal-superconductor junction, $S(0)=(2/5)|e|I_{\rm{exc}}$.