Semiclassical theory of shot noise in disordered superconductor–normal-metal contacts

We present a semiclassical theory of shot noise in diffusive superconductor–normal-metal (SN) contacts. At subgap voltages, we reproduce the doubling of shot noise with respect to conventional normal-metal contacts, which is interpreted in terms of an energy balance of electrons. Above the gap, the voltage dependence of the noise crosses over to the standard one with a voltage-independent excess noise. The semiclassical description of noise leads to correlations between currents at different electrodes of multiterminal SN contacts which are always of the fermionic type, i.e., negative. Using a quantum extension of the Boltzmann-Langevin method, we reproduce the peculiarity of noise at the Josephson frequency and obtain an analytical frequency dependence of noise at above-gap voltages.