We present theory for a current shot noise in mesoscopic diffusive superconductor-normal metal-superconductor (SNS) junctions. The current shot noise is tremendously enhanced at small applied voltage, V < Δ/e, due to the mechanism of multiple Andreev reflection (MAR), which creates long correlated trains of transmitted electrons. The central result for the MAR regime is a universal value for the noise power in the limit of small voltage and at zero physical temperature, which corresponds to the effective noise temperature of the order of superconducting energy gap Δ. At very small voltage, MAR is destroyed by inelastic relaxation, consequently, the level of noise reduces and approaches at V = 0 the thermal noise value. We investigate the suppression of MAR by inelastic scattering processes and analyze the crossover from the MAR regime to a hot electron regime.
Midgap states (MGS) exist at the Fermi level at surfaces and interfaces of d-wave superconductors for order parameter orientations such that a sign change of Andreev reflection can add a (pi) -shift in the Bohr-Sommerfeld quantization condition. MGS are basically robust features, but the detailed density of states, manifested e.g. in zero bias conductance peaks (ZBCP), is in principle a sensitive probe of junctions and interfaces, providing information about normal regions with suppressed order parameter, non-specular scattering from rough or disordered interfaces, impurity states, lifetimes, etc. Resonance coupling of MGS in d45/d+/- 45 SNINS junctions gives rise to large equilibrium Josephson critical current varies direct as (root)D, where D is the normal transparency of the junction. Spontaneous time-reversal symmetry breaking (TRSB) in d0/d45 junctions at low temperatures kBT << D(Delta) 0 is driven by a gain in Josephson energy for transparencies D >> (epsilon) 0/(lambda) .
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