Phase Dependent Current Statistics in a Short-Arm Andreev Interferometer

摘要

We calculate analytically the full counting statistics for a short normally conducting diffusive wire connecting a normal reservoir and a short superconductor-normal metal-superconductor junction, at arbitrary applied voltages and temperatures. The cumulant-generating function oscillates with the phase difference φ across the junction and approaches the normal-state value at φ = π. At T = 0 and at applied voltage much smaller than the proximity gap Δ_φ, the current noise P_I doubles and the third current cumulant C_3 is 4 times larger compared to the normal state; at eV Δ_φ they acquire large excess components. At the gap edge, eV = Δ_φ, the differential shot noise dP_I/dV exhibits sharp peak, while the differential Fano factor dP_I/dI turns to zero along with the differential resistance, which reflects the transmission resonance associated with the singularity of the density of states. At nonzero temperature, C_3 shows a non-monotonous voltage dependence with a dip near eV = Δ_φ; the zero-bias slope of C_3(V) is much larger (up to 5 times) than at the zero temperature.