Phase dependent current statistics in short-arm Andreev interferometer

Abstract

We calculate analytically the current statistics for a short diffusive wire between the normal reservoir and a short superconductor-normal metal-superconductor (SNS) junction, at arbitrary applied voltages and temperatures. The cumulant-generating function oscillates with the phase difference $ϕ$ across the junction, approaching the normal-state value at $ϕ=π$. At T=0 and at the 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 with respect to their values in the normal state; at $eV \gg Δ_ϕ$ they acquire large excess components. At the gap edge, $eV = Δ_ϕ$, the effective transferred charge defined through $dP_I/dI$ and $dP_I/dV$ approaches $0e$ and $3e$, respectively, which makes doubtful the interpretation of these quantities as physical elementary transferred charge. At $T \neq 0$, $C_3$ shows a non-monotonous voltage dependence with a dip near $eV = Δ_ϕ$.