Phase dependent current statistics in short-arm Andreev interferometer

TL;DR

This paper analytically studies phase-dependent current fluctuations in a short diffusive SNS junction, revealing oscillations, noise doubling at low voltages, and complex charge transfer behavior near the gap edge.

Contribution

It provides a detailed analytical calculation of current statistics in a short SNS junction, including phase dependence and behavior at various voltages and temperatures, which was not previously fully understood.

Findings

Current noise doubles at low voltage and zero temperature.

Third cumulant increases fourfold compared to the normal state.

Effective transferred charge varies non-trivially near the gap edge.

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 $\phi$ across the junction, approaching the normal-state value at $\phi=\pi$. At T=0 and at the applied voltage much smaller than the proximity gap $\Delta_\phi$, 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 $eV \gg \Delta_\phi$ they acquire large excess components. At the gap edge, $eV = \Delta_\phi$, 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 $eV = \Delta_\phi$.