Phase-dependent counting statistics in a short-arm Andreev interferometer

We calculate analytically the full counting statistics for short normal metal-superconductor junctions for arbitrary voltages and temperatures. We also consider the phase oscillations of the cumulant-generating function in Andreev interferometers. At $T=0$ and at applied voltage much smaller than the proximity gap ${\Delta }_{\varphi }$, the current noise $P_I$ doubles and the third current cumulant $C_3$ is 4 times larger compared to the normal state; at $eV⪢{\Delta }_{\varphi }$ they acquire large excess components. At the gap edge, $eV={\Delta }_{\varphi }$, the differential shot noise $d{P}_I∕dV$ exhibits sharp peak, while the differential Fano factor $d{P}_I∕dI$ 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 nonmonotonous voltage dependence with a dip near $eV={\Delta }_{\varphi }$; the zero-bias slope of $C_3\left(V\right)$ is much larger (up to 5 times) than at the zero temperature.

Figure 1

The model of Andreev interferometer. A diffusive wire of the length $L$ is attached between the normal reservoir and a short SNS junction of the width $d$ connected to a superconducting loop with the magnetic flux $\Phi$.

Figure 2

Shot noise power and third cumulant vs superconducting phase (a), (b) and vs voltage (c), (d) at different temperatures. Dashed lines are voltage dependencies in the normal state at $T=0$. In the panel (d), zero-bias slopes of the normalized $C_3\left(V\right)$ are indicated.

Figure 3

Effective transferred charge (a), differential noise (b), and differential resistance (inset) vs voltage at $\varphi =0$ (solid lines) and $\varphi =0.7\pi$ (dashed lines), $T=0$.