Cross Correlation of Incoherent Multiple Andreev Reflections

We use a semiclassical theory to calculate the current correlations in a multiterminal structure composed of a normal metallic dot connected to all superconducting leads at arbitrary voltage and temperature. This theory holds when the proximity effect is suppressed in the dot. At low voltage, $eV\ll \Delta$ ($\Delta$ is the superconducting gap in the leads), when charge transport is due to incoherent multiple Andreev reflections, the correlations are strongly enhanced compared to those in the normal state. Moreover, we predict that the cross correlation can be positive or negative depending on the properties of the point contacts between the dot and the leads. We also discuss the effect of inelastic scattering in the dot.

Figure 1

(a) Schematic device of a normal metallic dot connected to superconducting leads through point contacts with $N_{\alpha }$ channels of transparency ${\Gamma }_{\alpha }$. (b) Voltage dependence of the current in a device with $N_1=10N_2$, ${\Gamma }_1=1$, and ${\Gamma }_2=0.2$, at various temperatures. (c) Noise and (d) cross correlation for the same device. Here, $T_c$ is the critical temperature in the leads, and $\Delta (0)$ is the superconducting gap at zero temperature.

Figure 2

Zero-temperature cross correlation vs the ratio of channel numbers at the contacts for different values of the contact transparencies. (Note that the curves do not intersect exactly at the same point.)