Subgap noise of a superconductor–normal-metal tunnel interface

It is well established that the subgap conductivity through a normal-metal-insulator–superconductor (NIS) tunnel junction is strongly affected by interference of electron waves scattered by impurities. In this paper we investigate how the same phenomenon affects the low frequency current noise, $S$, for voltages $V$ and temperatures $T$ much smaller than the superconducting gap. If the normal metal is at equilibrium we find that the simple relation $S(V,T)=4e\coth (eV∕T)I(V,T)$ holds quite generally even for nonlinear $I\text{−}V$ characteristics. Only when the normal metal is out of equilibrium do noise and current become independent. Their ratio, the Fano factor, depends then on the details of the layout.

Figure 1

Experimental set up similar to Ref. 30. The magnetic flux dependence of the current and noise can be used to measure the doubling of the Fano factor with high accuracy.

Figure 2

Differential Fano factor $\mathcal{F}$ as a function of $V∕U$. Different curves represent different values of $u_0$ going from 0 to 1 in step of 0.1 starting from the top. Departure from the value 2 or $-2$ is due to the energy dependence of the tunneling matrix element.

Figure 3

(Color online) Fano factor as a function of $V∕U$ for $x∕L=9∕18$, $8∕18$, $4∕18$, and $1∕18$, from top to bottom. Full lines are obtained with Eq. (26). The dots indicate the result obtained with circuit theory. The inset shows the circuit used in the calculation.

Figure 4

(Color online) Comparison of the differential Fano factor $\mathcal{F}$ given by Eq. (29) (full lines) and by the numerical circuit theory simulation (dashed lines). The four dashed curves are obtained for $U=200E_{\text{th}}^W$ and $u_0=1∕18$, $4∕18$, $8∕18$, and $9∕18$ $(N=18)$.