Mesoscopic transition in the shot noise of diffusive superconductor–normal-metal–superconductor junctions

We experimentally investigated the current noise in diffusive superconductor-normal-metal-superconductor junctions with lengths between the superconducting coherence length ${\xi }_{\Delta }$ and the phase coherence length $L_{\Phi }$ of the normal metal $({\xi }_{\Delta }<L<L_{\Phi })$. We measured the shot noise over a large range of energy covering both the regimes of coherent and incoherent multiple Andreev reflections. The transition between these two regimes occurs at the Thouless energy where a pronounced minimum in the current noise density is observed. Above the Thouless energy, in the regime of incoherent multiple Andreev reflections, the noise is strongly enhanced compared to a normal junction, and grows linearly with the bias voltage. Semiclassical theory describes the experimental results accurately, when taking into account the voltage dependence of the resistance which reflects the proximity effect. Below the Thouless energy, the shot noise diverges with decreasing voltage, which may indicate the coherent transfer of multiple charges.

Figure 1

Differential conductance $dI∕dV$ vs bias voltage at various temperatures for sample l (data are shifted by 0.1, 0.2, and $0.35S$ for $T=500\mathrm{mK}$, $900\mathrm{mK}$, and $1.1\mathrm{K}$, respectively). Left inset: scanning electron micrograph of a typical sample. Right inset: resistance of the sample as a function of temperature. The drop at $T=1.2\mathrm{K}$ is due to the superconducting transition of the aluminum reservoirs.

Figure 2

Current noise density $S_I$ vs bias voltage at various temperatures. We observe a minimum at $\mathrm{eV}\approx E_{Th}$.

Figure 3

Current noise density times the resistance $R=V∕I$ vs bias voltage at various temperatures (the data curves are shifted successively by $10{\mathrm{pA}}^2∕\mathrm{Hz}$). The data at $100\mathrm{mK}$ can be compared to the theoretical prediction in the zero temperature limit [Eq. (1)] with $\Delta =165\mu \mathrm{eV}$ (dashed line). At higher temperatures, the thermal noise of quasiparticles outside the gap has to be taken into account. The predictions following Ref. 10 are shown as solid lines. The arrows indicate the thermal noise level $4k_{B}T$ corresponding to each data curve (including the shift).

Figure 4

Current noise times resistance, differential resistance, and resistance of sample 1 as a function of the voltage at small bias.

Figure 5

Fano factor vs the inverse voltage for two different samples. The Thouless energies are $7\mu \mathrm{V}$ for sample 1 (top panel) and $30\mu \mathrm{V}$ for sample $s$ (bottom panel). The solid lines have slopes $200\mu \mathrm{V}$ (top) and $340\mu \mathrm{V}$ (bottom). In the bottom panel, the incoherent regime is also clearly visible [dashed line is a fit according to Eq. (1)].