Thermal fluctuations and flux-tunable barrier in proximity Josephson junctions

The effect of thermal fluctuations in Josephson junctions is usually analyzed using the Ambegaokar-Halperin (AH) theory in the context of thermal activation. “Enhanced” fluctuations, demonstrated by broadening of current-voltage characteristics, have previously been found for proximity Josephson junctions. Here we report measurements of micrometer-scale normal metal loops contacted with thin superconducting electrodes, where the unconventional loop geometry enables tuning of the junction barrier with applied flux. We observe stronger “enhanced” fluctuations when the flux threading the normal metal loop is near an odd half-integer flux quantum, and for devices with thinner superconducting electrodes. These findings suggest that the activation barrier, which is the Josephson coupling energy of the proximity junction, is different from that for conventional macroscopic Josephson junctions. Simple one-dimensional quasiclassical theory is used to predict the interference effect due to the loop structure, but the exact magnitude of the coupling energy cannot be computed without taking into account the details of the sample dimensions. In this sense, the physics of nanoscale proximity junctions can be related to the thermally activated phase slips (TAPS) model for thin superconducting wires, and indeed our data can be better fitted with the TAPS model than with the AH theory. Besides shedding light on thermal fluctuations in proximity junctions, the findings here also demonstrate a different type of superconducting interference device with two normal branches sharing the same superconducting-normal interface on both sides of the device, which has technical advantages for making symmetrical interference devices.

Figure 1

Schematic diagrams of two SNS quantum interference devices: asymmetric (a) and symmetric (b). The normal-metal arms are shown in gold and the superconducting wires are shown in gray. The arrow in both figures corresponds to the direction of applied magnetic flux. Insets: Scanning electron micrographs of the devices measured; the scale bars are 1 $\mu$m. The calculated energy profiles of the asymmetric and symmetric devices are shown in (c) and (d), respectively, as a function of the external magnetic flux $\Phi$ and the phase difference across the two superconductors $\phi$, which is determined by the external current through the device. The energy profiles are calculated based on the quasiclassical theory, as described in the text.

Figure 2

Resistance as a function of applied magnetic flux for the asymmetric sample (a) and the symmetric sample (b) at 0.6 K (blue curves), 0.4 K (green curves), and 0.03 K (red curves). While the oscillations for the asymmetric device die out rapidly with decreasing temperature, the oscillations for the symmetric device survive to the lowest measurement temperature. (c) Magnetoresistance of the symmetric device around $\Phi ={\Phi }_0/2$ at four different temperatures. The solid lines are fits to the AH theory as described in the text. Below 0.15 K, the magnetoresistance does not change with temperature. (d) Critical current at zero applied flux for the symmetric and asymmetric devices. The plus symbols show the critical current expected from the fits of (c), multiplied by a factor of 5, as described in the text.

Figure 3

Differential resistance at 0.4 K for $s1$, (a), and for $s2$, (c). Different colors correspond to different applied magnetic flux: 0 (magenta), 0.25 (blue), 0.375 (red), and 0.5 (green) in units of ${\Phi }_0$. Solid lines are fits using the AH model. (b) and (d) show the flux dependence of the noise temperature $T_N$ (red) and critical current $I_c$ (blue) extracted from the AH fits of the differential resistance in (a) and (c). The insets are SEM images of the devices with false color enhancement. The area colored in gold is Au and the area colored in purple is Al. The white scale bars are 1 $\mu$m.

Figure 4

Current-voltage characteristics at 0.4 K for $s1$, (a) and (b) and $s2$, (c) and (d). The absolute value of voltage is plotted as the $y$ axis in (a) and (c), in logarithmic scale, and in (b) and (d), in linear scale. Solid lines are fits using AH theory with the same $T_N$ in Fig. 3.

Figure 5

Current-voltage characteristics at 0.4 K for $s1$, (a) and for $s2$, (c), fitted by $V\left(I\right)=V_0\sinh (I/I_0)$. In (b) and (d) the fitting parameter $V_0$ is plotted as a function of flux.

Figure 6

Resistance tail at zero field for $s1$, (a), and for $s2$, (b). The green lines are fits using Little's theory, the blue lines are fits using LAMH theory, and the red lines are fits combining Little's equation and quasiclassical theory for proximity junctions [$R_{\text{SNS}}\left(T\right)$]. The fitting parameters are listed in Table .

Figure 7

Schematic of the SNS SQUID with applied magnetic flux $\Phi$ and phase difference $\varphi$ between two superconducting reservoirs. Numbers 1–4 correspond to normal-metal wire segments.