Reversibility Of Superconducting Nb Weak Links Driven By The Proximity Effect In A Quantum Interference Device

We demonstrate the role of the proximity effect in the thermal hysteresis of superconducting constrictions. From the analysis of successive thermal instabilities in the transport characteristics of micron-size superconducting quantum interference devices with a well-controlled geometry, we obtain a complete picture of the different thermal regimes. These determine whether or not the junctions are hysteretic. Below the superconductor critical temperature, the critical current switches from a classical weak-link behavior to one driven by the proximity effect. The associated small amplitude of the critical current makes it robust with respect to the heat generation by phase slips, leading to a nonhysteretic behavior.

Figure 1

(a) SEM image of the $\mu$-SQUID $\mu S1$ with its current and voltage leads. The zoomed-in image shows the SQUID loop (with area $1\times 1\mu {\mathrm{m}}^2$) and the narrow leads. (b) Resistance versus temperature ($R\text{−}T$) plot. (c) Low-temperature portion of the $R\text{−}T$ plot for $\mu S1$ at 0.01 mA current.

Figure 2

(a) Schematic of the semi-infinite (in $+x$ direction) lead of SC material on a substrate at $T_b$ with an $N\text{−}S$ interface at $x=0$. Panel (b) shows the region near the $N\text{−}S$ interface with three differential elements of length $dx$ when the $N\text{−}S$ interface stabilizes near the heat source on the left.

Figure 3

(a)-(d) IVCs in the hysteretic regime for $\mu S1$ at different temperatures. A large hysteresis is seen at 4.25 K with two retrapping currents, $I_{r1}$ and $I_{r2}$. $I_c$ crosses $I_{r2}$ near 5.7 K and $I_{r1}$ around 7.25 K as seen in (e). Panel (f) shows the IVC of $\mu S1$ in the nonhysteretic regime above $T_h=7.25\mathrm{K}$. The inset of (e) gives a larger bias-current range plot to show the $I_{r2}$ transition.

Figure 4

Variation of $I_c$, $I_{r1}$, and $I_{r2}$ with $T_b$ for (a) $\mu S1$ and (b) $\mu S2$. The symbols are the data points. The continuous lines are fits given by (in mA and K) (a) $I_c=0.42(7.4-T_b)$ and (b) $I_c=0.29(7.4-T_b)$, while the other two are described by $I_{r1}=0.17(8.4-T_b{)}^{0.43}$ and $I_{r2}=0.37(8.7-T_b{)}^{0.5}$ for both of the devices. The cartoon pictures of the device shown in different regions depict the state of the device during current ramp-down, with blue showing SC and red showing the resistive portions. The light gray-shaded area shows the bistable region where the whole device is in the fully SC state during the current ramp-up from zero. In the dark gray-shaded region, only WLs are resistive.