Superconducting bistability in floating Al islands of hybrid Al/InAs nanowires

Abstract

We investigate a non-equilibrium aspect of the current-driven superconducting-normal phase transition in floating Al islands of epitaxial full-shell Al/InAs nanowires. Within a transition region discontinuous voltage jumps and hysteretic behaviour of the I-V characteristics are observed, associated with the destruction and recovery of the superconducting order parameter in the island. The strength of the two features varies strongly in different devices in a mutually correlated way and can be suppressed by a small magnetic field. Numerical calculation explains this behaviour in terms of a tiny non-equilibrium correction to the electronic energy distribution at low energies. The experiment demonstrates a critical failure of a two-temperature non-equilibrium model of the superconductor-normal transition in floating islands of hybrid nanowire devices.

Figures (4)

• Figure 1: Non-equilibrium features on the $I-V$ curve. (a): false color scanning electron micrograph of the device D1 with a schematics of the symmetrized quasi-four-terminal current-biased measurement. (b),(c): $I-V$ curves in the device D2 with a relatively weak hysteresis (b) and in the device D1 with a relatively strong hysteresis (c). Shown are small current/voltage ranges next to the transition points for the two sweep directions, as indicated by blue and red colors and respective arrows. In panel (b) the magnitude of the voltage jump $\delta V_\mathrm{C}$ observed for the upward sweep in the device D2 is indicated. Sub-panels in (c) show the effect of small variations of the bath temperature on the hysteresis in the device D1. All data is taken in $B$=$0$. For D1 back-gate and side-gate voltages are set to 15 V, see SM supplemental. For D2 the back-gate voltage is 32 V.
• Figure 2: Correlation between the voltage jump and hysteresis. The magnitude of the voltage jump $\delta V_\mathrm{c}$ measured on the upward sweep (see Fig. \ref{['Fig1']}b) is plotted as a function of the width $\delta T_\mathrm{c}$ of the hysteresis loop. $\delta T_\mathrm{c}$ is obtained from the difference of the electronic temperatures corresponding to the jumps on the upward and downward current sweeps, within the two-temperature model. The data from three devices with the weak hysteresis (D2-D4) and one device with the strong hysteresis (D1) are used, see legend. For the device D1 different symbols correspond to different bath temperatures from the sub-panels of Fig. \ref{['Fig1']}c. Solid line is the theoretical estimate, dotted lines are the fits based on the model calculation of Fig. \ref{['Fig3']}, see text. All experimental data is taken in $B$=$0$. Gate-voltages for D1 and D2 are the same as in Fig. \ref{['Fig1']}. For D5 the back-gate voltage is 32 V. No gate voltage was used for D2 and D3.
• Figure 3: Model of the quasiparticle non-equilibrium. (a): non-equilibrium correction $\delta f(E)$ to the EED in the Al island, controlled with the two parameters $\alpha$ and $w$. (b): dependence of the order parameter on the electronic temperature, which controls the equilibrium part of the EED with the fixed $\delta f(E)$, see the indicated $\alpha$ and $w$. The thick solid lines show the stable branch of $\Delta(T_\mathrm{e})$ for two sweep directions indicated with arrows. The discontinuous jump of the order parameter on the upward sweep is marked as $\Delta_\mathrm{c}$. The thick dashed line is the unstable branch of $\Delta(T_\mathrm{e})$. The thin dashed line is the equilibrium dependence calculated with $\delta f(E)\equiv0$. (c): colorscale plot of the width of the hysteresis loop $\delta T_\mathrm{c}$ as a function of $\alpha$ and $w$. (d): colorscale plot of the jump $\Delta_\mathrm{c}$ of the order parameter at the high temperature end of the hysteresis loop as a function of $\alpha$ and $w$. All data is calculated for $B=1\,$mT.
• Figure 4: Impact of the $B$-field. (a): color scale plot of the numerically calculated differential resistance of the device D1 as a function of $P_\mathrm{J}$ and $B$ (upward sweep). Dashed line indicates the position of the $R_\mathrm{diff}$ maximum extracted from similar data for the downward sweep. (b): the width of the hysteresis loop in units of the Joule power for the device D1 (symbols) and the model fit with the indicated $\alpha$ and $w=1\,$K (dashed line). (c): the same for the device D2. (d): magnified view of the transition region on the $I$-$V$ curve for a set of $B$-fields in device D2. A linear background corresponding to the slope in the normal state at high currents is subtracted from the data. Two sweep directions are indicated with separate colors and arrows. Gate voltages are the same as in Fig. \ref{['Fig1']}.