Inherent Stochasticity of Superconductor-Resistor Switching Behavior in Nanowires

We study the stochastic dynamics of superconductive-resistive switching in hysteretic current-biased superconducting nanowires undergoing phase-slip fluctuations. We evaluate the mean switching time using the master-equation formalism, and hence obtain the distribution of switching currents. We find that as the temperature is reduced this distribution initially broadens; only at lower temperatures does it show the narrowing with cooling naively expected for phase slips that are thermally activated. We also find that although several phase-slip events are generally necessary to induce switching, there is an experimentally accessible regime of temperatures and currents for which just one single phase-slip event is sufficient to induce switching, via the local heating it causes.

Figure 1

(a) Schematic of the experimental configuration described by our model: a superconducting nanowire is suspended between two thermal baths. (b) Sketch showing the attenuation of the order parameter in the core of a phase-slip. (c) Schematic of the simplified model. All phase slips are taken to occur in a central (i.e. shaded) segment of length $l$, which is assumed to be at a uniform temperature $T$; heat is carried away through the end segments, which are assumed to have no heat capacity. The temperature at the ends of the wire is fixed to be $T_b$. (d) Sketch of a typical temperature profile.

Figure 2

Effective potential $U(T,T_b,I)$ (dashed line) and mean first-passage time $\tau$ as functions of the temperature $T$ of the central segment for various bias currents $I$ and for $T_b=1.2\mathrm{K}$. The marks on the temperature axis indicate the temperatures that the central segment would have after $1,2,\dots ,10$ phase slips in the absence of cooling [as given by Eq. (5) for $T_0=T_b$].

Figure 3

Switching statistics. (a) Map showing $N(T_b,I)$ (see text) and the contour lines for the mean switching rates ${\tau }_s^{-1}=1$, ${10}^3$, ${10}^6{\mathrm{s}}^{-1}$ (solid) and the phase-slip rate $\Gamma$ (dashed). The depairing critical current (dashed-dotted line) is plotted for reference. (b) Switching-current distributions $P_{\mathrm{SW}}$ obtained at various values of $T_b$ and for sweep rate $r=58\mu \mathrm{A}/\mathrm{s}$. (c) The logarithms of ${\tau }_s^{-1}$ (colored lines) and of $\Gamma$ (thinner black lines) as a function of $I$, obtained for the same set of $T_b$ values as used in panel (a). The colors of the ${\tau }_s^{-1}$ plots correspond to different values of $N(T_b,I)$ [as indicated in the legend of panel (a)].