Experimental limits of the observation of thermally activated phase-slip mechanism in superconducting nanowires

The shape of experimentally observed $R\left(T\right)$ transition of thin superconducting wires is analyzed. From theoretical point of view, broadening of the transition in quasi-one-dimensional superconducting channels is typically associated with phase-slip mechanism. It is shown that such interpretation can be misleading if to consider geometrical inhomogeneity and finite dimensions of real samples studied in experiments. The analysis is based on experimental fact that for many superconducting materials the critical temperature depends on the characteristic dimension of a sample: film thickness or wire cross section.

Figure 1

(Color online) Empirical dependence of critical temperature $T_c$ on cross section $\sigma$ for aluminum nanowires. Line is guide for eyes. Inset: SPM measured distribution of cross sections of a typical lift-off fabricated nanowire: length $L=10\mu \mathrm{m}$ and effective diameter ${\sigma }^{1∕2}\approx 75\mathrm{nm}$.

Figure 2

(Color online) Simulated dependence of normalized resistance on temperature for the sample from Fig. 1, inset. Solid dots (●) stand for calculations using Eq. (4) and $T_c\left(\sigma \right)$ data from Fig. 1. Solid line is TAPS calculation using realistic fitting parameters: cross section ${\sigma }^{1∕2}=75\mathrm{nm}$, thermodynamic critical field $B_c\left(0\right)=10\mathrm{mT}$, BCS coherence length ${\xi }_0=1.6\mu \mathrm{m}$, and mean free path $\ell =30\mathrm{nm}$. Gray shaded region corresponds to TAPS fitting allowing $\pm 10\%$ variation of $\ell$ and $B_c$.

Figure 3

(Color online) Bottom panel: SPM image of a typical aluminum wire with four probes. Top panel solid blue line: SPM measured variation of the wire cross section $\sigma$ along the sample including the node region. Inset: black dots (●) correspond to simulated $R\left(T\right)$ dependence based on Eq. (4) and $T_c\left(\sigma \right)$ data from Fig. 1 without taking into consideration the node regions. Diamonds (◇) are results of similar calculations with contribution of the node regions within the limits indicated by the two arrows. Blue open circles (엯) is experimentally measured $R\left(T\right)$ dependence. Simulations, SPM image and experimental data are for the same wire as in the inset of Fig. 1 and in Fig. 2.