Dissipation in quasi-one-dimensional superconducting single-crystal $\mathrm{Sn}$ nanowires

Electrical transport measurements were made on single-crystal $\mathrm{Sn}$ nanowires to understand the intrinsic dissipation mechanisms of a one-dimensional superconductor. While the resistance of wires of diameter larger than $70\mathrm{nm}$ drops precipitously to zero at $T_c$ near $3.7\mathrm{K}$, a residual resistive tail extending down to low temperature is found for wires with diameters of 20 and $40\mathrm{nm}$. As a function of temperature, the logarithm of the residual resistance appears as two linear sections, one within a few tenths of a degree below $T_c$ and the other extending down to at least $0.47\mathrm{K}$, the minimum temperature of the measurements. The residual resistance is found to be ohmic at all temperatures below $T_c$ of $\mathrm{Sn}$. These findings are suggestive of a thermally activated phase slip process near $T_c$ and quantum fluctuation-induced phase slip process in the low-temperature regime. When the excitation current exceeds a critical value, the voltage-current $\left(V\text{−}I\right)$ characteristics show a series of discrete steps in approaching the normal state.

Figure 1

Panels (a) and (b), respectively, show the FESEM images of the surface and cross section of home-made AAM membranes. (c)and (d), respectively, show the TEM images of the randomly distributed freestanding $\mathrm{Sn}$ nanowires fabricated with PCM, and the electron diffraction pattern of the individual $40\mathrm{nm}$ wire showing [100] orientation.

Figure 2

(a) Resistance vs temperature of 20 and $100\mathrm{nm}$ $\mathrm{Sn}$ wires fabricated with AAM and PCM, respectively, in the wide temperature range of $0.47–300\mathrm{K}$. The resistance value of $100\mathrm{nm}$ wires was normalized to that of $20\mathrm{nm}$ wires at $5\mathrm{K}$ by multiplicative a factor of 230. A schematic arrangement for the transport measurement is shown in the inset. Figure 1b summarizes the results of our $R\left(T\right)$ measurement in low-temperature range for the 20, 40, 60, 70, and $100\mathrm{nm}$ $\mathrm{Sn}$ nanowire arrays. The solid lines for 20, 40 and $60\mathrm{nm}$ wires are the calculation results based on TAPS model near $T_c$ and QPS model below $T_c$ with four adjusting parameters, while those for 70 and $100\mathrm{nm}$ wires were made based on only the TAPS model with two fitting parameters.

Figure 3

$V\text{−}I$ curves of (a) 70, (b) 40, and (c) $20\mathrm{nm}$ $\mathrm{Sn}$ nanowire arrays measured at different temperatures in linear scale. Panels (d), (e), and (f) show log-log plots of $V$ versus $I$. These plots show more clearly the data in the low current limit.

Figure 4

$V\text{−}I$ curves of $20\mathrm{nm}$ $\mathrm{Sn}$ wires measured at $2.5\mathrm{K}$ and different magnetic fields aligned parallel to the wires.

Figure 5

$I_c\text{−}T$ plot for $20\mathrm{nm}$ $\mathrm{Sn}$ wires.