Quantitative test of a quantum theory for the resistive transition in a superconducting single-walled carbon nanotube bundle

The phenomenon of superconductivity depends on the coherence of the phase of the superconducting order parameter. The resistive transition in quasi-one-dimensional superconductors is broad because of a large phase fluctuation. We show that the resistive transition of a superconducting single-walled carbon nanotube bundle is in quantitative agreement with the Langer-Ambegaokar-McCumber-Halperin (LAMH) theory. We also demonstrate that the resistive transition below $T_c^{*}=0.89T_{c0}$ is simply proportional to $\exp [-(3\beta T_c^{*}∕T){(1-T∕T_c^{*})}^{3∕2}]$, where the barrier height has the same form as that predicted by the LAMH theory and $T_{c0}$ is the mean-field superconducting transition temperature.

Figure 1

The temperature dependence of the two-probe resistance for a SWNT bundle that consists of about 350 tubes. The data are extracted from Ref. 6.

Figure 2

The temperature dependence of the two-probe resistance for a SWNT bundle below $0.88T_{c0}$. The solid line is the curve best fitted by Eq. (10) with $\beta =2.99\pm 0.05$ and $T_c^{*}=0.394\pm 0.002\mathrm{K}$. Reducing or increasing the temperature region for the fit tends to worsen the fit quality. It is striking that the on-tube resistance below $0.88T_{c0}$ decreases exponentially to zero.

Figure 3

The temperature dependence of the two-probe resistance for a SWNT bundle below $0.06R_N$. The solid line is the curve fitted to the data below $0.06R_N$ by Eq. (11) predicted by the LAMH theory. The estimated region of validity for the LAMH theory is below $0.07R_N$ for dirty wires where $l⪡{\xi }_{BCS}$ (Ref. 11). The condition of $l⪡{\xi }_{BCS}$ is well satisfied in the SWNT bundle (see text).