Superconducting diamagnetic fluctuations in ropes of carbon nanotubes

We report low-temperature magnetization measurements on a large number of purified ropes of single wall carbon nanotubes. In spite of a superparamagnetic contribution due to the small ferromagnetic catalytical particles still present in the sample, at low temperature $(T<0.5\mathrm{K})$ and low magnetic field $(H<80\mathrm{Oe})$, a diamagnetic signal is detectable with an amplitude equal to $\frac{1}{3}$ of the total magnetization signal. This low-temperature diamagnetism can be interpreted as the Meissner effect in ropes of carbon nanotubes which have previously been shown to exhibit superconductivity from transport measurements [M. Kociak, A. Y. Kasumov, S. Guéron, B. Reulet, I. I. Khodos, Y. B. Gorbatov, V. T. Kolkov, L. Vaccarini, and H. Bouchiat, Phys. Rev. Lett. 86, 2416 (2001)]. Its amplitude corresponds to a field expulsion of the order ${10}^{-3}$ and is in agreement with simple expectations taking into account the intertube Josephson coupling.

Figure 1

(Color online) Field dependence of the total magnetization of the sample at various temperatures below $3.5\mathrm{K}$. Lower inset: field dependence of $\Delta M(T,H)=M(T,H)-M(3.5,H)$ for different temperatures showing that the hysteretic component of the magnetization is independent of temperatures below $3.5\mathrm{K}$. (This remains true up to $T=35\mathrm{K}$.) Upper inset: transmission electron microscopy image of one of the SWNT ropes in the sample.

Figure 2

(a) Renormalized magnetization $M(T,H)-M(35\mathrm{K},H)∕H_{\mathit{loc}}\left(H\right)$ as a function of temperature between $70\mathrm{mK}$ and $35\mathrm{K}$ for $H=20\mathrm{Oe}$ and $H=150\mathrm{Oe}$ compared to the fit with two assemblies of superparamagnetic particles whose adjusted volumic distributions are shown in the inset. The deviations at low temperature for the data taken at $20\mathrm{Oe}$ are the signature of the Meissner effect. (b) Temperature dependence of the field cooled renormalized magnetization: $\Delta \chi (T,H)=\Delta M(T,H)∕H_{\mathit{loc}}\left(H\right)$ for various values of magnetic field. Inset: Field dependence of the local field obtained by renormalization of the temperature dependent data above $1\mathrm{K}$ up to $3.5\mathrm{K}$ (circles) and up to $30\mathrm{K}$ (squares).

Figure 3

Temperature dependence of the renormalized magnetization after the substraction of the data at $H=150\mathrm{Oe}$: $\Delta {\chi }_{\mathit{dia}}(T,H)=\Delta \chi (T,H)-\Delta \chi (T,150)$. Inset: Reconstitution, using Eq. (4), of the field dependence of the diamagnetic contribution for various temperatures.