Intertube effects on one-dimensional correlated state of metallic single-wall carbon nanotubes probed by ${}^{13}\mathbf{C}$ NMR

The electronic states in isolated single-wall carbon nanotubes (SWCNTs) have been considered as an ideal realization of a Tomonaga-Luttinger liquid (TLL). However, it remains unclear whether one-dimensional correlated states are realized under local environmental effects such as the formation of a bundle structure. Intertube effects originating from other adjacent SWCNTs within a bundle may drastically alter the one-dimensional correlated state. In order to test the validity of the TLL model in bundled SWCNTs, low-energy spin excitation is investigated by nuclear magnetic resonance (NMR). The NMR relaxation rate in bundled mixtures of metallic and semiconducting SWCNTs shows a power-law temperature dependence with a theoretically predicted exponent. This demonstrates that a TLL state with the same strength as that for effective Coulomb interactions is realized in a bundled sample, as in isolated SWCNTs. In bundled metallic SWCNTs, we found a power-law temperature dependence of the relaxation rate, but the magnitude of the relaxation rate is one order of magnitude smaller than that predicted by theory. Furthermore, we found an almost doubled magnitude of the Luttinger parameter. These results indicate suppressed spin excitations with reduced Coulomb interactions in bundled metallic SWCNTs, which are attributable to intertube interactions originating from adjacent metallic SWCNTs within a bundle. Our findings give direct evidence that bundling reduces the effective Coulomb interactions via intertube interactions within bundled metallic SWCNTs.

Figure 1

${}^{13}\mathrm{C}$ NMR for bundles of mixed semiconducting and metallic SWCNTs at 295 K under 9.4 T.

Figure 2

Temperature dependence of ${\left(T_{1}T\right)}^{-1}$ for bundled SWCNT samples with different metallicity measured under 9.4 T. The closed squares represent bundles of mixed metallic and semiconducting SWCNTs. The closed diamonds represent bundles of highly concentrated metallic SWCNTs. The open circles represent bundles of mixed metallic and semiconducting SWCNTs from Ref. [26]. The solid lines represent fits to $T^{\alpha }$.

Figure 3

Comparison between the experimental ${\left(T_{1}T\right)}^{-1}$ and that calculated by TLL theory for (a) bundled mixtures of metallic and semiconducting SWCNTs and (b) bundled metallic SWCNTs. Note that the ${\left(T_{1}T\right)}^{-1}$ value in (a) is three times larger than those in Fig. 1 because of spin-diffusion averaging (see text). The calculated results based on Ref. [37] reproduce the experimental ${\left(T_{1}T\right)}^{-1}$ quite wellin (a).