# Intertube effects on one-dimensional correlated state of metallic single-wall carbon nanotubes probed by 13C NMR

## TL;DR

This study uses 13C NMR to investigate how bundling affects the one-dimensional correlated electronic states in metallic single-wall carbon nanotubes, revealing suppressed Coulomb interactions due to intertube effects.

## Contribution

It provides experimental evidence that bundling modifies the Tomonaga-Luttinger liquid state by reducing Coulomb interactions through intertube effects in metallic SWCNTs.

## Key findings

- Power-law temperature dependence of NMR relaxation rate observed in bundled SWCNTs.
- Relaxation rate magnitude is an order of magnitude smaller than theoretical predictions.
- Luttinger parameter nearly doubled in bundled metallic SWCNTs.

## Abstract

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.