Electronic instabilities in 3D arrays of small-diameter (3,3) carbon nanotubes

TL;DR

This paper analyzes the electronic instabilities in small-diameter (3,3) carbon nanotubes, revealing critical behavior leading to metallic destabilization without superconductivity, especially in large arrays where Coulomb interactions are screened.

Contribution

It provides a detailed theoretical analysis of electronic instabilities in (3,3) carbon nanotubes considering phonon-mediated and Coulomb interactions, including effects of array assembly.

Findings

Destabilization of metallic behavior via critical charge stiffness behavior.

Critical behavior involves divergent compressibility or vanishing excitation velocity.

No significant superconducting correlations are observed at the transition.

Abstract

We investigate the electronic instabilities of the small-diameter (3,3) carbon nanotubes by studying the low-energy perturbations of the normal Luttinger liquid regime. The bosonization approach is adopted to deal exactly with the interactions in the forward-scattering channels, while renormalization group methods are used to analyze the low-energy instabilities. In this respect, we take into account the competition between the effective e-e interaction mediated by phonons and the Coulomb interaction in backscattering and Umklapp channels. Moreover, we apply our analysis to relevant experimental conditions where the nanotubes are assembled into large three-dimensional arrays, which leads to an efficient screening of the Coulomb potential at small momentum-transfer. We find that the destabilization of the normal metallic behavior takes place through the onset of critical behavior in some of the two charge stiffnesses that characterize the Luttinger liquid state. From a physical point of view, this results in either a divergent compressibility or a vanishing renormalized velocity for current excitations at the point of the transition. We observe anyhow that this kind of critical behavior occurs without the development of any appreciable sign of superconducting correlations.