Eur. Phys. J. B 51, 571-581 (2006)
https://doi.org/10.1140/epjb/e2006-00252-4

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

¹ Instituto de Estructura de la Materia, Consejo Superior de Investigaciones Científicas, Serrano 123, 28006 Madrid, Spain
² Istituto Nazionale di Fisica Nucleare - Laboratori Nazionali di Frascati, via E. Fermi 40, 00044 Frascati, Italy

Corresponding author: ^a enrico.perfetto@roma2.infn.it

Received: 21 October 2005
Published online: 22 June 2006

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.