Acoustic phonon exchange, attractive interactions, and the Wentzel-Bardeen singularity in single-wall nanotubes

TL;DR

This paper develops a low-energy theory for electrons in metallic single-wall nanotubes, revealing strong attractive interactions and a potential superconducting transition at a critical radius, with implications for experimental observation.

Contribution

It introduces a continuum elastic model accounting for acoustic phonon exchange, predicting a Wentzel-Bardeen singularity and superconducting fluctuations in thin nanotubes.

Findings

Strong attractive interactions predicted for thin nanotubes.

Critical radius for singularity approximately 3.6 Å, accessible experimentally.

Conditions for Peierls transition discussed.

Abstract

We derive the effective low-energy theory for interacting electrons in metallic single-wall carbon nanotubes taking into account acoustic phonon exchange within a continuum elastic description. In many cases, the nanotube can be described as a standard Luttinger liquid with possibly attractive interactions. We predict surprisingly strong attractive interactions for thin nanotubes. Once the tube radius reaches a critical value $R_0 \approx 3.6\pm 1.4$ \AA, the Wentzel-Bardeen singularity is approached, accompanied by strong superconducting fluctuations. The surprisingly large $R_0$ indicates that this singularity could be reached experimentally. We also discuss the conditions for a Peierls transition due to acoustic phonons.