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

We derive the effective low-energy theory for interacting electrons in metallic single-wall carbon nanotubes, taking into account phonon exchange due to twisting, stretching, and breathing modes 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)approximate to3.6+/-1.4 Angstrom, 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.