Narrow gap carbon nanotubes as candidate excitonic insulators

Ultraclean suspended carbon nanotubes, predicted to be metallic by band theory, always exhibit a many-body transport gap at low temperature. Whereas the correlated ground state was early interpreted as a Mott insulator, it was more recently predicted that, in gapless (armchair) tubes, the gap is enforced by the permanent condensation of excitons. Here we investigate exciton instabilities in these carbon nanotubes. We show that the long range Colomb interaction remains largely unscreened even in the presence of Fermi points and stabilizes the excitonic insulator (EI) phase in all narrow-gap nanotubes. Moreover we show that the EI phase persists to observable temperatures for the large radii nanotubes commonly used in experiments.