Current instability and diamagnetism in small-diameter carbon nanotubes

We investigate the electronic instabilities in carbon nanotubes of short radius, looking for the breakdown of the Luttinger liquid regime from the singular behavior of the charge stiffnesses at low energies. We show that such a breakdown is realized in the undoped (3,3) nanotubes through the onset of phase separation into regions with opposite electronic current. The phenomenology derived from this regime is consistent with the formation of a pseudogap in the single-particle spectrum as well as with a divergent diamagnetic susceptibility, as observed in the experiments carried out in carbon nanotubes of small diameter.