Exciton-Peierls mechanism and universal many-body gaps in carbon nanotubes

"Metallic" carbon nanotubes exhibit quasiparticle gaps when isolated from a screening environment. The gap-opening mechanism is expected to be of electronic origin, but the precise nature is debated. In this work, we show that hybrid density functional theory predicts a set of excitonic instabilities capable of opening gaps of the size found in experiment. The excitonic instabilities are coupled to vibrational modes and, in particular, the modes associated with the ${\bf \Gamma}-E_{2g}$ and ${\bf K}-A'_1$ Kohn anomalies of graphene, inducing Peierls lattice distortions with a strong electron-phonon coupling. In the larger tubes, the longitudinal optical phonon mode becomes a purely electronic dimerization that is fully symmetry conserving in the zigzag and chiral tubes, but breaks the symmetry in the armchair tubes. The resulting gaps are universal (i.e., independent of chirality) and scale as 1/R with tube radius.