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

TL;DR

This paper demonstrates that excitonic instabilities coupled with vibrational modes induce universal, radius-dependent gaps in metallic carbon nanotubes, explaining experimental observations through a combined electronic and lattice mechanism.

Contribution

It reveals a unified exciton-Peierls mechanism causing universal gaps in metallic nanotubes, integrating excitonic and phononic effects with a symmetry-conserving lattice distortion.

Findings

Excitonic instabilities predicted by hybrid DFT open observed gaps.

Gaps scale as 1/R, independent of chirality.

Lattice distortions involve specific vibrational modes and electron-phonon coupling.

Abstract

"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.