Binding and spontaneous condensation of excitons in narrow-gap carbon nanotubes

TL;DR

This paper demonstrates that narrow-gap carbon nanotubes inherently form an excitonic insulator phase due to strong electron-hole interactions, with a detailed analysis of exciton binding energies and stability related to nanotube structure.

Contribution

It extends previous work by showing all stable narrow-gap nanotubes are excitonic insulators, providing a scaling law for exciton binding energy and a self-consistent calculation of the transport gap.

Findings

All stable narrow-gap nanotubes are excitonic insulators.

Derived a scaling law for exciton binding energy based on nanotube radius and chirality.

Computed the transport gap considering excitonic effects with first-principles validated screening.

Abstract

Ultraclean, undoped carbon nanotubes are observed to be always insulating, even when the gap predicted by band theory is zero: the residual band gap is then thought to have a many-body origin. Here we theoretically show that the correlated insulator is excitonic in $all stable$ narrow-gap tubes irrespective of their size, thus extending our previous claim, limited to gapless (armchair) tubes [D.~Varsano, S.~Sorella, D.~Sangalli, M.~Barborini, S.~Corni, E.~Molinari, M.~Rontani, Nature Communications $\mathbf{8}$, 1461 (2017)]. We derive the scaling law of the exciton binding energy with the tube radius and chirality, and compute self-consistently the fundamental transport gap of the excitonic insulator, by enhancing the two-band model with an accurate treatment of screening validated from first principles. Our findings point to the broader connection between the exciton length scale, dictated by structure, and the stability of the excitonic phase.