Correlation gap in armchair carbon nanotubes

TL;DR

This paper investigates how electron-electron interactions influence the energy gap in armchair carbon nanotubes, revealing that the previously predicted exponential scaling is valid only for moderate interaction strengths.

Contribution

The study provides a detailed analysis of the correlation gap scaling in armchair nanotubes using Hubbard model, Hartree-Fock, and Renormalisation Group methods, refining previous predictions.

Findings

Scaling of the gap as exp(-nt/U) is valid only for moderate U.

Derived the gap scaling as a function of n for fixed U.

Discussed implications for the magnitude of the correlation gap in nanotubes.

Abstract

We revisit the problem of the correlation gap in (n,n) armchair carbon nanotubes, that would be metallic in the absence of electron-electron correlations. We attack the problem in the context of a Hubbard model with on-site repulsion U only, and we show that the scaling of the gap as exp(-nt/U) predicted by Balents and Fisher (Phys. Rev. B 55, R11973 (1997)), can only be valid if U is not too large, even for very large values of n. Using Hartree--Fock calculations and Renormalisation Group arguments we derive the scaling of the gap as a function of n for a given value of U. Possible applications for the magnitude of the correlation gap in armchair carbon nanotubes will be discussed.