On the Coulomb interaction in chiral-invariant one-dimensional electron systems

TL;DR

This paper investigates how Coulomb interactions affect the low-energy electronic properties of one-dimensional systems like metallic carbon nanotubes, revealing significant renormalization effects and a crossover from 2D to 1D behavior.

Contribution

It introduces a renormalization group analysis of Coulomb interactions in chiral 1D electron systems, highlighting the impact on Fermi velocity and Luttinger liquid behavior.

Findings

Strong renormalization of Fermi velocity at large number of subbands

Transition to Luttinger liquid behavior at low energies

Wavefunction renormalization leads to vanishing quasiparticle weight

Abstract

We consider a one-dimensional electron system, suitable for the description of the electronic correlations in a metallic carbon nanotube. Renormalization group methods are used to study the low-energy behavior of the unscreened Coulomb interaction between currents of well-defined chirality. In the limit of a very large number n of subbands we find a strong renormalization of the Fermi velocity, reminiscent of a similar phenomenon in the graphite sheet. For small n or sufficiently low energy, the Luttinger liquid behavior takes over, with a strong wavefunction renormalization leading to a vanishing quasiparticle weight. Our approach is appropriate to study the crossover from two-dimensional to one-dimensional behavior in carbon nanotubes of large radius.