The spectrum of interacting metallic carbon nanotubes: Exchange effects and universality

TL;DR

This paper analyzes the low energy spectrum of finite size metallic carbon nanotubes, revealing exchange effects, spin triplet ground states, and the impact of Coulomb interactions on their electronic properties.

Contribution

It derives a comprehensive low energy Hamiltonian including Coulomb scattering processes and explores their effects on the spectrum and ground state configurations.

Findings

Ground state is a spin 1 triplet for certain electron counts.

Short ranged Coulomb processes induce exchange effects.

Lifting of spin-charge separation at higher energies.

Abstract

The low energy spectrum of finite size metallic single-walled carbon nanotubes SWNTs) is determined. Starting from a tight binding model for the $p_{z}$ electrons, we derive the low energy Hamiltonian containing all relevant scattering processes resulting from the Coulomb interaction, including the short ranged contributions becoming relevant for small diameter tubes. In combination with the substructure of the underlying honeycomb lattice the short ranged processes lead to various exchange effects. Using bosonization the spectrum is determined. We find that the ground state is formed by a spin 1 triplet, if $4n+2$ electrons occupy the SWNT and the branch mismatch is smaller than the exchange splitting. Additionally, we calculate the excitation spectra for the different charge states and find the lifting of spin-charge separation as well as the formation of a quasi-continuum at higher excitation energies.