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

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.

arXiv commentEuropean Physical Journal B (2008) in press

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• The two classes of low energy spectra in finite carbon nanotubes
• Exchange effects in spin polarized transport through carbon nanotube quantum dots
• Enhanced NMR relaxation of Tomonaga-Luttinger liquids and the magnitude of the carbon hyperfine coupling in single-wall carbon nanotubes
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• Spin and valley manipulation in single and double electrostatic silicene quantum dots
• Spectrum and Franck-Condon factors of interacting suspended single-wall carbon nanotubes
• Linear conductance of an interacting carbon nanotube ring
• Spin-dependent transport through interacting graphene armchair nanoribbons
• Pseudo-spin-dependent scattering in carbon nanotubes
• Two-electron n-p double quantum dots in carbon nanotubes
• Graphene armchair nanoribbon single-electron transistors: The peculiar influence of end states
• Nagaoka spin-valley ordering in silicene quantum dots
• Inter- and intra-band Coulomb interactions between holes in silicon nanostructures