Core-hole induced misalignment between Van Hove singularities and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>K</mml:mi></mml:math>-edge fine structure in carbon nanotubes

We investigate the relationship between the -edge fine structure of isolated single-wall carbon nanotubes (SWCNTs) and the Van Hove singularities (VHSs) in the conduction-band density of states. To this end, we model x-ray absorption spectra of SWCNTs using the final-state approximation and the Bethe-Salpeter equation (BSE) method. Both methods can reproduce the experimental fine structure, where the BSE results improve on peak positions and amplitude rations compared to the final-state approximation. When the fine structure in the modeled spectra is related to the VHSs, significant differences are found. We suggest that these differences arise due to modifications of the core exciton wave functions induced by the confinement along the circumference. Additionally, we analyze the character of core excitons in SWCNTs, and we find that the first bright excitons are Frenkel excitons, while higher-lying excitons are charge resonance states. Finally, we suggest that the qualitative picture based on VHSs in the density of states holds when there is a large energy gap between successive VHSs.