Core-hole induced misalignment between Van-Hove singularities and K-edge fine structure in carbon nanotubes

TL;DR

This study explores how core-hole effects cause misalignment between Van Hove singularities and K-edge fine structures in carbon nanotubes, using advanced modeling to improve understanding of their electronic excitations.

Contribution

It demonstrates that core exciton wavefunctions are modified by confinement, affecting the relation between VHSs and X-ray absorption spectra in SWCNTs.

Findings

BSE method improves spectral peak predictions over final-state approximation

Core exciton wavefunctions are altered by circumferential confinement

First bright excitons are Frenkel, higher excitons are charge resonance

Abstract

We investigate the relationship between the K-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 wavefunctions induced by the confinement along the circumference. Additionally, we analyze the character of core excitons in SWCNTs and 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.