Insights into the need for ab-initio calculations to accurately predict the optical properties of metallic carbon nanotubes based on experimental confrontation

In this article, we conduct comparative studies on the optical properties of metallic carbon nanotubes. Firstly, we compare the complex dielectric constant predicted by an analytical model, the Linear Surface Conductivity Model, with \textit{ab initio} calculations based on Density Functional Theory. We highlight the similarities and differences between these two models, with the major discrepancy being a significantly different behavior of the plasma frequency with respect to the carbon nanotube diameter. In the second step, we compare the predictions of these models with experimental measurements of the dielectric function. We demonstrate that the screened plasma frequency serves as a reliable quantifier for distinguishing between the two models. In conclusion, we find that the \textit{ab initio} calculations more accurately describe the optical properties of metallic carbon nanotubes compared to the commonly used Linear Surface Conductivity Model.