Optical transitions in metallic single-walled carbon nanotubes

We report vertical electronic transitions of 20 metallic single-walled carbon nanotubes calculated as band energy differences from Kohn-Sham density functional theory. Our first-order transitions (E-11) calculated with hybrid functionals (containing a portion of exact exchange) are in very good agreement with available experimental data. Recently, we have reported similar agreement between experiment and theory for semiconducting tubes. We find that the trigonal warping splitting in the band structure of metallic tubes is about 1.5 to 2 times larger than that reported previously.