Fermi level dependent optical transition energy in metallic single-walled carbon nanotubes

The influence of electron (hole) doping on the electronic structure of metallic single-walled carbon nanotubes (m-SWCNTs) is discussed by first principles calculations. The lattice constant c along the nanotube axis of m-SWCNTs (an (8, 8) armchair and a (12, 0) zigzag SWCNT, as examples) is calculated as a function of the Fermi energy. We find that the lengths of c for both sample nanotubes remain unchanged when the Fermi level changes between the first pair of van Hove singularities (VHS) states, while c decreases with increasing or decreasing Fermi level beyond that region. The decrease in c results in a decrease of the C–C bond length parallel to the tube axis (BA), while it increases the C–C bond length perpendicular to the tube axis (BR). By studying the energy separation (E11M) between the first pair of VHS states, we also find that E11M shows a similar behavior to those shown by c with changing Fermi level. Our study gives theoretical support for the optical properties of CNTs that are observed by electron/hole doping.