Family Effects on Excitons in Semiconducting Carbon Nanotubes

Family behavior of excitons is studied in carbon nanotubes based on a k center dot p scheme. Effects responsible for family pattern are characterized by two parameters beta representing higher-order terms in the effective Hamiltonian responsible for trigonal warping and p representing amount of effective flux due to curvature and lattice distortion. These parameters are determined through comparison with empirical formula of the lowest exciton and experiments of two-photon absorption giving excited exciton states. The observed family pattern can be reproduced much better for the first gap than for the second gap.