Effect of electron-hole asymmetry on cross-polarized excitons in carbon nanotubes

Excitonic absorption of semiconducting carbon nanotubes for polarization perpendicular to the tube axis is theoretically studied in an effective-mass approximation including higher-order terms describing trigonal warping, curvature, lattice distortion, and electron-hole asymmetry. Asymmetry between electrons and holes causes brightening of dark excitons leading to additional low-energy peaks in optical absorption spectra. In comparison with parallel polarization, chiral-angle dependence of excitation energy is weak because of the cancellation of higher-order corrections between relevant valence and conduction bands.