Impurity-induced valley mixing of excitons in semiconducting carbon nanotubes

We have studied effects of a short-range impurity on excitons and optical spectra in semiconducting carbon nanotubes within the effective-mass theory. The short-range scattering by a single impurity induces the mixing between several exciton states consisting of intra- or inter-valley electron-hole pairs and largely modifies these exciton energy levels. We have found that a dark exciton state, which can never couple to the bright one even under such a valley mixing, always has the lowest energy. The bright exciton peak in absorption spectra splits into two peaks with increasing the strength of the impurity potential. In addition, the calculated spectra suggest that a weak continuum absorption with no peaks may be observed, corresponding to the first excited states of the excitons with finite center-of-mass momenta.