Auger recombination of excitons in one-dimensional systems

Abstract

In tightly confined one-dimensional (1D) systems, the effective Coulomb interaction is greatly enhanced and optical transitions generally lead to the formation of strongly bound excitons. When more than one exciton is present, the Coulomb interaction also leads to rapid exciton-exciton annihilation through an Auger recombination process. This effect, which may be significant even at low exciton densities, can be described by a rate law governing two-body interactions. The Auger recombination rate for excitons in a strongly confined 1D system is analyzed. The rate increases sharply with exciton binding energy, but varies only weakly with temperature. An explicit expression for the Auger recombination rate in terms of the exciton binding energy, optical matrix element and reduced carrier mass is derived for a two-band model in which the Coulomb interaction is approximated by a point-contact potential. Results for the prototypical 1D system of single-walled carbon nanotubes are obtained and compared with experiment.