Size dependence of exciton-exciton scattering in semiconductor quantum wires

The exciton dephasing kinetics due to exciton-exciton scattering is studied in ${\mathrm{In}}_{0.135}{\mathrm{Ga}}_{0.865}\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ quantum wires both experimentally and theoretically as a function of the wire width. By degenerate four-wave mixing studies, we observe a strong increase of the exciton-density-dependent dephasing rate for decreasing wire widths between 85 nm and 29 nm. This surprising result is explained quantitatively within a multisubband model in terms of the increase of the exchange part of the exciton-exciton interaction with increasing confinement.