Enhanced exciton-phonon scattering in ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ quantum wires

We have investigated the dephasing of excitons due to scattering by acoustic phonons in quantum wires by means of temperature-dependent time-integrated four-wave mixing. Free-standing ${\mathrm{In}}_{0.135}{\mathrm{Ga}}_{0.865}\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ quantum wires with lateral sizes between 29 and 85 nm have been studied. By measuring the phase relaxation time of the excitonic resonance at low carrier densities, we have determined the homogeneous linewidth. From the temperature dependence of the homogeneous linewidth at temperatures between 5 and 30 K, we have evaluated the temperature coefficient ${\gamma }_{\mathrm{ac}},$ which is a measure for the exciton-acoustic phonon scattering strength. ${\gamma }_{\mathrm{ac}}$ is found to increase with decreasing wire width. It is shown that this dependence on the wire width is consistent with a microscopic theory of exciton-acoustic phonon coupling.