Optical phonons in GaAs/AlAs quantum wires

Phonon-dispersion curves of semiconductor quantum wires are studied in a realistic rigid-ion model. We introduce an approach for solving the rigid-ion model in quantum wires, which avoids direct computation of the Coulomb interaction. Our calculations demonstrate the interesting anisotropic behavior of long-wavelength optical phonons in quantum wires. In particular, we show that frequencies of several optical phonons approach different values as the wave vector approaches the zone center from three different axes. We have also shown that the lateral confinement in a quantum wire on the interface modes leads to the edge modes.