ACOUSTIC-PHONON MODES OF RECTANGULAR QUANTUM WIRES

Acoustic phonon modes of a free-standing rectangular quantum wire comp osed of cubic crystals are theoretically investigated using an algorit hm developed to analyse data from resonant ultrasound spectroscopy. Th e normal phonon modes are classified according to their spatial symmet ries into a compressional mode termed the dilatational mode and non-co mpressional modes referred to as the flexural, torsional, and shear mo des. The formalism that we present is quite general and can be applied to wires of any cubic material. As an example, the dispersion relatio ns are obtained for square and rectangular wires of GaAs, taking into account the anisotropic elasticity of the material. The dispersion cur ves for a rectangular wire are compared with those of the approximate hybrid modes referred to as the thickness and width modes, and the val idity of the modes is discussed. The existence of edge modes is confir med by examining the spatial distribution of displacement vectors.