Valence-subband structures of GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As quantum wires: The effect of split-off bands

The valence-subband dispersion for GaAs quantum wires in ${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As host material is calculated in a coupled-band effective-mass model in which the split-off bands are included. We derive the symmetry-adapted basis functions valid at all k for quantum wires of square and rectangular cross sections. Coupling to the split-off bands is seen to leave the uppermost valence subband largely unaffected near the zone center while the other subbands are more markedly affected. This is in contrast to the case of quantum wells where only the light-hole subbands are coupled to the split-off subbands at the zone center.