Subbands, exchange, and correlation effects on collective excitations in parabolic-quantum-well wires

The plasmon collective excitations in quasi-one-dimensional quantum-well wires are calculated for two- and three-subband model by using the self-consistent-field approximation theory proposed by Singwi, Tosi, Land, and Sjölander [Phys. Rev. 176, 589 (1968)] for the response function of the electron system. The present calculations are applied to GaAs-${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$${\mathrm{Al}}_{\mathrm{x}}$As parabolic-quantum-well wires with the appropriate form factors that take into account the influence of the width of the electron layer. Quantities such as the effective potential, the static structure factor, the pair-correlation function, and the plasmon dispersion relation are calculated as a function of energy difference between subbands and electron density. We found that exchange and correlation effects may be quantitatively significant for quasi-one-dimensional electron gas with a parabolic confinement potential. In the case where more than one subband is occupied, we found an additional plasmonlike intersubband mode. We also found significant differences due to the presence of the local-field correction included in our model calculation when compared to the corresponding random-phase approximation results.