Coupling of lateral and vertical electron motion in GaAs-${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum wires and dots

Electronic excitations in ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As-GaAs quantum wires and quantum dots have been investigated by means of resonant inelastic light scattering. At low frequencies, we find quasi-one-dimensional and quasi-zero-dimensional confined plasmons. Interestingly, we observe, at higher frequencies, not only the original two-dimensional (2D) intersubband excitations, but additional modes ${\mathrm{\omega }}_{\mathit{k}}$ in polarized scattering geometry. The experimental finding is that the frequencies of these modes obey the relation ${\mathrm{\omega }}_{\mathit{k}}^2$≊${\mathrm{\omega }}_{2\mathrm{D}}^2$+${\mathrm{\omega }}_{\mathrm{}1\mathrm{D}/0\mathrm{D}}^2$, where ${\mathrm{\omega }}_{2\mathrm{D}}$ is the frequency of the vertical intersubband charge-density excitation. ${\mathrm{\omega }}_{1\mathrm{D}}$ is a lateral quasi-one-dimensional confined plasmon frequency in wires and ${\mathrm{\omega }}_{0\mathrm{D}}$ is the frequency of a quasi-zero-dimensional confined plasmon in dots. This relation shows that the additional modes are collective charge-density excitations, which occur due to a coupling of lateral and vertical electron motion. © 1996 The American Physical Society.