Intrawell and interwell coupling of plasmons in multilayer modulation-doped GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As quantum wells

Using electronic Raman scattering and calculations of the full random-phase-approximation inverse dielectric function, we show that in a modulation-doped GaAs/${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As multiple-quantum-well structure with N quantum wells and M occupied subbands per well, the intrawell interactions split the plasmon dispersion into M groups of modes. The interwell Coulomb interactions split each group further into N eigenmodes and differ strongly between the different groups of plasmon modes. We observe ‘‘acoustic’’ plasmon modes in regions where Landau damping occurs. The splitting of the plasmon modes measures the strengths of the interwell and the intrawell interactions in modulation-doped GaAS/${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As quantum wells. We determine the plasmon dispersion by electronic Raman scattering for a sample with three filled subbands per well and five superimposed wells. The present work shows how Raman scattering can be used to characterize multiple quantum wells with multiple subband occupations.