Angle-resolved Raman spectroscopy of the collective modes in an electron bilayer

Electronic Raman scattering from ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ double quantum well structures has been used to observe the acoustic and optic plasmon modes of an electron bilayer system. Angle-resolved measurements allowed direct determination of their dispersions for several separations of the electron layers; these were well described by corresponding dispersion calculations in the random-phase approximation (RPA). Qualitative agreement was obtained between measurements of the relative intensities of the acoustic and optic modes and calculations using a simple nonresonant RPA formalism for the Raman scattering cross section. The markedly different linewidths observed for the acoustic and optic modes are interpreted in terms of the greater localization of the electric fields of the acoustic plasmon, which is therefore much less susceptible to impurity damping than is the optic plasmon.