PLASMON AND SHEAR MODES IN CORRELATED SUPERLATTICES

The dynamical matrix, dielectric response tensor, and dispersion relat ions for a strongly correlated unmagnetized superlattice are formulate d in the quasilocalized charge approximation. Analysis of the dispersi on relations at wavelengths long compared with the spacing d between a djacent layers indicates that the random-phase-approximation (RPA) col lective-mode structure is substantially modified by particle correlati ons. In earlier works [see, e.g., G. Kalman, Y. Ren, and K. I. Golden, Phys. Rev. B 50, 2031 (1994)] the authors reported the existence of a long-wavelength energy gap in the acoustic plasmon band generated by strong interlayer correlations. The present analysis indicates the exi stence of a gapped shear mode band which is wholly maintained by Coulo mbic interlayer interactions over and above the RPA. When interlayer i nteractions are taken into account only through the average RPA field, the band collapses into a single shear mode which exhibits the long-w avelength acoustic dispersion characteristic of the correlated two-dim ensional electron liquid. Other interesting effects include (i) an opt ical-phonon crystal-like dispersion exhibited by the in-phase plasmon at long wavelengths for d sufficiently small; and (ii) an acoustic-pho non dispersion exhibited by the in-phase shear mode at long wavelength s.