Plasmon and shear modes in correlated superlattices

The dynamical matrix, dielectric response tensor, and dispersion relations for a strongly correlated unmagnetized superlattice are formulated in the quasilocalized charge approximation. Analysis of the dispersion relations at wavelengths long compared with the spacing d between adjacent layers indicates that the random-phase-approximation (RPA) collective-mode structure is substantially modified by particle correlations. 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 existence of a gapped shear mode band which is wholly maintained by Coulombic interlayer interactions over and above the RPA. When interlayer interactions are taken into account only through the average RPA field, the band collapses into a single shear mode which exhibits the long-wavelength acoustic dispersion characteristic of the correlated two-dimensional electron liquid. Other interesting effects include (i) an optical-phonon crystal-like dispersion exhibited by the in-phase plasmon at long wavelengths for d sufficiently small; and (ii) an acoustic-phonon dispersion exhibited by the in-phase shear mode at long wavelengths.