Retardation effects on collective excitations in correlated superlattices

Abstract

The authors analyze the effects of electrodynamic retardation on the collective modes in an unmagnetized infinite superlattice modeled as an array of parallel two-dimensional plasma layers embedded in a dielectric substrate. The present work concentrates for the most part on correlated semiconductor superlattices, although the model is equally well suited to metallic superlattices consisting of an alternating array of thin metal layers and thick insulator slabs (e.g., 50 \AA{} Al layers and 500 \AA{} ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ slabs). The analysis is based on the transverse magnetic (TM) and transverse electric (TE) dispersion relations recently formulated by the authors in the retarded quasilocalized charge approximation (RQLCA) [K. I. Golden, G. Kalman, L. Miao, and R. R. Snapp, Phys. Rev. B 55, 16 349 (1997)]. In the nonretarded limit, the QLCA mode structure consists of (i) an isolated in-phase plasmon mode, (ii) a band of gapped plasmons, (iii) an in-phase acoustic shear mode, and (iv) a band of gapped shear modes. This paper presents numerical and approximate analytical solutions of the long-wavelength RQLCA dispersion relations for the collective modes (i)--(iv) all the way down to very small wave numbers where retardation effects can be especially pronounced. Additionally, this work presents insightful approximate analytical formulas for the electromagnetic mode frequencies and gap widths, which add to the literature on the infinite sequences of TM- and TE-polarized electromagnetic bands. Some noteworthy effects that emerge from this study are as follows: (a) The appearance of ultralow frequency shear modes arising from the combined effect of retardation and strong coulomb interactions; the quasilocalization basis of the theory suggests that these modes can propagate when the two-dimensional plasma layers are in a crystalline phase. (b) A negative random-phase approximation shift in the bulk-plasma frequency induced by electrodynamic retardation; this effect can be appreciable in insulator/metal superlattices.