RETARDATION EFFECTS ON COLLECTIVE EXCITATIONS IN CORRELATED SUPERLATTICES

The authors analyze the effects of electrodynamic retardation on the c ollective modes in an unmagnetized infinite superlattice modeled as an array of parallel two-dimensional plasma layers embedded in a dielect ric substrate. The present work concentrates for the most part on corr elated semiconductor superlattices, although the model is equally well suited to metallic superlattices consisting of an alternating array o f thin metal layers and thick insulator slabs (e.g., 50 Angstrom Al la yers and 500 Angstrom Al2O3 slabs). The analysis is based on the trans verse magnetic (TM) and transverse electric (TE) dispersion relations recently formulated by the authors in the retarded quasilocalized char ge approximation (RQLCA) [K. I. Golden, G. Kalman, L. Miao, and R. R. Snapp, Phys. Rev. B 55, 16349 (1997)]. In the nonretarded limit, the Q LCA 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 disp ersion relations for the collective modes (i)-(iv) all the way down to very small wave numbers where retardation effects can be especially p ronounced. Additionally, this work presents insightful approximate ana lytical formulas for the electromagnetic mode frequencies and gap widt hs, 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 frequen cy shear modes arising from the combined effect of retardation and str ong coulomb interactions; the quasilocalization basis of the theory su ggests that these modes can propagate when the two-dimensional plasma layers are in a crystalline phase. (b) A negative random-phase approxi mation shift in the bulk-plasma frequency induced by electrodynamic re tardation; this effect can be appreciable in insulator/metal superlatt ices. [S0163-1829(98)05516-7].