Ki. Golden et al., RETARDATION EFFECTS ON COLLECTIVE EXCITATIONS IN CORRELATED SUPERLATTICES, Physical review. B, Condensed matter, 57(16), 1998, pp. 9883-9892
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].