Collective excitations in semiconductor superlattices

TLDR

Electronic collective modes of many equally spaced, parallel two‑dimensional electron layers are examined using a self‑consistent‑field approach. The study analyzes how a perpendicular static magnetic field modifies the collective‑mode spectrum via self‑consistent‑field and hydrodynamic approximations, and extends the theory to alternating electron‑hole layers. Plasmon dispersion relations for finite and infinite periodic systems are derived, revealing that the optical‑plasmon frequency approaches the 2D or 3D limits depending on qa, and that magnetoplasmons, helicons, and Alfvén waves can coexist, underscoring relevance to semiconductor superlattices.

Abstract

Electronic collective modes of a system of large numbers of equally spaced, parallel two-dimensional electron layers are discussed within a self-consistent-field approach. Plasmon dispersion relations for the finite system as well as for the infinite periodic system are obtained. It is shown that the optical-plasmon frequency of the periodic system goes into the known two- or three-dimensional limit, respectively, depending on whether $\mathrm{qa}\ensuremath{\gg}1$ or $\mathrm{qa}\ensuremath{\ll}1$, where $q$ is the wave number in the two-dimensional plane and $a$ is the layer spacing. Effect of a uniform static external magnetic field oriented normal to the two-dimensional layers, on the collective-mode spectrum, is discussed with the use of the self-consistent-field and hydrodynamic approximations. It is shown that magnetoplasmons, helicon, and Alfv\'en waves can all exist in such a periodic system under suitable conditions. The theory is generalized to a system where the alternate layers are electrons and holes. The relevance of these results to semiconductor superlattice systems (both types I and II) is pointed out.