Collective excitations in semiconductor superlattices

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 $\mathrm{qa}\gg 1$ or $\mathrm{qa}\ll 1$, 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 Alfvén 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.