Floquet's theorem, and the general qualitative features of the band structure, are described in the one-dimensional case. The discussion includes a little-known unstable state at band edges that is not a Floquet function. This “band edge state” can in certain cases play a role in a thin crystalline layer, analogous to the role of a surface state in a semi-infinite crystal. Some incorrect and misleading statements about Floquet's and Bloch's theorems, which are widespread in expository accounts of the subject, are pointed out.

No abstract

The authors present RPA calculations of the spectra of acoustic plasmons in GaSb, SnTe and Bi. They find that acoustic plasmons only just exist in Bi, having a small critical wavevector of about 10 mu m-1, beyond which they do not exist. In n-GaSb with 1.4*1024 electrons/m3, the calculations give an acoustic plasmon with velocity about 105 ms-1 and relative damping mod omega " mod / omega ' about 0.1. The acoustic plasmon exists for wavevectors up to at least 100 mu m-1 (where the RPA breaks down). In p-SnTe with 1.5*1026 holes/m3, they find an acoustic plasmon with velocity about 2*105 ms-1 and relative damping about 0.1. The spectrum ends abruptly at a critical wavevector which is about 100 mu m-1. They conclude that the prospects for observing acoustic plasmons are poor in Bi, but good in GaSb and SnTe.

No abstract

Acoustic plasmons in a two-component degenerate Fermi gas are analysed, using the random-phase approximation dielectric function with exact analytic continuation into the lower half of the complex frequency plane. The acoustic plasmon spectrum, in reduced variables, depends on four parameters-the ratio of Thomas-Fermi screening wavevectors of the two plasmas, the ratio of Fermi velocities, and the densities of the two plasmas. The dependence of the spectrum on these parameters is surveyed. The first two of the abovementioned parameters are the most important. Acoustic plasmons can exist even when the two plasmas have equal effective mass. The range of parameters giving weakly damped acoustic plasmons is described. The spectrum has an abrupt cut-off (maximum wavevector); this corresponds to the onset of Landau damping in both plasmas. The experimental results of Pinczuk, Shah and Wolff on acoustic plasmons in the GaAs electron-hole plasma are reanalysed. For this purpose the extension to a three-component plasma is made, since the light holes, although few in number, have a significant effect on the results. In this system the 'upper acoustic plasmon' does not exist, contrary to what is implicitly assumed by Pinczuk, Shah and Wolff in their analysis. The 'lower acoustic plasmon' does exist, and its phase velocity agrees, within the errors of theory and experiment, with their experimental result.