Acoustic Plasmons and Transverse Modes in Semimetals and Semiconductors

Available from UMI in association with The British Library. A model dielectric tensor, based on the random -phase approximation with exact analytic continuation into the lower half of the complex frequency plane, is obtained for a two component degenerate Fermi gas. The crystalline character of the system is allowed for in the effective mass approximation. The carriers are assumed to occupy ellipsoidal pickets in k-space. The collective excitations (longitudinal and transverse) of the system are obtained by solving the dispersion equation. For small wavevectors, the longitudinal spectrum consists of two modes: ordinary and acoustic plasmons. An analytic expression for the phase velocity of the acoustic plasmon in the Pines-Froehlich approximation is derived. The damping depends on the orientations of both sets of ellipsoids, while the real part depends on the orientations of the ellipsoids constituting the slower component in the plasma. The model is applied to SnTe. Two systems with different hole concentrations have been studied. The acoustic plasmon exists for some but not all directions of the wavevector. The magnitude of its phase velocity at zero wavevector depends on the hole concentration. Varying the hole concentration from 5.7 times 10^{25 } m^{-3} to 13.2 times 10^{25 }m^{-3} makes its existence confined only to the regions near the (100) and (111)/surd3 directions and also results in an increase of 60% and 30% in the real and imaginary parts of the phase velocity, respectively. The spectrum has an abrupt cut-off (maximum wavevector); this corresponds to the onset of Landau damping in both plasmas. This maximum wavevector is direction dependent. In the second category of excitations (transverse), besides two well-known electromagnetic modes a third mode has been found. The existence of this mode depends on direction; it does not exist in the (100) and (111)/ surd3 directions. The spectrum has a singularity (critical wavevector), at which the third mode merges with one of the modes corresponding to the anomalous skin effect resulting in the appearance of a non-zero real part of the frequency. This mode can travel faster than the fastest carrier in the plasma but its relative damping is about 1.