Two-stream instabilities in solid-state plasmas caused by conventional and unconventional mechanisms

We employ the linear-response theory of collisionless plasmas and the linear-response theory of carriers in a static, homogeneous electric field, with collisions approximated by the relaxation-time approximation [Phys. Rev. B 39, 8464 (1989)] to study instabilities with respect to charge-density perturbations of counterstreaming charged particles. We treat both bulk (three-dimensional) systems and systems where the carriers drift along adjacent two-dimensional conducting planes (as in a semiconductor heterostructure). Instabilities occur in both the three- and two-dimensional systems, for both the collisionless plasma case (as in conventional plasma theory) and for the case of carriers driven by an electric field (which we call ‘‘electric-field-induced instability’’). The physical mechanism that causes the electric-field-induced two-stream instability is linked to the presence of the driving electric field and scattering and is different from that of the conventional collisionless plasma instability. In a pair of adjacent quantum wells with ${\mathrm{Al}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Ga}}_{\mathit{x}}$As/GaAs-type parameters, we obtain an instability at very large drift velocities that may not be experimentally attainable. We speculate that by drifting carriers in a superlattice of alternating electron and hole layers, an instability could be obtained experimentally, and that such an instability could be used to produce a terahertz oscillator.