Two-Stream Instability in Anisotropic Semimetals

Abstract

Dispersion relations for two-stream instabilities in electron—hole plasmas in bismuth and pyrolytic graphite have been obtained. The band structure of these anisotropic semimetals has been incorporated into the dispersion relations. These dispersion relations were numerically evaluated for the growth rate and frequency of oscillation for waves propagating in the three principal crystal axes of bismuth and for the wave propagating in the a-plane of pyrolytic graphite. For the wave propagating along the trigonal axis of bismuth there is one optical branch and one acoustical branch. For the acoustic branch the growth rate exceeds the collision damping at an applied electric field of 7 V/cm. The frequency of oscillation where the growth rate is maximum is 510 GHz, which is in the submillimeter-wave range (λ≈0.6 mm). For the wave propagating along the binary axis there is an optical branch, a high-frequency acoustical branch, and a low-frequency acoustical branch. The high-frequency branch is damped even for electrons drifting with velocity near the Fermi velocity. The low-frequency branch exhibits growth but the threshold electric field of 15 V/cm is higher than the field required for the trigonal case. The frequency which corresponds to the peak growth rate for this electric field is 2.3×1012 cps, or λ = 130 μ, which falls in the far-infrared region. Waves propagating along the bisectrix axis of bismuth exhibit anomalous behavior which results in two coupled acoustic modes. The threshold conditions for pyrolytic graphite are less favorable than those for bismuth. The threshold electric field is 160 V/cm which is very much higher than the threshold for bismuth. The frequency of oscillation corresponding to peak growth rate is 3×1013 Hz, or λ = 10 μ, which is in the near-infrared range.