The amplification coefficient α of acoustic phonons is theoretically investigated in a three-dimensional Dirac semimetal (3DDS) driven by a dc electric field E causing the drift of the electrons. It is numerically studied as a function of the frequency ω q, drift velocity v d, electron concentration ne, and temperature Tin the Dirac semimetal Cd3As2. We find that the amplification of acoustic phonons (α ∼ hundreds of cm-1) takes place when the electron drift velocity v d is greater than the sound velocity v s. The amplification is found to occur at small E (∼few V/cm) due to large electron mobility. The frequency dependence of αshows amplification in the THz regime with a maximum α m occurring at the same frequency ω q m for different v d. The α m is found to increase with increasing v d. α vs ω q for different ne also shows a maximum, with α m shifting to higher ω q for larger ne. Each maximum is followed by a vanishing α at nearly “2k f cutoff,” where k f is the Fermi wave vector. It is found that α m/ne and ω q m/n e 1/3 are nearly constant. The α m ∼ ne can be used to identify the 3DDS phase as it differs from α m ∼ n e 1/3 dependence in conventional bulk Cd3As2 semiconductor.
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