Amplification of terahertz frequency acoustic phonons by drifting electrons in three-dimensional Dirac semimetals

Abstract

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 ωq, drift velocity vd, electron concentration ne, and temperature T in the Dirac semimetal Cd3As2. We find that the amplification of acoustic phonons (α ∼ hundreds of cm-1) takes place when the electron drift velocity vd is greater than the sound velocity vs. The amplification is found to occur at small E (∼few V/cm) due to large electron mobility. The frequency dependence of α shows amplification in the THz regime with a maximum αm occurring at the same frequency ωqm for different vd. The αm is found to increase with increasing vd. α vs ωq for different ne also shows a maximum, with αm shifting to higher ωq for larger ne. Each maximum is followed by a vanishing α at nearly “2kf cutoff,” where kf is the Fermi wave vector. It is found that αm/ne and ωqm/ne1/3 are nearly constant. The αm ∼ ne can be used to identify the 3DDS phase as it differs from αm ∼ ne1/3 dependence in conventional bulk Cd3As2 semiconductor.