Cerenkov emission of acoustic phonons electrically generated from three-dimensional Dirac semimetals

Abstract

Cerenkov acoustic phonon emission is theoretically investigated in a three-dimensional Dirac semimetal (3DDS) when it is driven by a dc electric field E. Numerical calculations are made for Cd3As2 in which mobility and electron concentration are large. We find that Cerenkov emission of acoustic phonons takes place when the electron drift velocity vd is greater than the sound velocity vs. This occurs at small E (∼few V/cm) due to large mobility. Frequency (ωq) and angular (θ) distribution of phonon emission spectrum P(ωq, θ) are studied for different electron drift velocities vd (i.e., different E) and electron concentrations ne. The frequency dependence of P(ωq, θ) shows a maximum Pm(ωq, θ) at about ωm ≈ 1 THz and is found to increase with the increasing vd and ne. The value of ωm shifts to higher region for larger ne. It is found that ωm/ne1/3 and Pm(ωq, θ)/ne2/3 are nearly constants. The latter is in contrast with the Pm(ωq, θ)ne1/2 = constant in conventional bulk semiconductor. Each maximum is followed by a vanishing spectrum at nearly “2kf cutoff,” where kf is the Fermi wave vector. Angular dependence of P(ωq, θ) and the intensity P(θ) of the phonon emission shows a maximum at an emission angle 45° and is found to increase with increasing vd. P(θ) is found to increase linearly with ne giving the ratio P(θ)/(nevd) nearly a constant. We suggest that it is possible to have the controlled Cerenkov emission and generation of acoustic phonons with the proper choice of E, θ, and ne. 3DDS with large ne and mobility can be a good source of acoustic phonon generation in ∼THz regime.