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A theoretical model is presented for the phonon limited mobility of theDirac-Fermion gas in a three-dimensional (3D) Dirac semimetal Cd$_3$As$_2$considering scattering from both the acoustic and the optical phonons.Screening effects are taken into account and it is found that they lead to asignificant enhancement of the mobility. Simple analytical equations and powerlaws are obtained in both the Bloch-Gruneisen and equipartition regimes. Thedependence of mobility on the temperature $T$ and the electron density $n_e$ isinvestigated. It is found that optical phonon limited mobility $\mu_{op}$dominates over the acoustic phonon limited mobility $\mu_{ap}$ in the highertemperature region. There is a crossover of $\mu_{ap}$ and $\mu_{op}$ and thecrossover temperature $T_c$ shifts to higher value with increasing $n_e$. Ourcalculations of the mobility are in good agreement with the recent experimentaldata. Comparison is also made with the results in the conventional 3D electrongas in a degenerate semiconductor.

Phonon limited mobility of the Dirac-Fermions in a three-dimensional Dirac semimetal Cd$_3$As$_2$