A theoretical model is presented for the phonon limited mobility of the Dirac-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 a significant enhancement of the mobility. Simple analytical equations and power laws are obtained in both the Bloch-Gruneisen and equipartition regimes. The dependence of mobility on the temperature $T$ and the electron density $n_e$ is investigated. It is found that optical phonon limited mobility $\mu_{ op}$ dominates over the acoustic phonon limited mobility $\mu_{ ap}$ in the higher temperature region. There is a crossover of $\mu_{ ap}$ and $\mu_{ op}$ and the crossover temperature $T_c$ shifts to higher value with increasing $n_e$. Our calculations of the mobility are in good agreement with the recent experimental data. Comparison is also made with the results in the conventional 3D electron gas in a degenerate semiconductor.
Categories: cond-mat.mtrl-sci cond-mat.mes-hall