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

TL;DR

This paper presents a theoretical model for phonon-limited mobility in 3D Dirac semimetal Cd$_3$As$_2$, highlighting the effects of screening, temperature, and electron density on mobility, and comparing with experimental data and conventional electron gases.

Contribution

The study introduces a comprehensive analytical model for phonon-limited mobility in 3D Dirac semimetals, accounting for screening and different phonon regimes, and compares results with experimental data and traditional electron gases.

Findings

Screening significantly enhances mobility.

Optical phonons dominate at higher temperatures.

Crossover temperature increases with electron density.

Abstract

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.