Carrier screening, transport, and relaxation in three-dimensional Dirac semimetals

A theory is developed for the density and temperature-dependent carrier conductivity in doped three-dimensional (3D) Dirac materials focusing on resistive scattering from screened Coulomb disorder due to random charged impurities (e.g., dopant ions and unintentional background impurities). The theory applies both in the undoped intrinsic (``high-temperature,'' $T\ensuremath{\gg}{T}_{F})$ and the doped extrinsic (``low-temperature,'' $T\ensuremath{\ll}{T}_{F})$ limit with analytical scaling properties for the carrier conductivity obtained in both regimes, where ${T}_{F}$ is the Fermi temperature corresponding to the doped free carrier density (electrons or holes). The scaling properties describing how the conductivity depends on the density and temperature can be used to establish the Dirac nature of 3D systems through transport measurements. We also consider the temperature-dependent conductivity limited by the acoustic phonon scattering in 3D Dirac materials. In addition, we theoretically calculate and compare the single-particle relaxation time ${\ensuremath{\tau}}_{s}$, defining the quantum level broadening, and the transport scattering time ${\ensuremath{\tau}}_{t}$, defining the conductivity, in the presence of screened charged impurity scattering. A critical quantitative analysis of the ${\ensuremath{\tau}}_{t}/{\ensuremath{\tau}}_{s}$ results for 3D Dirac materials in the presence of long-range screened Coulomb disorder is provided.