Carrier screening, transport, and relaxation in 3D Dirac semimetals

TL;DR

This paper develops a comprehensive theory for carrier conductivity in 3D Dirac semimetals, analyzing effects of Coulomb disorder and phonon scattering across different temperature and doping regimes, with implications for experimental identification.

Contribution

It introduces analytical scaling laws for conductivity in doped 3D Dirac materials considering Coulomb disorder and phonon effects, aiding experimental characterization of Dirac systems.

Findings

Scaling laws for conductivity in doped and undoped regimes

Comparison of quantum and transport relaxation times

Impact of Coulomb disorder on carrier scattering

Abstract

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", $T \gg T_F$) and the doped extrinsic ("low-temperature", $T \ll T_F$) 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 $\tas$, defining the quantum level broadening, and the transport scattering time $\tat$, defining the conductivity, in the presence of screened charged impurity scattering. A critical quantitative analysis of the $\tat/\tas$ results for 3D Dirac materials in the presence of long-range screened Coulomb disorder is provided.