Optical conductivity and resistivity in a four-band model for ZrTe$_5$ from ab-initio calculations

ZrTe$_5$ is considered a potential candidate for either a Dirac semimetal or a topological insulator in close proximity to a topological phase transition. Recent optical conductivity results motivated a two-band model with a conical dispersion in 2D, in contrast to density functional theory calculations. Here, we reconcile the two by deriving a four-band model for ZrTe$_5$ using $\textbf{k} \cdot \textbf{p}$ theory, and fitting its parameters to the ab-initio band structure. The optical conductivity with an adjusted electronic structure matches the key features of experimental data. The chemical potential varies strongly with temperature, to the point that it may cross the gap entirely between zero and room temperature. The temperature-dependent resistivity displays a broad peak, and confirms theoretically the conclusions of recent experiments attributing the origin of the resistivity peak to the large shift of the chemical potential with temperature.