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ZrTe$_5$ is considered a potential candidate for either a Dirac semimetal ora topological insulator in close proximity to a topological phase transition.Recent optical conductivity results motivated a two-band model with a conicaldispersion 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 theab-initio band structure. The optical conductivity with an adjusted electronicstructure matches the key features of experimental data. The chemical potentialvaries strongly with temperature, to the point that it may cross the gapentirely between zero and room temperature. The temperature-dependentresistivity displays a broad peak, and confirms theoretically the conclusionsof recent experiments attributing the origin of the resistivity peak to thelarge shift of the chemical potential with temperature.

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