Distinguishing the gapped and Weyl semimetal scenario in ZrTe$_5$: insights from an effective two-band model

TL;DR

This study compares the transport properties of gapped and Weyl semimetal states in ZrTe$_5$ using an effective two-band model, highlighting features that could distinguish these phases experimentally.

Contribution

The paper extends a two-band model to include a negative band gap, revealing how it leads to a Weyl semimetal state and analyzing its transport signatures compared to the gapped phase.

Findings

Optical conductivity shows characteristic frequency dependencies in both phases.

Differences between phases are prominent only at very low carrier concentrations and temperatures.

Transport properties depend on Fermi energy and crystal direction.

Abstract

Here we study the static and dynamic transport properties of a low energy two-band model proposed previously in E. Martino et al. [PRL 122, 217402 (2019), arXiv:1905.00280], with an anisotropic in-plane linear momentum dependence, and a parabolic out-of-plane dispersion. The model is extended to include a negative band gap, which leads to the emergence of a Weyl semimetal (WSM) state, as opposed to the gapped semimetal (GSM) state when the band gap is positive. We calculate and compare the zero and finite frequency transport properties of the GSM and WSM cases. The $dc$ properties that are calculated for the GSM and WSM cases are Drude spectral weight, mobility and resistivity. We determine their dependence on the Fermi energy and crystal direction. The in- and out-of-plane optical conductivities are calculated in the limit of the vanishing interband relaxation rate for both semimetals. The main common features are an $\omega^{1/2}$ in-plane and $\omega^{3/2}$ out-of-plane frequency dependence of the optical conductivity. We seek particular features related to the charge transport that could unambiguously point to one ground state over the other, based on the comparison with the experiment. Differences between the WSM and GSM are in principle possible only at extremely low carrier concentrations, and at low temperatures.