Optical conductivity of the type-II Weyl semimetal ${\mathrm{TaIrTe}}_4$

${\mathrm{TaIrTe}}_4$ is an example of a candidate Weyl type-II semimetal with a minimal possible number of Weyl nodes. Four nodes are reported to exist in a single plane in $k$ space. The existence of a conical dispersion linked to Weyl nodes has yet to be shown experimentally. Here, we use optical spectroscopy as a probe of the band structure on a low-energy scale. Studying optical conductivity allows us to probe intraband and interband transitions with zero momentum. In ${\mathrm{TaIrTe}}_4$, we observe a narrow Drude contribution and an interband conductivity that may be consistent with a tilted linear band dispersion up to 40 meV. The interband conductivity allows us to establish the effective parameters of the conical dispersion; effective velocity $v=1.1\times {10}^4$ m/s and tilt $\gamma =0.37$. The transport data, Seebeck and Hall coefficients, are qualitatively consistent with conical features in the band structure. Quantitative disagreement may be linked to the multiband nature of ${\mathrm{TaIrTe}}_4$.

Figure 1

(a) The unit cell of ${\mathrm{TaIrTe}}_4$. Purple balls are tellurium atoms. The green and brown octahedra contain, respectively, tantalum and iridium atoms. The metal-metal zigzag chains run along the $a$ axis. (b) Resistivity as a function of temperature, in zero magnetic field and in 14 T. Magnetic field is applied along the $c$ axis. (c) Thermoelectric power or Seebeck coefficient as a function of temperature. The black line shows a linear fit below 60 K, whose slope may be used to extract the Fermi level position. (d) Hall coefficient and Hall mobility as a function of temperature.

Figure 2

(a) Reflectance measured at near-normal incidence for light polarized in the $ab$ plane, at several different temperatures. (b) The real part of the optical conductivity, ${\sigma }_1$, as a function of incident photon energy, in the far-infrared and midinfrared range (up to 400 meV), shown for the same set of temperatures as in (a). The inset shows the imaginary part of the optical conductivity, ${\sigma }_2$, below 900 ${\mathrm{cm}}^{-1}$. (c) Low- and high-temperature ${\sigma }_1$ as a function of incident photon energy, shown in the entire experimental range, on a logarithmic scale.

Figure 3

(a) Optical conductivity in the far-infrared range, showing the Drude component. The dots represent the values of ${\sigma }_{\text{dc}}$ determined by the measurement of the temperature-dependent resistivity. The inset shows the temperature dependence of the Drude scattering rate, $1/\tau$. It is extracted from ${\sigma }_1\left(\omega \right)$ using a Drude-Lorentz model. (b) Decomposition of ${\sigma }_1\left(\omega \right)$ at 5 K into the Drude term (orange), and an interband term (cyan). The model curve (blue) captures the Drude contribution, interband contribution from an undertilted conical dispersion (red color, $\gamma =0.37$), and a phonon contribution. For comparison, the best overtilted conical fit to the interband excitations is shown in a dotted line ($\gamma =2.8$). (c) Theoretically calculated Hall coefficient $R_H$, and Seebeck coefficient $S$ within the tilted conical model. The inset in (c) shows a sketch of a tilted linearly dispersing band (1) and a trivial band (2); both bands cross the Fermi level. In the tilted cone, the low-energy interband transitions (vertical arrow) contribute to the optical conductivity. There is no contribution to the interband conductivity from the sketched trivial band. Both bands, however, contribute to the intraband conductivity, which is related to the measured $S$ and $R_H$.