Interband optical conductivity of the [001]-oriented Dirac semimetal ${\mathrm{Cd}}_3{\mathrm{As}}_2$

We measured the optical reflectivity of [001]-oriented $n$-doped ${\mathrm{Cd}}_3{\mathrm{As}}_2$ in a broad frequency range (50–22 000 ${\mathrm{cm}}^{-1}$) for temperatures from 10 to 300 K. The optical conductivity, $\sigma \left(\omega \right)={\sigma }_1\left(\omega \right)+\mathrm{i}{\sigma }_2\left(\omega \right)$, is isotropic within the (001) plane; its real part follows a power law, ${\sigma }_1\left(\omega \right)\propto {\omega }^{1.65}$, in a large interval from 2000 to $8000{\mathrm{cm}}^{-1}$. This behavior is caused by interband transitions between two Dirac bands, which are effectively described by a sublinear dispersion relation, $E\left(k\right)\propto {\left|k\right|}^{0.6}$. The momentum-averaged Fermi velocity of the carriers in these bands is energy dependent and ranges from $1.2\times {10}^5$ to $3\times {10}^5$ m/s, depending on the distance from the Dirac points. We detect a gaplike feature in ${\sigma }_1\left(\omega \right)$ and associate it with the Fermi level positioned around 100 meV above the Dirac points.

Figure 1

Reflectivity of [001]-cut ${\mathrm{Cd}}_3{\mathrm{As}}_2$ for selected temperatures between 10 and 300 K measured with ${\mathbf{E}}_{\omega }\parallel$ [110], see text. Ordinate numbers are given for the measurements at 10 K, while the curves obtained at $T=50$, 100, and 300 K are downshifted by $-0.1,-0.2$, and $-0.3$, respectively. The inset sketches the dispersion of the Dirac bands in ${\mathrm{Cd}}_3{\mathrm{As}}_2$. In general, the Fermi-level position is not necessarily at the Dirac points.

Figure 2

Overall optical conductivity on log-log scale (upper frame) and dielectric permittivity (bottom frame) of ${\mathrm{Cd}}_3{\mathrm{As}}_2$ measured within the (001) plane. The straight line in the upper frame represents ${\sigma }_1\left(\omega \right)\propto {\omega }^{1.65}$. The diagram in the upper frame sketches the proposed band dispersion in ${\mathrm{Cd}}_3{\mathrm{As}}_2$ near one of the Dirac points. The inset of the bottom frame displays positive ${\varepsilon }^{\prime }$ on a linear $x$ scale.

Figure 3

Optical conductivity from Fig. 2 re-plotted on double-linear scale for $\omega <6000{\mathrm{cm}}^{-1}$. The straight green line represents the linear conductivity with $v_F=1.7\times {10}^5$ m/s. The inset shows the Fermi velocity calculated using Eq. (4) from ${\sigma }_1\left(\omega \right)$ at 10 K. Red dotted line is a guide to the eye $(v_F$ saturates at some point as $\omega \to 0)$.

Figure 4

Optical conductivity of ${\mathrm{Cd}}_3{\mathrm{As}}_2$ measured within the (001) plane at $T=10$ K, plotted together with a description of the interband portion of ${\sigma }_1\left(\omega \right)$ given by Eqs. (5) and (6). Deviations between the experiment and theory at higher frequencies are due to neglecting the deviations from linearity of the Dirac bands in Eqs. (5) and (6), as discussed in the text.

Figure 5

Low-frequency part of optical conductivity in ${\mathrm{Cd}}_3{\mathrm{As}}_2$. The vertical arrows indicate the positions of the phonons. The inset shows dc-resistivity as a function of temperature measured within the (001) plane.