Alloying-induced enhancement of thermopower in the Dirac-semimetal system ${\mathrm{Cd}}_{3-x}{\mathrm{Zn}}_x{\mathrm{As}}_2$

${\mathrm{Cd}}_3{\mathrm{As}}_2$ is one of the prototypical topological Dirac semimetals. Here, we manipulate the band inversion responsible for the emergence of Dirac nodes by alloying ${\mathrm{Cd}}_3{\mathrm{As}}_2$ with topologically trivial ${\mathrm{Zn}}_3{\mathrm{As}}_2$. The carrier density monotonically decreases and the resistivity is enhanced as $x$ is increased. For larger $x$, the thermoelectric figure of merit exhibits comparably large values exceeding 0.3 at room temperature, due to the combined effects of a strong enhancement of the thermopower, an only moderate increase in the resistivity, and a suppression of the thermal conductivity. Complementary quantum-oscillation data and optical-conductivity measurements allow us to infer that the Dirac nodes are gapped out, and a band structure with a partly flat dispersion likely emerges in the higher-$x$ region in ${\mathrm{Cd}}_{3-x}{\mathrm{Zn}}_x{\mathrm{As}}_2$.

Figure 1

Temperature dependence of (a) resistivity and (b) absolute value of the Hall coefficient $|R_{\mathrm{H}}|$ for ${\mathrm{Cd}}_{3-x}{\mathrm{Zn}}_x{\mathrm{As}}_2$. Here, $R_{\mathrm{H}}$ is negative for all $x$ and the whole temperature range examined. (c) Carrier densities as a function of doping level $x$. Here, $n_{\mathrm{H}}$ ($n_{\mathrm{Q}}$) denotes the carrier density derived from Hall coefficient data (quantum oscillations). $n_{\mathrm{Q}}$ is derived assuming an isotropic Fermi surface (of spherical shape).

Figure 2

Temperature dependence of the Seebeck coefficient (a) for $x=0$, 0.2, and 0.6 and (b) for $x=0.8$, 1.0, and 1.2. (c) Thermal conductivity for $x=0$, 0.6, and 1.2. (d) Absolute value of the Seebeck coefficient $|S_{xx}|$ and (e) figure of merit $ZT$ at 300 K plotted as a function of the charge carrier density $n_{\mathrm{H}}$ for $0\le x\le 1.2$. In (d), the dashed curve indicates the semiclassical expectation $|S_{xx}|\propto n^{-1/3}$ assuming a $k$-linear band dispersion. The broad light-red shaded curve is merely a guide to the eye. In (e), the vertical bar at each data point reflects the scattering of the results obtained on different samples with the same composition.

Figure 3

Magnetoresistivity at various temperatures for (a) $x=0$, (b) 0.6, and (c) 0.8, respectively. (d) Landau level fan diagram for $x=0$ (blue), 0.6 (red), and 0.8 (green) at $T=2$ K. In the inset, background-corrected quantum oscillations ${\rho }_{\mathrm{osc}}/{\rho }_{\mathrm{BG}}$ for $x=0$ are shown as a function of $1/B$. (e) Temperature dependence of the amplitude of ${\rho }_{\mathrm{osc}}/{\rho }_{\mathrm{BG}}$ at selected field strengths as indicated in brackets next to the respective Zn concentrations [color code is the same as in (d)].

Figure 4

(a) Optical-conductivity spectra at 10 K for $x=0$ (blue), 0.8 (red), and 1.2 (green). The spectra are shifted by 100 ${\mathrm{\Omega }}^{-1}{\mathrm{cm}}^{-1}$ with respect to each other for clarity. Solid black lines indicate the respective offsets. Triangles denote the threshold of interband transitions. The shaded region for $x=0$ denotes the Drude peak. The sharp peaks below 0.1 eV are attributed to optical phonons. Schematic illustration of the band dispersion for (b) $x=0$ and (c) $x=1.2$. The red arrow denotes the optical interband transition at the threshold energy marked with triangles in (a). The horizontal plane indicates the Fermi level $E_{\mathrm{F}}$. See text for details.