Enhancement of spin-orbit coupling in Dirac semimetal ${\mathrm{Cd}}_3{\mathrm{As}}_2$ films by Sb doping

We present a study on magnetotransport in films of the topological Dirac semimetal ${\mathrm{Cd}}_3{\mathrm{As}}_2$ doped with Sb grown by molecular beam epitaxy. In our weak antilocalization analysis, we find a significant enhancement of the spin-orbit scattering rate, indicating that Sb doping leads to a strong increase of the pristine band-inversion energy. We discuss possible origins of this large enhancement by comparing Sb-doped ${\mathrm{Cd}}_3{\mathrm{As}}_2$ with other compound semiconductors. Sb-doped ${\mathrm{Cd}}_3{\mathrm{As}}_2$ will be a suitable system for further investigations and functionalization of topological Dirac semimetals.

Figure 1

(a) Schematic band-structure change induced by Sb doping in ${\mathrm{Cd}}_3{\mathrm{As}}_2$. The band inversion is expected to be enhanced by Sb doping, which exhibits a larger spin-orbit coupling than As. Electron carriers caused by As and Sb deficiency are also expected to be reduced. (b) Cross-section HAADF-STEM (high-angle annular dark-field scanning transmission electron microscopy) image and (c) XRD $\theta –2\theta$ scan of a ${\mathrm{Cd}}_3{\left({\mathrm{As}}_{0.85}{\mathrm{Sb}}_{0.15}\right)}_2$ film grown on a CdTe substrate. The asterisks denote peaks from the CdTe substrate. (d) XRD $\theta –2\theta$ scans magnified around the $\left(448\right) {\mathrm{Cd}}_3{\left({\mathrm{As}}_{1-y}{\mathrm{Sb}}_y\right)}_2$ film peak with different Sb concentrations $y$. The Sb concentrations are estimated using Vegard's law, which linearly interpolates the lattice constants between $y=0$ and 0.15 films determined by EDX (energy dispersive x-ray) analyses.

Figure 2

(a) Longitudinal resistance $R_{\mathrm{xx}}$ and Hall resistance $R_{\mathrm{yx}}$ of ${\mathrm{Cd}}_3{\left({\mathrm{As}}_{0.85}{\mathrm{Sb}}_{0.15}\right)}_2$ film at 2 K. The magnetic field $B$ is applied out of plane. Mobility vs carrier density summarized for our ${\mathrm{Cd}}_3{\left({\mathrm{As}}_{1-y}{\mathrm{Sb}}_y\right)}_2$ films in (b) $n$-type and (c) $p$-type regions. (d)–(h) Hall resistance times thickness $R_{\mathrm{yx}}t$ and (i)–(m) magnetoresistance ratio for our ${\mathrm{Cd}}_3{\left({\mathrm{As}}_{1-y}{\mathrm{Sb}}_y\right)}_2$ films at 2 K. In (g) and (h), the curves are multiplied by ten for clarity.

Figure 3

(a) Normalized magnetoresistivity $\mathrm{\Delta }{\rho }_{\mathrm{WAL}}/{\rho }^2\left(0\right)=[\mathrm{\Delta }{\rho }_{\mathrm{total}}-\mathrm{\Delta }{\rho }_{\mathrm{orb}}]/{\rho }_{\mathrm{total}}^2\left(0\right)$ of the ${\mathrm{Cd}}_3{\left({\mathrm{As}}_{1-y}{\mathrm{Sb}}_y\right)}_2$ films at 2 K. Trajectories of the scattered electrons for (b) three-dimensional and (c) two-dimensional weak antilocalization. (d)–(g) Temperature dependence of the normalized magnetoresistivity for $y=0.07$, 0.12, 0.15, and 0.24. The red curves are fits to the three-dimensional weak antilocalization model [Eq. (3)]. The theory assumes that the magnetic field is within the range satisfying $\gamma <1$ [see Eq. (3) in the main text]. The magnetoresistivity below 7 K is not shown for $y=0.07$ because $L_{\varphi }<t$ is not satisfied at lower temperature (see also the Supplemental Material).

Figure 4

(a) Dephasing scattering rate $1/{\tau }_{\varphi }$ and (b) spin-orbit scattering rate $1/{\tau }_{\mathrm{SO}}$ as a function of temperature for $y=0.07$, 0.12, 0.15, and 0.24. The horizontal bars on the right axis in (a) represent the temperature-independent residual scattering rate extracted from the fit at 7 K for $y=0.07$ and at 2 K for $y=0.12$, 0.15, and 0.24. (c) Spin-orbit scattering rate $1/{\tau }_{\mathrm{SO}}$ vs dephasing scattering rate $1/{\tau }_{\varphi }$ summarized for the ${\mathrm{Cd}}_3{\left({\mathrm{As}}_{1-y}{\mathrm{Sb}}_y\right)}_2$ films. Data taken at different temperatures as shown in (a) and (b) are plotted. For comparison, $1/{\tau }_{\mathrm{SO}}$ vs $1/{\tau }_{\varphi }$ previously reported for three-dimensional systems ($•{\mathrm{In}}_{1-x}{\mathrm{Pb}}_x\mathrm{Sb}$ [40], $▴{\mathrm{Pb}}_{1-x}{\mathrm{Eu}}_x\mathrm{Te}$ [41]) and two-dimensional systems ($▽{\mathrm{Ga}}_{1-x}{\mathrm{In}}_x\mathrm{As}$ [46], $\diamond$ GaAs/${\mathrm{Al}}_{1-x}{\mathrm{Ga}}_x\mathrm{As}$ [47], $\bowtie$ InSb [48], $\square {\mathrm{Al}}_{1-x}{\mathrm{Ga}}_x\mathrm{N}$/GaN [49, 50]) are also plotted. $1/{\tau }_i$ ($1/{\tau }_{\varphi }$ at ${\tau }_0\to \infty$) is shown for ${\mathrm{Pb}}_{1-x}{\mathrm{Eu}}_x\mathrm{Te}$ instead of $1/{\tau }_{\varphi }$.