Absence of Dirac states in ${\mathrm{BaZnBi}}_2$ induced by spin-orbit coupling

We report magnetotransport properties of ${\mathrm{BaZnBi}}_2$ single crystals. Whereas electronic structure features Dirac states, such states are removed from the Fermi level by spin-orbit coupling (SOC) and consequently electronic transport is dominated by the small hole and electron pockets. Our results are consistent with not only three-dimensional, but also with quasi-two-dimensional portions of the Fermi surface. The SOC-induced gap in Dirac states is much larger when compared to isostructural ${\mathrm{SrMnBi}}_2$. This suggests that not only long-range magnetic order, but also mass of the alkaline-earth atoms $A$ in ${ABX}_2(A=$ alkaline-earth, $B=$ transition-metal, and $X=$ Bi/Sb) are important for the presence of low-energy states obeying the relativistic Dirac equation at the Fermi surface.

Figure 1

(a) Powder XRD pattern and refinement results of ${\mathrm{BaZnBi}}_2$. The data are shown by (+), fitting and difference curves are given by the red and green solid line, respectively. Ticks mark reflections of I4/mmm space group (top) and residual Bi (bottom). Inset in (a) shows crystal structure of ${\mathrm{BaZnBi}}_2$. Ba atoms are denoted by green balls. Zn atoms are denoted by gray balls. Bi1 atoms denote Bi positions forming ${\mathrm{ZnBi}}_4$ tetrahedron. Bi2 atoms denote Bi positions forming 2D square lattices. Blue lines define the unit cell. (b) Heat capacity of ${\mathrm{BaZnBi}}_2$. (c) The magnetic field $\left(B\right)$ dependence of the in-plane magnetoresistance MR at different temperatures for heat capacity.

Figure 2

The calculated band structure, total and partial density of states from Ba, Zn, Bi1, and Bi2 (a)–(d) of ${\mathrm{BaZnBi}}_2$. Thick circles in (a), (c) denote the $5p_x$ band derived from Bi2 square lattices. The results shown are without (a), (b) and with (c), (d) spin-orbit coupling. Corresponding calculated Fermi surfaces are shown without (e) and with spin-orbit coupling (f).

Figure 3

(a) Band structure calculations for hypothetical ${\mathrm{BaZnBi}}_2$ where Ba is 5% closer to Bi2 plane, all other parameters remaining unchanged. This leaves the mass of $A$ the same, while mimicking steric effects (lattice parameter change) due to different $A$ size. (b) Band structure calculation for ${\mathrm{BaZnBi}}_2$ in its true unit cell but where spin-orbit coupling is selectively switched off on the Ba atoms only.

Figure 4

(a) Temperature dependence of the in-plane resistivity ${\rho }_a\left(T\right)$ and $c$-axis resistivity ${\rho }_c\left(T\right)$ of the ${\mathrm{BaZnBi}}_2$ single crystal in $B=0$ and 9 T magnetic fields, respectively. Large resistivity anisotropy indicates that the $c$-axis interlayer coupling of conductive Bi crystallographic square layers is small. (b) Field dependence of transverse magnetoresistance at 2 K for ${\rho }_a$ (filled circles) and ${\rho }_c$ (filled squares), respectively. (c) Cantilever oscillation as a function of magnetic field at different temperatures and its oscillatory component as a function of $1/B$ (d). (e) FFT spectra at various temperatures, data in (c), (d), and (e) use same legend. (f) Temperature dependence of the FFT amplitudes at different frequencies, the solid line is the fitting curve using Lifshitz-Kosevich formula.

Figure 5

(a) Angular-dependent MR for in-plane resistivity ${\rho }_a\left(T\right)$ at different tilt angles. inset shows the configuration of the measurement. (b) Tilt angle $\theta$ dependence of ${\rho }_a\left(T\right)$ at $B=18$ T and $T=0.91$ K. The red line is the fitting curve using $|cos(\theta \left)\right|$. dHvA oscillatory components at various tilt angles $\theta$ (c), and corresponding FFT spectra (d), the dashed lines are guides to the eyes. Data in (c) are using same scale and shifted vertically for clarity, while FFT spectra are normalized and shifted vertically. (c), (d) Cantilever oscillation as a function of magnetic field at different tilt angles $\theta$ and corresponding FFT amplitude. (e) The angular dependence of the oscillation frequencies $F_{\alpha },F_{\beta }$, and $F_{\gamma }$. $F_{\beta }$, and $F_{\gamma }$ can be fitted very well by $|cos(\theta \left)\right|$, indicating the quasi-2D feature of $\beta$ and $\gamma$ Fermi surface.