Anisotropic Dirac Fermions in a Bi Square Net of ${\mathrm{SrMnBi}}_2$

We report the observation of highly anisotropic Dirac fermions in a Bi square net of ${\mathrm{SrMnBi}}_2$, based on a first-principles calculation, angle-resolved photoemission spectroscopy, and quantum oscillations for high-quality single crystals. We found that the Dirac dispersion is generally induced in the $(\mathrm{SrBi}{)}^{+}$ layer containing a double-sized Bi square net. In contrast to the commonly observed isotropic Dirac cone, the Dirac cone in ${\mathrm{SrMnBi}}_2$ is highly anisotropic with a large momentum-dependent disparity of Fermi velocities of $\sim 8$. These findings demonstrate that a Bi square net, a common building block of various layered pnictides, provides a new platform that hosts highly anisotropic Dirac fermions.

Figure 1

(a) ${\mathrm{SrMnBi}}_2$ crystal structure with two building blocks of (b) a MnBi layer and (c) a Bi square net. Note the double-sized unit cell in the Bi square net. (d) X-ray diffraction pattern from basal planes of a cleaved crystal, showing only ($00l$) reflections. An optical image of a crystal with a scale of $250\mu \mathrm{m}$ is shown in the inset. (e) Magnetic susceptibilities $\chi (T)$ at $H=1\mathrm{T}$ parallel and perpendicular to the $c$ axis in zero-field-cooled (open) and field-cooled (solid) runs. A kink in $\chi (T)$ at $T_N\sim 290\mathrm{K}$ is clearly seen in the inset. (f) In-plane resistivity $\rho (T)$. It follows a quadratic $T$ dependence at low temperatures as shown in the inset.

Figure 2

(a) Band structures of ${\mathrm{SrMnBi}}_2$ and (b) total (gray line) and local Mn (red solid line) DOS are shown in the upper panel. The lower panel shows local DOSs at Bi (red solid line) and Sr (blue dashed line) sites in the SrBi layer. (c) Band structure of the isolated $(\mathrm{SrBi}{)}^{+}$ layer where the line thickness represents the Bi $6p_{x,y}$ orbital character. (d) Anisotropic energy surfaces around the Dirac point $k_0=(0.208,0.208)$ for the $(\mathrm{SrBi}{)}^{+}$ layer. (e) Dispersions near the Dirac point parallel or perpendicular to the $\Gamma \mathrm{\text{−}}M$ symmetry line. SOC in the Bi bands is turned on for the results in (a) and (b), while SOC is not considered for the results in (c), (d), and (e).

Figure 3

(a) ARPES intensity map at $E_F$. (b) Calculated FS. (c) Intensity plot and (d) momentum distribution curves of the ARPES data normal to the $\Gamma \mathrm{\text{−}}M$ line (cut 1). ARPES data along cut 2 (e) and cut 3 (f) parallel to the $\Gamma \mathrm{\text{−}}M$ line. The cut directions are shown in (a).

Figure 4

(a) Magnetic field dependence of $\Delta {\rho }_{xx}(H)/{\rho }_0$ and ${\rho }_{xy}$ of ${\mathrm{SrMnBi}}_2$. (b) Hall SdH oscillations $\Delta {\sigma }_{xy}={\sigma }_{xy}-⟨{\sigma }_{xy}⟩$ as a function of $1/H$ at various temperatures, where ${\sigma }_{xy}={\rho }_{xy}/({\rho }_{xx}^2+{\rho }_{xy}^2)$. (c) Cyclotron mass and dingle plots for $\Delta {\sigma }_{xy}$. (d) SdH fan diagram plotting the measured $1/B_n$ with the filling factor $n$, which is estimated from the $\Delta {\sigma }_{xy}$ versus $1/B_n$ plot shown in the inset.