Two-dimensional Dirac dispersion in the layered compound ${\mathrm{BaCdSb}}_2$

We report a comprehensive study of the electronic structure of layered compound $\mathrm{Ba}\mathrm{Cd}{\mathrm{Sb}}_2$ by using electrical transport measurements, first-principles calculations, and angle-resolved photoemission spectroscopy (ARPES). The samples show semiconductorlike temperature dependence of resistivity and low carrier density. The Shubnikov-de Haas (SdH) oscillations with a single frequency reveal a small two-dimensional (2D) cylinderlike Fermi surface (FS), a light cyclotron effective mass, and trivial Berry's phase. Quantum limit can be achieved under a moderate magnetic field. The calculated bands without any renormalization are well consistent with the ARPES results, showing the Dirac band crossing with 2D character near the Fermi energy and a gap of about 34 meV at the Dirac point induced by spin-orbit interaction. The SdH oscillations can be identified to the Dirac band by the similar cross sectional areas of FSs. Our findings indicate $\mathrm{Ba}\mathrm{Cd}{\mathrm{Sb}}_2$ is a promising material for researching the quantum phenomena of the 2D Dirac fermions.

Figure 1

(a) Crystal structure of $\mathrm{Ba}\mathrm{Cd}{\mathrm{Sb}}_2$. (b) XRD pattern of $\mathrm{Ba}\mathrm{Cd}{\mathrm{Sb}}_2$ single crystal with $\left(00l\right)$ reflections. (c) Temperature dependence of resistivity with current flowing in the $ab$ plane. The inset shows the Hall resistivity as the function of magnetic field at $T=2$ K.

Figure 2

(a) Field dependence of resistivity with different field orientations. The inset depicts the measurement configuration. (b) Angle dependence of the extreme positions of oscillations. The red and blue dashed lines are the fitting curves using the 2D relation $B\left(\phi \right)=B_0/cos\phi$. (c) Resistivity derivative $d{\rho }_{xx}/dB$ versus $1/B_{\mathrm{v}}=1/(Bcos\phi )$. (d) Landau fan diagram of Landau level index $n$ versus 1/$B$. (e) Field dependent resistivity at temperatures varying from 2 K to 20 K. (f) The difference between the peak and valley values of resistivity as the function of temperature. The dashed line is the fitting curve.

Figure 3

(a) Total and orbital-projected DOS around $E_{\mathrm{F}}$. The different colors indicate the different orbitals. (b) Calculated bands with SOC along the high-symmetry directions. The Dirac band is marked by the dashed circle. SOC opens the energy gap of $\sim 34$ meV at the cone point. (c) Orbital-projected dispersions along the $\mathrm{\Gamma }\text{−}M$ path. The Dirac band is mainly contributed by Sb $p$ orbital (blue) hybridized with partial Cd $d$ orbital (green). (d) Calculated bulk FSs in the 3D BZ with marked high-symmetry points. (e) Calculated 2D FSs. The shadow at the BZ center is induced by the holelike band at $\mathrm{\Gamma }$ ($Z$) point below $E_{\mathrm{F}}$. (f) Measured FSs ($E_{\mathrm{F}}\pm 20$ meV) taken with 100-eV photons in $\sigma$ geometry. (g) Sketch of the experimental polarization setup. The $\pi$ and $\sigma$ polarizations are for electric fields parallel and perpendicular to the mirror plane (red), respectively.

Figure 4

(a),(b) Intensity plot and corresponding second derivative plot along the $\mathrm{\Gamma }\text{−}M$ direction in $\pi$ geometry, taken with 100-eV photons. The red solid lines are calculated bands without renormalization and without shift. The linear band (LB) and the Dirac point (DP) are indicated by the white arrows. (c) and (d) correspond to (a) and (b), respectively, but taken in $\sigma$ geometry. (e) Enlarged view of (b) shows the Dirac bands near $E_{\mathrm{F}}$, as indicated by the dashed white lines. (f) Momentum distribution curves correspond to (a) showing the Dirac bands near $E_{\mathrm{F}}$. The black sticks are guides to the bands.