Absence of Dirac fermions in layered ${\mathrm{BaZnBi}}_2$

Using angle-resolved photoemission spectroscopy and density functional theory (DFT) we study the electronic structure of layered ${\mathrm{BaZnBi}}_2$. Our experimental results show no evidence of Dirac states in ${\mathrm{BaZnBi}}_2$ originated either from the bulk or the surface. The calculated band structure without spin-orbit interaction shows linear band dispersions at $X$ along the $X\text{−}M$ high-symmetry line. In addition, the calculations suggest a gapless band crossing point along the $\mathrm{\Gamma }\text{−}M$ high-symmetry line. However, as soon as the spin-orbit interaction is turned on, the band crossing point is significantly gapped out. These observations suggest that the Dirac fermions in ${\mathrm{BaZnBi}}_2$ are trivial similar to the Dirac states observed in grapheme. The experimental observations are in good agreement with the DFT calculations.

Figure 1

(a) Tetragonal crystal structure of ${\mathrm{BaZnBi}}_2$. (b) Calculated bulk band structure without SOC (top panel) and with SOC (bottom panel). (c) Three-dimensional (3D) view of the Brillouin zone with projected surface two-dimensional (2D) Brillouin zone on the top. (d) 3D Fermi surface obtained with SOC. (e) Experimental measuring geometry in which the $s$- and $p$-polarized lights are defined with respect to the scattering plane (SP) and the analyzed entrance slit (ES). (f) Parity of the Bi $p$ states are defined with respect to the measuring geometry as shown in (e). In this measuring geometry, the states $p_x$ and $p_z$ are even, while the state $p_y$ is odd. Thus, using $p$-polarized light one could detect the states $p_x$ and $p_z$ and using $s$-polarized light one could detect $p_y$ states.

Figure 2

Calculated bulk band structure. Top: Total band structure of (a) ${\mathrm{BaZnBi}}_2$, and band dispersions contributed by (b) ${\mathrm{Bi}}_1$ and (c) ${\mathrm{Bi}}_2$ atoms near the Fermi level. Bottom: Band structure of (d) $p_z$ (${\mathrm{Bi}}_1$), (e) $p_z$ (${\mathrm{Bi}}_2$), (f) $p_x+p_y$ (${\mathrm{Bi}}_1$), and (g) $p_x+p_y$ (${\mathrm{Bi}}_2$).

Figure 3

Slab calculations performed on ${\mathrm{BaZnBi}}_2$ including SOC. (a) The supercell of ${\mathrm{BaZnBi}}_2$ in the $b\text{−}c$ plane (left panel): termination 1 (T1) leaves out the ${\mathrm{Bi}}_2^1$ layer on the top of the sample surface (middle panel), termination 2 (T2) leaves out the ${\mathrm{Bi}}_2^2$ layer on the top of the sample surface (middle panel), and termination 3 (T3) leaves out the ${\mathrm{Bi}}_1$ layer on the top of the sample surface (right panel). (b) Surface states obtained after T1 cleavage. (c) Surface states obtained after T2 cleavage. (d) Surface states obtained after T3 cleavage. (e) Orbital resolved surface states are shown in the $\overline{X}\text{−}\overline{M}$ high symmetry line after T2 cleavage.

Figure 4

ARPES data of ${\mathrm{BaZnBi}}_2$. (a) Fermi surface maps taken with different photon energies (70 and 100 eV) and polarizations ($s$ and $p$). (b, c) EDMs taken along cuts 1 and 2 (left panel) and corresponding second derivative (right panel) using $p$- and $s$-polarized photons, respectively, along the $\mathrm{\Gamma }\text{−}X$ high-symmetry line. (d) EDMs taken along cuts 3, 4, and 5 from left to right, respectively. (e) Respective second derivatives of (d). In (d) the white and green dashed lines are guides to the eye representing the band dispersions. Furthermore, DS represents Dirac states.

Figure 5

(a) Fermi surface map taken along the $X\text{−}M$ orientation in the $k_y\text{−}{k}_z$ plane. (b) Photon-energy-dependent momentum distribution curves (MDCs) extracted from (a) around the Fermi level with an energy integration of 15 meV. (c) Photon-energy-dependent EDMs. In the figure, the red dashed lines represent linear dispersive bands, while the green dashed curves represent the quadratic bands.