Evidence of topological insulator state in the semimetal LaBi

By employing angle-resolved photoemission spectroscopy combined with first-principles calculations, we performed a systematic investigation on the electronic structure of LaBi, which exhibits extremely large magnetoresistance (XMR), and is theoretically predicted to possess band anticrossing with nontrivial topological properties. Here, the observations of the Fermi-surface topology and band dispersions are similar to previous studies on LaSb [L.-K. Zeng, R. Lou, D.-S. Wu, Q. N. Xu, P.-J. Guo, L.-Y. Kong, Y.-G. Zhong, J.-Z. Ma, B.-B. Fu, P. Richard, P. Wang, G. T. Liu, L. Lu, Y.-B. Huang, C. Fang, S.-S. Sun, Q. Wang, L. Wang, Y.-G. Shi, H. M. Weng, H.-C. Lei, K. Liu, S.-C. Wang, T. Qian, J.-L. Luo, and H. Ding, Phys. Rev. Lett. 117, 127204 (2016)], a topologically trivial XMR semimetal, except the existence of a band inversion along the $\mathrm{\Gamma }\text{−}X$ direction, with one massless and one gapped Dirac-like surface state at the $X$ and $\mathrm{\Gamma }$ points, respectively. The odd number of massless Dirac cones suggests that LaBi is analogous to the time-reversal $Z_2$ nontrivial topological insulator. These findings open up a new series for exploring novel topological states and investigating their evolution from the perspective of topological phase transition within the family of rare-earth monopnictides.

Figure 1

Crystal structure and FS topologies of LaBi. (a) Crystal structure of LaBi. (b) Bulk BZ and the (001)-projected surface BZ of LaBi. (c) FS intensity plot of LaBi recorded with $h\nu =84\mathrm{eV}$, corresponding to the $k_z\sim \pi$ plane, obtained by integrating the spectral weight within $\pm 10$ meV with respect to $E_F$. $a^{\prime }$ is the half of the lattice constant $a$ of the face-center-cubic unit cell. Red solid and dashed lines represent the 3D BZ and 2D surface BZ, respectively. (d) Calculated 3D FSs using the PBE functional.

Figure 2

Band dispersions along high-symmetry lines taken at the $k_z\sim$ 0 ($h\nu =53\mathrm{eV}$) and $k_z\sim \pi$ ($h\nu =84\mathrm{eV}$) planes of LaBi. (a),(b) Photoemission intensity plot along the $\mathrm{\Gamma }\text{−}X$ direction and corresponding second derivative plot recorded with $h\nu =53\mathrm{eV}$, respectively. Red dashed curves are guides to the eye for the band anticrossing feature. (c),(d) Same as (a),(b) but along the $X\text{−}W\text{−}X$ directions. (e),(f) Same as (c),(d) but measured with $h\nu =84\mathrm{eV}$, displaying more prominent surface band features around the left $X$ point. (g) EDC plot of (e) around the right $X$ point. (h) Single EDC at the right $X$ point in (e), highlighted by blue curve in (g). By fitting the EDC with two Lorentzian profiles, shown as green curves, we extract the peak positions, marked by two vertical dashed lines, and determine the presence of a surface band gap of $\sim 23$ meV. The blue curve is the superimposed fitting result. (i) MDC plot of (e) around the left $X$ point. The binding energy of DP is $\sim -0.14$ eV, as highlighted by the blue curve. (j) EDC plot of (a) to demonstrate the existence of band anticrossing and bulk band gap. A shoulder on the outer hole band is resolved and highlighted by a black curve. Blue dots in (g), (i), and (j) are extracted peak positions, serving as guides to the eye.

Figure 3

Photon energy dependence of the band structure along the $\mathrm{\Gamma }\text{−}X$ direction of LaBi. (a) Photoemission intensity plot at $E_F$ in the $k_y\text{−}{k}_z$ plane at $k_x=0$ measured with photon energies from 20 to 100 eV. Red curves from bottom to top indicate the momentum locations taken at $h\nu =30$, 40, 53, 84, and 92 eV, respectively. The inner potential is estimated to be 14 eV. Green dashed ellipse represents the electronlike FS at $X$. (b) MDC plot of (a) around the BZ boundary. (c) Same as (a) but at $E=-0.14$ eV, the binding energy of the DP at $X$. (d) MDC plot of (c) around the BZ boundary. Red and blue dashed lines in (a),(b) and (c),(d) demonstrate the $k_z$ independence of the Fermi crossings and DP of the SS around $X$, respectively.

Figure 4

Calculated band structure along $\overline{\mathrm{\Gamma }}\text{−}\overline{M}\text{−}\overline{X}\text{−}\overline{\mathrm{\Gamma }}$ for a semi-infinite slab of LaBi. The sharp red curves represent the SSs for (001) surface, whereas the shaded regions show the spectral weight of projected bulk bands.