Spectroscopic evidence for the realization of a genuine topological nodal-line semimetal in LaSbTe

The nodal line semimetals have attracted much attention due to their unique topological electronic structure and exotic physical properties. A genuine nodal-line semimetal is qualified by the presence of Dirac nodes along a line in the momentum space that are protected against the spin-orbit coupling. In addition, it requires that the Dirac points lie close to the Fermi level, allowing one to dictate the macroscopic physical properties. Although the material realization of nodal-line semimetals have been theoretically predicted in numerous compounds, only a few of them have been experimentally verified and the realization of a genuine nodal-line semimetal is particularly rare. Here we report the realization of a genuine nodal-line semimetal in LaSbTe. We investigated the electronic structure of LaSbTe by band structure calculations and angle-resolved photoemission (ARPES) measurements. Taking spin-orbit coupling into account, our band structure calculations predict that a nodal line is formed in the boundary surface of the Brillouin zone, which is robust and lies close to the Fermi level. The Dirac nodes along the X-R line in momentum space are directly observed in our ARPES measurements, and the energies of these Dirac nodes are all close to the Fermi level. These results constitute clear evidence that LaSbTe is a genuine nodal-line semimetal, providing a platform to explore for novel phenomena and possible applications associated with the nodal-line semimetals.

Figure 1

Band structure calculations and the nodal-line configuration of LaSbTe. (a) Crystal structure of LaSbTe. The Sb atoms shown with blue balls form square nets, which are sandwiched between the two La-Te layers. The gray arrow indicates the cleavage plane between the LaTe layers. (b) Schematic of a 3D Brillouin zone of LaSbTe. (c) Calculated nodal lines formed by the $\beta \text{−}\gamma$ band (NL1-NL5) and $\alpha \text{−}\beta$ band (NLE1 and NLE2) in the 3D Brillouin zone. (d), (e) Calculated bulk band structures without (d) and with SOC (e) along high-symmetry directions by first-principles calculations. We label the two conduction bands and one valence band close to the Fermi level with $\alpha$ (red), $\beta$ (purple), and $\gamma$ (blue), respectively. The Dirac points are marked by red arrows.

Figure 2

Fermi surface of LaSbTe. [(a)–(c)] The Fermi surface and constant energy contours of LaSbTe measured with photon energy of 55 eV (a), 85 eV (b), and 95 eV (c), respectively, under $LH$ polarization. [(d)–(f)] The DFT calculated Fermi surface and constant energy contours of LaSbTe with ${\mathrm{k}}_z$ corresponding to 0.5 $\pi$/c (d), 0.75 $\pi$/c (e), and 0 $\pi$/c (f), respectively.

Figure 3

Measured band structures of LaSbTe and their comparison with band structure calculations. [(a)–(c)] Band structures of LaSbTe measured along $\overline{\mathrm{\Gamma }}\text{−}\overline{M}$ (a), $\overline{\mathrm{\Gamma }}\text{−}\overline{X}$ (b), and $\overline{X}\text{−}\overline{M}$ (c) directions, respectively, with a photon energy of 55 eV. The left and right panels in [(a)–(c)] are measured under LV and LH polarization geometries, respectively. [(d)–(f)] The second derivative images of the original data corresponding to [(a)–(c)]. The red and orange lines mark the two branches of the linearly dispersed Dirac bands. [(g)–(i)] The calculated bulk band structures of LaSbTe with SOC along $\overline{\mathrm{\Gamma }}\text{−}\overline{M}$ (g), $\overline{\mathrm{\Gamma }}\text{−}\overline{X}$ (h), and $\overline{X}\text{−}\overline{M}$ (i) momentum directions for ${\mathrm{k}}_z$ = 0.5 $\pi$/c plane. [(j)–(l)] The calculated band structures of LaSbTe with SOC along $\overline{\mathrm{\Gamma }}\text{−}\overline{M}$ (j), $\overline{\mathrm{\Gamma }}\text{−}\overline{X}$(k), and $\overline{X}\text{−}\overline{M}$ (l) directions for a seven-unit-cell-thick slab. The intensity of color bar represents the proportion of surface states contributed by the topmost unit cell of LaSbTe. Here, the BB, SB, and the DP indicate the bulk band, surface band, and the Dirac point, respectively.

Figure 4

Dirac nodal line along X-R direction. (a) Photon-energy-dependent ARPES intensity measurement of LaSbTe crossing the zone center along $\overline{\mathrm{\Gamma }}\text{−}\overline{X}$ direction. (b) Band structures measured along $\overline{\mathrm{\Gamma }}\text{−}\overline{X}$ direction at different photon energies. To highlight the bands, these images are from the second derivative of the original data. The Dirac points are marked by red arrows.