Observation of spin-polarized surface states in the nodal-line semimetal ${\mathrm{SnTaS}}_2$

The superconductor ${\mathrm{SnTaS}}_2$ is theoretically predicted to be an intriguing topological nodal line semimetal without consideration of spin-orbit coupling. By carrying out angle-resolved photoemission (ARPES) and spin-resolved ARPES measurements combined with band structure calculations, we have provided a complete picture of the electronic structure and spin polarization property for the prominent surface states of ${\mathrm{SnTaS}}_2$. The low-energy electronic states are dominated by surface states; two of them are from the S-terminated surface, while four of them are from the Sn-terminated surface. These give rise to interesting Fermi surface topology of ${\mathrm{SnTaS}}_2$: three pockets located at $\overline{\mathrm{\Gamma }}, \overline{M}$ and $\overline{K}$ for the S-terminated surface and two pockets surrounding $\overline{\mathrm{\Gamma }}$ and $\overline{K}$ for the Sn-terminated surface. We further reveal that two surface states that cross the Fermi level are spin-polarized. Since ${\mathrm{SnTaS}}_2$ is also a superconductor, our observations indicate that it may provide a new platform to explore topological superconductivity and other exotic properties.

Figure 1

The measured Fermi surface of ${\mathrm{SnTaS}}_2$. (a) Crystal structure of ${\mathrm{SnTaS}}_2$. It shows a layered structure formed by the alternative stacking of Sn and ${\mathrm{TaS}}_2$ layers. (b) Top view of crystal structure. (c) Three-dimensional (3D) Brillouin zone of ${\mathrm{SnTaS}}_2$ and the projected two-dimensional (2D) Brillouin zone. High symmetry points are marked. (d), (e) Fermi surface mapping (d) and constant energy contour at the binding energy of 0.3 eV (e) measured with a photon energy of 27 eV. (f) Schematic Fermi surface of ${\mathrm{SnTaS}}_2$ based on the measured Fermi surface (d) and related band structure analysis. The Fermi surface sheets originated from bulk, and surface states are drawn by black lines and red lines, respectively.

Figure 2

Band structures of ${\mathrm{SnTaS}}_2$ measured along high symmetry directions and their comparison with band structure calculations. (a) Band structure measured along $\overline{\mathrm{\Gamma }}-\overline{K}$ with a photon energy of 27 eV under the LH polarization geometry. The location of the momentum cut is marked by Cut1 in the inset of (f). (b) Calculated bulk band structures of ${\mathrm{SnTaS}}_2$ with SOC along $\mathrm{\Gamma }$-K. (c) The calculated band structures of ${\mathrm{SnTaS}}_2$ with SOC along $\mathrm{\Gamma }$-K for a six-unit-cell-thick slab. The surface states are marked by red curves. (d) Calculated band structures of ${\mathrm{SnTaS}}_2$ along $\mathrm{\Gamma }$-K combining the bulk bands in (b) and the surface states in (c). (e) Band structure measured along $\overline{K}-\overline{M}-\overline{K}$ with a photon energy of 27 eV under the LH polarization geometry. The location of the momentum cut is marked by Cut2 in the inset of (f). (f) Corresponding second derivative image of (e) with respect to the energy. (g)–(i) Same as (b)–(d) but along K-M-K.

Figure 3

Decomposed contribution by different unit layer in the calculated band structures of ${\mathrm{SnTaS}}_2$ for a six-unit-cell-thick slab. For simplicity, the SOC is not considered in the calculations. (a) Structure of the six-unit-cell-thick slab used in the calculation. The first layer corresponds to the Sn-terminated surface, while the sixth layer corresponds to the S-terminated surface. (b)–(g) Contribution of band structures by different unit layers from the first layer (b) to the sixth layer (g). The surface states SS1, SS3, SS4, and SS6 come from the first layer and are marked in (b). The surface states SS2 and SS5 come from the sixth layer and are marked in (g).

Figure 4

Spin polarization determination of the surface states in ${\mathrm{SnTaS}}_2$ (a) Band structure measured along $\overline{\mathrm{\Gamma }}-\overline{K}$. The location of the corresponding momentum Cut2 is marked by a purple line in (k). The SS2 surface state is observed that split into two branches labeled SS2U and SS2D. (b), (c) Spin-resolved EDCs (upper panels) and the corresponding spin polarization curves (lower panels) for determining the Z component of the spin polarization of the momentum points P1 (b) and P2 (c). The locations of P1 and P2 are marked in (a) and also in (k). (d), (e) Same as (b), (c) but for determining the Y component of the spin polarization of the momentum points P1 (d) and P2 (e). (f) Same as (a), but along $\overline{K}-\overline{M}-\overline{K}$ as marked by Cut3 in (k). The SS5 surface state shows a Rashba-like splitting that consists of two branches labeled SS5L and SS5R. (g), (j) Same as (b)–(e) but for the momentum points P3 and P4 marked in (f) and also in (k). (k) Schematic Fermi surface of ${\mathrm{SnTaS}}_2$. Relative to the sample orientation set by the first Brillouin zone, the three spin components (X, Y, and Z) are defined in the bottom-left inset. (l) Schematic Fermi surface of the S-terminated surface of ${\mathrm{SnTaS}}_2$ consisting of $\alpha , \gamma$ and $\delta$ sheets. (m) Fermi surface of the Sn-terminated surface with two sheets of $\beta$ and $\varepsilon$.