Evidence of topological nodal lines and surface states in the centrosymmetric superconductor ${\mathrm{SnTaS}}_2$

The discovery of signatures of topological superconductivity in superconducting bulk materials with topological surface states has attracted intensive research interest recently. Utilizing angle-resolved photoemission spectroscopy and first-principles calculations, here, we demonstrate the existence of topological nodal-line states and drumheadlike surface states in centrosymmetric superconductor $\mathrm{Sn}\mathrm{Ta}{\mathrm{S}}_2$, which is a type-II superconductor with a critical transition temperature of about 3 K. The valence bands from Ta $5d$ orbitals and the conduction bands from Sn $5p$ orbitals cross each other, forming two nodal lines in the vicinity of the Fermi energy without the inclusion of spin-orbit coupling (SOC), protected by the spatial-inversion symmetry and time-reversal symmetry. The nodal lines are gapped out by SOC. The drumheadlike surface states, the typical characteristics in nodal-line semimetals, are quite visible near the Fermi level. Our findings indicate that $\mathrm{Sn}\mathrm{Ta}{\mathrm{S}}_2$ offers a promising platform for exploring the exotic properties of the topological nodal-line fermions and helps in the study of topological superconductivity.

Figure 1

(a) Crystal structure of $\mathrm{Sn}\mathrm{Ta}{\mathrm{S}}_2$. (b) The top view of the crystal structure shows centrosymmetric structure. (c) Three-dimensional bulk and projected 2D BZs. (d) STM topography image of the cleaved $\mathrm{Sn}\mathrm{Ta}{\mathrm{S}}_2$ surface at $T=4$ K. Set point condition: $V=3$ V, $I=10$ pA. Inset: Atomic-resolved STM topography taken on $\mathrm{Ta}{\mathrm{S}}_2$ surface shows hexagonal atomic structure. Set point condition: $V=-0.6$ V, $I=10$ pA. (e) Scanning tunneling spectra ($dI/dV$) taken on the $\mathrm{Ta}{\mathrm{S}}_2$ surface at $T=0.4$ K under a magnetic field of 0 (blue) and 0.013 T (red) perpendicular to the sample surface. The superconducting gap of about 0.35 meV is estimated by fitting the blue points with the Dynes function.

Figure 2

(a) Total and orbital-projected DOS within $\pm 2$ eV at $E_{\mathrm{F}}$. The different colors indicate the different orbitals. (b) and (c) The calculated bulk bands with their orbital characters along the high-symmetry directions without and with SOC, respectively. (d) and (e) Enlarged views of bulk band structure without and with SOC on the $M-K-\mathrm{\Gamma }$ plane around $E_{\mathrm{F}}$, respectively, show nodal-line structure. The band crossings in (d) are indicated by N1, N2, and $\mathrm{N}{2}^{\prime }$. The gapped nodes in (e) are indicated by D1, D2, and $\mathrm{D}{2}^{\prime }$. (f) and (g) The calculated constant-energy surfaces without SOC at $E_{\mathrm{F}}$ and $E_{\mathrm{F}}-0.39$ eV, respectively, show nodal lines (NL1 and NL2) as indicated by the arrows. (h) and (i) Band structures with SOC for the 30-unit-thick layer. The bands with separation and the gray shaded regions present the bulk bands, and the others are surface bands. Projected band structures for the Sn-terminated (red) and S-terminated (blue) (001) surfaces of $\mathrm{Sn}\mathrm{Ta}{\mathrm{S}}_2$ are shown in (i). The surface states connecting the nodes are indicated by the arrows.

Figure 3

(a) Integrated intensity plots on the $k_z-k_{\parallel }$ plane at $E_F\pm 10$ meV. (b) Corresponding second-derivative plots of (a). The red line indicates a band with weak $k_z$ dispersion. (c) Bottom: Photoemission intensity plots taken along the $A-H$ direction with 48-eV photons ($k_z\sim \pi$). Top: MDC is taken along the red solid line, and the peaks are indicated by the turquoise arrows. (d) Corresponding second-derivative plots of (c). The observed surface state is indicated by the arrow. (e) Projected band structures for the two terminated (001) surfaces along $\overline{\mathrm{\Gamma }}\text{−}\overline{K}$. (f)–(h) Integrated intensity plots at $E_F\pm 10$ meV taken with 60-eV ($k_z\sim 0$), 72-eV ($k_z\sim \pi$), and 84-eV ($k_z\sim 0$) photons, respectively.

Figure 4

(a)–(c) Photoemission intensity plots along the $\mathrm{\Gamma }-K, K-M$, and $\mathrm{\Gamma }-M$ directions, respectively. (d)–(f) DFT-projected bulk bands and surface bands of the Sn-terminated (001) surface along the $\mathrm{\Gamma }-K, K-M$, and $\mathrm{\Gamma }-M$ directions, respectively, corresponding to (a)–(c). The surface states and the Dirac nodes are indicated by the black arrows and the transparent dots, respectively. (g) MDCs around the nodal-line feature near the $K$ point along $\mathrm{\Gamma }-K$, as indicated by the dashed rectangle in (a). (h) MDCs around the nodal-line feature near the $K$ point along $K-M$, as indicated by the dashed rectangle in (b). The dashed lines are guides to the bands.