Anisotropic superconductivity in the topological crystalline metal ${\mathrm{Pb}}_{1/3}{\mathrm{TaS}}_2$ with multiple Dirac fermions

Topological crystalline metals and semimetals (TCMs) have stimulated great research interest, which broadens the classification of topological phases and provides a valuable platform to explore topological superconductivity. Here, we report the discovery of superconductivity and topological features in Pb-intercalated transition-metal dichalcogenide ${\mathrm{Pb}}_{1/3}\mathrm{Ta}{\mathrm{S}}_2$. Systematic measurements indicate that ${\mathrm{Pb}}_{1/3}\mathrm{Ta}{\mathrm{S}}_2$ is a quasi-two-dimensional (q-2D) type-II superconductor ($T{}_c\approx 2.8$ K) with a significantly enhanced anisotropy of upper critical field (${\gamma }_{H_{c2}}=H_{c2}^{ab}/H_{c2}^c\approx 17$). In addition, first-principles calculations reveal that ${\mathrm{Pb}}_{1/3}\mathrm{Ta}{\mathrm{S}}_2$ hosts multiple topological Dirac fermions in the electronic band structure. We discover four groups of Dirac nodal lines on the $k_z=\pi$ plane and two sets of Dirac points on the rotation or screw axes, which are protected by crystalline symmetries and robust against spin-orbit coupling (SOC). Dirac-cone-like surface states emerge on the (001) surface because of band inversion. Our work shows that the TCM candidate ${\mathrm{Pb}}_{1/3}\mathrm{Ta}{\mathrm{S}}_2$ is a promising arena to study the interplay between superconductivity and topological Dirac fermions.

Figure 1

(a) The crystal structure of ${\mathrm{Pb}}_{1/3}\mathrm{Ta}{\mathrm{S}}_2$ along different directions. (b) XRD pattern of the single crystal with ($00l$) reflections; the inset of the right panel enlarges the (0010) reflection.

Figure 2

(a) $T$ dependence of the electrical resistivity ${\rho }_{ab}$ of ${\mathrm{Pb}}_{1/3}\mathrm{Ta}{\mathrm{S}}_2$ single crystal. The inset shows the superconducting transition around $T_c$. (b) $T$ dependence of dc magnetic susceptibility ($H$//$ab, H$ = 2 Oe) around $T_c$. (c) Magnetic field dependence of Hall resistivity for ${\mathrm{Pb}}_{1/3}\mathrm{Ta}{\mathrm{S}}_2$ at different temperatures. Inset: the Hall coefficient vs temperature. [(d), (e)] The low $T$ resistivity under different magnetic fields of single crystal parallel and perpendicular to the $ab$ plane, respectively. (f) $T$ dependence of the $H_{c2}$ with two-band fits for both directions; the black line dictates the Pauli paramagnetic limit.

Figure 3

(a) Magnetization $M\left(H\right)$ curves at various temperatures of ${\mathrm{Pb}}_{1/3}\mathrm{Ta}{\mathrm{S}}_2$ single crystal; the inset shows the loop taken at 1.8 K. (b) The superconducting $H\text{−}T$ phase diagram of ${\mathrm{Pb}}_{1/3}\mathrm{Ta}{\mathrm{S}}_2$.

Figure 4

Electronic structure of ${\mathrm{Pb}}_{1/3}\mathrm{Ta}{\mathrm{S}}_2$. (a) Electronic bands along a high-symmetry path. Energy is measured from the Fermi level. Orange and green distinguish crossing bands with different symmetry operation eigenvalues or irreducible representations (IRs). Dirac line and point degeneracies are labeled and highlighted in blue. Note that along the $\mathrm{\Gamma }\text{−}M\text{−}K\text{−}H$ line, all the seemingly gap closings are actually open at the meV scale except for DP2 and those at point $H$. Insets display enlarged views of the band structure. The band gap in the left inset is exaggerated to enhance the visibility. (b) Brillouin zone (BZ) and surface BZ of ${\mathrm{Pb}}_{1/3}\mathrm{Ta}{\mathrm{S}}_2$. High-symmetry points are marked. Dirac nodal lines and points are indicated. (c) Momentum-resolved densities of states (DOS) of a semi-infinite (001) Pb-terminated slab. Yellow and dark red correspond to high and low densities, respectively. The bulk nodes as well as surface states are highlighted.