Superconductivity in S-rich phases of lanthanum sulfide under high pressure

Pressure, a fundamental thermodynamic variable, enables phase transitions to exotic phases with unique physical properties, such as superconductivity. In this work we perform a complete study of crystal structures and relevant electronic properties of La–S crystalline systems in a pressure range of 0–200 GPa. A structural search based on first-principles swarm-intelligence identifies two hitherto unknown pressure-stabilized stoichiometries, namely, ${\mathrm{LaS}}_3$ and ${\mathrm{LaS}}_5$, in addition to the previously reported compounds. We find that the S-S bonding patterns in La–S compounds evolve in the following sequence with increasing S content and pressure: Atomic S, ${\mathrm{S}}_2$ dimers, one-dimensional linear S chains, and two-dimensional S ladders. Further electron-phonon calculations show that both ${\mathrm{LaS}}_3$ and ${\mathrm{LaS}}_5$ are superconductors with critical temperatures of 13.6 K at 100 GPa and 11 K at 120 GPa, respectively. The softened acoustic phonon branches are responsible for their superconductivity. Our current work is expected to guide future experimental studies investigating superconductivity and structural features of La–S system and more, in general, of other rare-earth chalcogenides.

Figure 1

Stability of La–S compounds. (a) Enthalpy of formation per atom of La–S compounds with respect to decomposition into elemental La and S solid phases. The energetically stable phases at each pressure, which form the vertices of the convex hull of thermodynamic stability (solid lines), are shown by solid symbols. Dotted lines that directly connect data points with the same composition are visual guides. The $dhcp$ (0 GPa), $dfcc$ (50 GPa), and $fcc$ (100–200 GPa) structures of elemental La solids [22, 23, 24, 25] and $Fddd$ (0 GPa), $I{4}_{1}acd$ (50 GPa), $C2/m$ (100–150 GPa), and $R\overline{3}$ (200 GPa) structures of elemental S solids were used as the reference materials to calculate the formation enthalpies [26, 27, 28, 29, 30, 31]. (b) Pressure-composition phase diagram of stable La–S binary compounds. The detailed enthalpies for each compound as a function of pressure are shown in the SM [32], Fig. S1.

Figure 2

Predicted stable crystal structures of La–S compounds under pressure: (a) $R\overline{3}$ ${\mathrm{La}}_3{\mathrm{S}}_4$ at 50 GPa, (b) $Cmce$ ${\mathrm{LaS}}_2$ at 50 GPa, (c) $Pm\overline{3}$ ${\mathrm{LaS}}_3$ at 25 GPa, (d) $P{4}_2/mmc$ at 100 GPa, (e) $Pm\overline{3}n$ ${\mathrm{LaS}}_3$ at 150 GPa, and (f) $C2/c$ ${\mathrm{LaS}}_5$ at 150 GPa. Green and yellow spheres represent La and S atoms, respectively. The blue spheres in (f) depict the S ladder configuration of ${\mathrm{LaS}}_5$. The dashed line marks the building block of each structure.

Figure 3

Two dimensional cut of the ELF displaying atomic S atoms (a), ${\mathrm{S}}_2$ dimers (b-d), linear S-chains (e), and S-ladders (f) in ${\mathrm{LaS}}_x$ compounds. The structures (a)–(f) correspond to those in Fig. 2.

Figure 4

Calculated electron losses and gains for each La and S in ${\mathrm{LaS}}_x$ at 100 GPa.

Figure 5

Phonon dispersion, the $e\text{−}ph$ coupling coefficient, $\lambda (\omega$) and Eliashberg spectral function ${\alpha }^{2}F\left(\omega \right)$ of $P{4}_2/mmc$ ${\mathrm{LaS}}_3$ (a) and $C2/c$ ${\mathrm{LaS}}_5$ (b) at high pressures. The radius of the circles are proportional to the EPC strength.

Figure 6

Calculated $\lambda$, logarithmic average phonon frequency ${\omega }_{\text{log}}$, and estimated $T_{\text{c}}$ for (a) ${\mathrm{LaS}}_3$ and (b) ${\mathrm{LaS}}_5$ as a function of pressure. Solid and dashed lines in (a) denote the $P{4}_2/mmc$ and $Pm\overline{3}n$ structure of ${\mathrm{LaS}}_3$, respectively.