Superconducting, plastic, and superionic states driven by four-membered lithium rings in a high-pressure lithium-lead compound (2024)

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  Figure 1

  Thermodynamic stability and crystal structure of lithium-lead system. (a) Convex hulls at 50, 100, and 150 GPa. Solid symbols represent thermodynamically stable structures, while hollow symbols denote unstable ones. (b) Phase diagrams from 0 to 150 GPa. The structures predicted in this work are indicated in red, while previously known ones are shown in gray bars. (c) The crystal structure of $I_4$/mmm ${\mathrm{Li}}_4\mathrm{Pb}$. (d) $T$-graphene-like stacking layer, and (e) electron localization function (ELF) map for the stacking layer (001) of $I_4$/mmm ${\mathrm{Li}}_4\mathrm{Pb}$ at 50 GPa. For intuitive understanding, we added Li-Li bonds inside (red) and outside (blue) rings in the stacking layer in (d). Lithium and lead atoms are depicted as green and black balls, respectively.

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  Figure 2

  Superconducting properties of $I_4$/mmm ${\mathrm{Li}}_4\mathrm{Pb}$ at 50 GPa. (a) The phonon spectrum, PHDOS, ${\alpha }^{2}F\left(\omega \right)$, and $\lambda \left(\omega \right)$. The magenta circle sizes are proportional to the coupling strength. (b) Accumulated $q$-dependent coupling factor λ($q$) along the Brillouin zone path, which follows the equation $\lambda \left(\mathit{q}\right)={\sum }_j\frac{{\gamma }_{\mathit{q}j}}{{\omega }_{\mathit{q}j}^2}$ and is normalized by $\lambda \left(\mathrm{\Gamma }\right)$. (c) Orbital-projected band structure and density of states. The size of the colored circles corresponds to the contribution of electrons from the respective orbital, as indicated in the labels. (d) $B_2$_g mode at the Γ point, as depicted with red arrows.

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  Figure 3

  Dynamic properties of $I_4$/mmm ${\mathrm{Li}}_4\mathrm{Pb}$ around 50 GPa. MSDs of Li and Pb atoms at (a) 800 K (plastic state) and (c) 1800 K (superionic state). (b) Rotation energy barrier of a single four-membered lithium ring in a 3 × 3 × 3 supercell. The pattern of collective rotation of four-membered lithium rings is visualized with black arrows. (d) Radial distribution function $g$($r$) between Li-Li, Li-Pb, and Pb-Pb at different temperatures.

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  Figure 4

  Temperature induced behaviors of $I_4$/mmm ${\mathrm{Li}}_4\mathrm{Pb}$. Left: (a) Pressure-temperature phase diagram. The magenta, orange, red, green, blue, and cyan points (areas) represent superconductor, undistorted solid, distorted solid, plastic, superionic, and liquid phases, respectively. Right: Snapshots of different phases including (b) distorted solid, (c) plastic, (d) superionic, and (e) liquid states.

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