Prediction of high-$T_c$ superconductivity in ternary lanthanum borohydrides

The study of superconductivity in compressed hydrides is of great interest due to measurements of high critical temperatures $\left(T_c\right)$ in the vicinity of room temperature, beginning with the observations of ${\mathrm{LaH}}_{10}$ at 170–190 GPa. However, the pressures required for synthesis of these high-$T_c$ superconducting hydrides currently remain extremely high. Here we show the investigation of crystal structures and superconductivity in the La-B-H system under pressure with particle-swarm intelligence structure-searches methods in combination with first-principles calculations. Structures with seven stoichiometries, LaBH, ${\mathrm{LaBH}}_4, {\mathrm{LaBH}}_6, {\mathrm{LaBH}}_7, {\mathrm{LaBH}}_8$, La(${\mathrm{BH})}_3$, and $\mathrm{La}{\left({\mathrm{BH}}_4\right)}_3$ were predicted to become stable under pressure. Remarkably, the hydrogen atoms in ${\mathrm{LaBH}}_8$ were found to bond with B atoms in a manner that is similar to that in ${\mathrm{H}}_3\mathrm{S}$. Lattice dynamics calculations indicate that ${\mathrm{LaBH}}_7$ and ${\mathrm{LaBH}}_8$ become dynamically stable at pressures as low as 109 and 48 GPa, respectively. Moreover, the two phases were predicted to be superconducting with a critical temperature $T_c$ of 93 K and 156 K at 110 GPa and 55 GPa, respectively (${\mu }^{*}$ = 0.1). The present results provide guidance for future experiments targeting hydride superconductors with both low synthesis pressures and high $T_c$.

Figure 1

Calculated convex hull of the La-B-H system is presented at 100, 150, 200, and 300 GPa, respectively. Thermodynamically stable and metastable stoichiometries are shown as purple circles and blue triangles, respectively.

Figure 2

The predicted crystal structures of ternary hydrides under pressure. (a) $P6$/mmm-LaBH, (b) Pmma-${\mathrm{LaBH}}_3$, (c) $P{2}_1/m\text{−}{\mathrm{LaBH}}_4$, (d) $C2/c\text{−}{\mathrm{LaBH}}_6$, (e) $P\overline{3}m1\text{−}{\mathrm{LaBH}}_7$, and (f) $\mathit{Fm}\overline{3}m\text{−}{\mathrm{LaBH}}_8$. Magenta, blue and green balls represent La, B, and H atom, respectively.

Figure 3

The Calculated ELF with isosurface value of 0.6 and ELF in the (1 1 0) plane for (a) $P\overline{3}m1\text{−}{\mathrm{LaBH}}_7$ and (b) $\mathit{Fm}\overline{3}m\text{−}{\mathrm{LaBH}}_8$ at 110 and 55 GPa, respectively.

Figure 4

The calculated electronic band structure, density of states, and Fermi surfaces of $P\overline{3}m1\text{−}{\mathrm{LaBH}}_7$ and $\mathit{Fm}\overline{3}m\text{−}{\mathrm{LaBH}}_8$ at 110 and 55 GPa, respectively.

Figure 5

Calculated phonon dispersion curves (red circle area proportional to associated EPC), projected phonon density of states (PDOS), the Eliashberg phonon spectral function ${\alpha }^{2}F$($\omega$)/$\omega$ and its integral $\lambda$($\omega$) of (a) $P\overline{3}m1\text{−}{\mathrm{LaBH}}_7$ at 110 GPa, (b) $\mathit{Fm}\overline{3}m\text{−}{\mathrm{LaBH}}_8$ at 200 GPa, and (c) $\mathit{Fm}\overline{3}m\text{−}{\mathrm{LaBH}}_8$ at 55 GPa.