Ternary Na-P-H superconductor under high pressure

Most of the H-rich superconductors have so far been discovered to be clathrate structures. Several clathrate hydrides, including ${\mathrm{H}}_3\mathrm{S}$, ${\mathrm{LaH}}_{10}$, and ${\mathrm{CaH}}_6$, were predicted to be excellent superconductors through structural searches and were later confirmed through experimental synthesis. Here, we conduct extensive crystal structure searches and first-principles calculations for ternary Na-P-H hydrides under high pressure. Two stoichiometries of ${\mathrm{NaPH}}_6$ and ${\mathrm{NaPH}}_8$ in ternary Na-P-H hydrides are found to be stable under 200 GPa. The $P\overline{6}m2$ phase of the ${\mathrm{NaPH}}_6$ hydride is identified as a novel ternary layered H-rich superconductor, exhibiting a high critical temperature $T_c$ of 112.2 K under 200 GPa. Our calculations indicate that the high $T_c$ of the ${\mathrm{NaPH}}_6$ hydride under high pressure is attributed to the high density of hydrogen $s$ states present at the Fermi level. Furthermore, a metastable $Pm\overline{3}$ phase of the clathrate ${\mathrm{NaPH}}_6$ hydride is uncovered under 350 GPa and displays an exceptional $T_c$ of 201.4 K. These results suggest that ternary alkali metal Na-based hydrides hold promise as high-$T_c$ superconductors under high pressure and offer critical insights into the design and synthesis of novel category high-temperature superconductors.

Figure 1

(a)–(d) The 3D convex hulls constructed based on the formation enthalpies related to the elemental Na, P, and H at 100, 200, 300, and 400 GPa, respectively; the solid dotted (${\mathrm{NaPH}}_6$ and ${\mathrm{NaPH}}_8$) represent the energetically stable structures.

Figure 2

Crystal structures for ${\mathrm{NaPH}}_6$: (a) and (b) a supercell of $P\overline{6}m2{\mathrm{NaPH}}_6$ at 200 GPa in different views, with the kagome lattice formed by H atoms in the H-P layer, (c) the $Pm\overline{3}$ structure at 350 GPa, and (d) the $R\overline{3}m$ structure at 200 GPa. The sodium atoms are yellow, the phosphorus atoms are purple, and the hydrogen atoms are pink.

Figure 3

(a) Calculated electronic band structures and density of states of $P\overline{6}m2{\mathrm{NaPH}}_6$ and (b)–(d) the Fermi surface sheets of the $P\overline{6}m2{\mathrm{NaPH}}_6$ structure at 350 GPa.

Figure 4

Phonon dispersion curves (the radius of the red circle is parallel to phonon linewidths); phonon density of states projected on Na, P, and H atoms; and the Eliashberg spectral function ${\alpha }^{2}F\left(\omega \right)$ together with the electron-phonon integral $\lambda (\omega$) at 350 GPa for (a) the $P\overline{6}m2$ phase of ${\mathrm{NaPH}}_6$, (b) the $Pm\overline{3}$ phase of ${\mathrm{NaPH}}_6$, (c) the $R\overline{3}m$ phase of ${\mathrm{NaPH}}_6$, and (d) the $Pm$ phase of ${\mathrm{NaPH}}_8$.

Figure 5

Projected crystal orbital Hamiltonian population (pCOHP) of the predicted compounds: (a) the $P\overline{6}m2$ phase of ${\mathrm{NaPH}}_6$, (b) the $R\overline{3}m$ phase of ${\mathrm{NaPH}}_6$, (c) the $Pm\overline{3}$ phase of ${\mathrm{NaPH}}_6$, and (d) the $Pm$ phase of ${\mathrm{NaPH}}_8$ at 350 GPa.