Predicted pressure-induced s-d electron transition of hydrogen in electride ${\left({\mathrm{Na}}_2\mathrm{He}\right)}_4\mathrm{H}$

Unexpected pressure-induced s-d electron transition had been observed in various $s$-block metals. However, it is noteworthy that no such transition has been reported for hydrogen, a unique element within the $s$ block of the periodic table. Here, we propose using a zero-dimensional electride state, similar to a diamond anvil cell, to pressurize hydrogen under high pressure. The s-d electron transition of hydrogen was confirmed in our predicted electride ${\left({\mathrm{Na}}_2\mathrm{He}\right)}_4\mathrm{H}$ at 200 GPa. The electride-state interstitial quasiatoms arranged themselves in a regular octahedral configuration centered at the hydrogen atom. This arrangement established a highly symmetrical Coulomb repulsion field, further compressing and triggering the central hydrogen atom to undergo an s-d transition. Additionally, our results indicate that the hydrogen doping results in the metallization and superconductivity of electride ${\left({\mathrm{Na}}_2\mathrm{He}\right)}_4\mathrm{H}$. The electride-state interstitial quasiatoms around hydrogen atoms dominate the superconductivity of ${\left({\mathrm{Na}}_2\mathrm{He}\right)}_4\mathrm{H}$. The presence of ${\left({\mathrm{Na}}_2\mathrm{He}\right)}_4\mathrm{H}$ provides an example to confirm the promotion effect of the electride state on the superconductivity of electrides.

Figure 1

(a) Convex hull of ${\mathrm{Na}}_2{\mathrm{HeH}}_x$. Solid and hollow balls correspond to thermodynamically stable and metastable stoichiometries, respectively. (b) Phase transition diagram of five stable compounds. (c) Crystal structures of $P4/mmm\text{−}{\left({\mathrm{Na}}_2\mathrm{He}\right)}_{16}\mathrm{H}$ at 150 GPa, $P4/mmm\text{−}{\left({\mathrm{Na}}_2\mathrm{He}\right)}_8\mathrm{H}$ at 120 GPa, Fm$\overline{3}m\text{−}{\left({\mathrm{Na}}_2\mathrm{He}\right)}_4\mathrm{H}$ at 200 GPa, $P4/mmm\text{−}{\left({\mathrm{Na}}_2\mathrm{He}\right)}_2\mathrm{H}$ at 120 GPa, and $P\text{−}3m1\text{−}\left({\mathrm{Na}}_2\mathrm{He}\right)\mathrm{H}$ at 120 GPa. Yellow, blue, and pink balls represent Na, He, and H atoms, respectively.

Figure 2

(a) Band structure and projected density of states (PDOS) of ${\left({\mathrm{Na}}_2\mathrm{He}\right)}_4\mathrm{H}$ at 200 GPa. (b) The three-dimensional (3D) and corresponding two-dimensional (2D) band-decomposed charge density distributions for the (110) plane within the energy interval of −0.1 and 0 eV. The left, middle, and right sections correspond to contributions from bands I, II, and III, respectively. The isosurface level is set as $4.22\times {10}^{-4}e{\AA }^{-3}$ for 3D charge density distributions, and the maximum 2D charge density is $5.89\times {10}^{-4}e{\AA }^{-2}$. (c) The schematic diagram of the ISQs located at the six vertices of a regular octahedron centered at the H atom. (d) The COHP of ISQs around H atoms and H pairs. (e) Comparison of the PDOS of H of Fm$\overline{3}m\text{−}{\left({\mathrm{Na}}_2\mathrm{He}\right)}_4\mathrm{H}$ and C2/$c$-H at 200 GPa.

Figure 3

(a) The 2D band-decomposed charge density distributions of ${\left({\mathrm{Na}}_2\mathrm{He}\right)}_4\mathrm{H}$ within the energy interval of –0.1 and 0 eV at various pressures: the left, middle, and right correspond to the contributions from band I, II, and III, respectively. The (100) plane was selected for intuitiveness. The maximum 2D charge density was $7.41\times {10}^{-4}e{\AA }^{-2}$. (b) The integral projected density of states (IPDOS) of atomic H and the content of each occupied orbital of H at the Fermi level at 200–300 GPa. The IPDOS values of the $s$, $p$, and $d$ orbitals at the Fermi level are labeled in black, orange, and blue, respectively.

Figure 4

(a) Electronic band structure of ${\left({\mathrm{Na}}_2\mathrm{He}\right)}_4\mathrm{H}$ at 200 GPa. (b) 3D Fermi surface (FS) of bands I, II, and III. (c) 2D plots of FS projected in the (100), (110), and (111) planes. Blue, green, and red lines represent bands I, II, and III, respectively. (d) Nesting function $\xi \left(q\right)$ of ${\left({\mathrm{Na}}_2\mathrm{He}\right)}_4\mathrm{H}$ at 200 GPa. (e) Calculated phonon dispersion, projected phonon DOS, Eliashberg spectral function ${\alpha }^{2}F\left(\omega \right)$, and integrated electron-phonon coupling (EPC) parameter λ(ω) of ${\left({\mathrm{Na}}_2\mathrm{He}\right)}_4\mathrm{H}$ at 200 GPa. (f) The calculated λ and the contributions of three types of atoms to λ. $T_c$ at various pressures is shown in the columns.