Hydrogen Pentagraphenelike Structure Stabilized by Hafnium: A High-Temperature Conventional Superconductor

The recent discovery of ${\mathrm{H}}_3\mathrm{S}$ and ${\mathrm{LaH}}_{10}$ superconductors with record high superconducting transition temperatures $T_c$ at high pressure has fueled the search for room-temperature superconductivity in the compressed superhydrides. Here we introduce a new class of high $T_c$ hydrides with a novel structure and unusual properties. We predict the existence of an unprecedented hexagonal ${\mathrm{HfH}}_{10}$, with remarkably high value of $T_c$ (around 213–234 K) at 250 GPa. As concerns the novel structure, the H ions in ${\mathrm{HfH}}_{10}$ are arranged in clusters to form a planar “pentagraphenelike” sublattice. The layered arrangement of these planar units is entirely different from the covalent sixfold cubic structure in ${\mathrm{H}}_3\mathrm{S}$ and clathratelike structure in ${\mathrm{LaH}}_{10}$. The Hf atom acts as a precompressor and electron donor to the hydrogen sublattice. This pentagraphenelike ${\mathrm{H}}_{10}$ structure is also found in ${\mathrm{ZrH}}_{10}$, ${\mathrm{ScH}}_{10}$, and ${\mathrm{LuH}}_{10}$ at high pressure, each material showing a high $T_c$ ranging from 134 to 220 K. Our study of dense superhydrides with pentagraphenelike layered structures opens the door to the exploration of a new class of high $T_c$ superconductors.

Figure 1

(a) Formation enthalpies of predicted ${\mathrm{HfH}}_x$ ($x=1–24$), including ZPEs with respect to decomposition into Hf and H under pressure. The $Im\overline{3}m$ structure for hafnium [63], the $P{6}_3/mc$, $C2/c$, and $Cmca\text{−}12$ structures for hydrogen [57] were adopted. Open symbols represent unstable configurations with respect to mixing lines on the convex hull, while solid symbols on the convex hull represent stable configurations. The red star near the convex hull represents the ${\mathrm{HfH}}_{10}$ phase with higher enthalpy. (b) The crystal structure of layered $P{6}_3/mmc$ in ${\mathrm{HfH}}_{10}$, where the layers are stacked in an ABAB fashion. (c) A layer of the $P{6}_3/mmc$ structure. (d) ELF on the (001) plane. Golden (large) and small (blue) spheres represent Hf and H atoms, respectively.

Figure 2

Projected electronic DOS of (a) $P{6}_3/mmc\text{−}{\mathrm{HfH}}_{10}$ and (b) $P{6}_3/mmc\text{−}{\mathrm{ZrH}}_{10}$ at 300 GPa. (c) Total electronic DOS of ${\mathrm{H}}_3\mathrm{S}$, ${\mathrm{LaH}}_{10}$, ${\mathrm{HfH}}_{10}$, and ${\mathrm{ZrH}}_{10}$ around the van Hove singularities at 300 GPa.

Figure 3

Phonon dispersion curves (left), density of states (middle), and Eliashberg spectral function ${\alpha }^{2}F(\omega )$ together with the electron-phonon integral $\lambda (\omega )$ (right) of (a) ${\mathrm{HfH}}_{10}$ and (b) ${\mathrm{ZrH}}_{10}$ at 300 GPa. The size of the solid dot on phonon spectra signifies the contribution to electron-phonon coupling.

Figure 4

Calculated superconducting parameters for ${\mathrm{YH}}_{10}$, ${\mathrm{LaH}}_{10}$, ${\mathrm{HfH}}_{10}$, and ${\mathrm{ZrH}}_{10}$ at 300 GPa. The obtained $T_c$ using G-K equation with ${\mu }^{*}=0.13$ ($T_c$), the critical temperature caused by the interaction of electrons with optical phonons ($T_c^0$), EPC parameter ($\lambda$), strength of the interaction of electrons with optical phonons (${\lambda }_{\mathrm{opt}}$), electronic DOS at the Fermi level $N({ϵ}_f)$, and the contribution of H atoms DOS to the total DOS at the Fermi energy ($P_H$).