Second group of high-pressure high-temperature lanthanide polyhydride superconductors

Rare-earth polyhydrides formed under pressure are promising conventional superconductors, with the critical temperature $T_c$ in compressed ${\mathrm{LaH}}_{10}$ almost reaching room temperature. Here, we report a systematic computational investigation of the structural and superconducting properties of rare-earth (RE) polyhydrides formed under pressure across the whole lanthanide series. Analyses of the electronic and dynamical properties and electron-phonon coupling interaction for the most hydrogen-rich hydrides ${\mathrm{REH}}_n$ ($n=8,9,10$) that can be stabilized below 400 GPa show that enhanced $T_c$ correlates with a high density of H $s$ states and low number of RE $f$ states at the Fermi level. In addition to previously predicted and measured ${\mathrm{LaH}}_{10}$ and ${\mathrm{CeH}}_9$, we suggest ${\mathrm{YbH}}_{10}$ and ${\mathrm{LuH}}_8$ as additional potential high-$T_c$ superconducters. They form a “second island” of high-$T_c$ superconductivity amongst the late lanthanide polyhydrides, with an estimated $T_c$ of 102 K for ${\mathrm{YbH}}_{10}$ at 250 GPa.

Figure 1

(a), (b) Convex hull construction for polyhydrides Yb-H and Lu-H phases relative to ${\mathrm{REH}}_3$ and ${\mathrm{H}}_2$ under pressure range from 100 to 400 GPa; filled (open) symbols represent the stable (metastable) phases. (c) Stability pressure-composition H-rich phase diagram of ${\mathrm{REH}}_n$ (RE = La, Ce, Yb, Lu; $n=8,9,10$) systems.

Figure 2

Crystal structures of lanthanide polyhydrides and corresponding RE-centered H cages. Small (large) spheres represent H (RE) atoms. (a) $Fm\overline{3}m{\mathrm{REH}}_8$, (b) $F\overline{4}3m{\mathrm{REH}}_9$, (c) $P{6}_3/mmc{\mathrm{REH}}_9$, and (d) $Fm\overline{3}m{\mathrm{REH}}_{10}$.

Figure 3

(a) Calculated electronic DOS of H $s$-states and RE atom $f$-states at the Fermi level in different polyhydrides. (b) Maximum $T_c$ for lanthanide polyhydrides, including the experimentally confirmed ${\mathrm{LaH}}_{10}$ (250 K) [26, 27], ${\mathrm{PrH}}_9$ ($\sim 9$ K) [30], and ${\mathrm{NdH}}_9$ ($\sim 4.5$ K) [32], and theoretically predicted ${\mathrm{CeH}}_9$ (117 K) [28], ${\mathrm{HoH}}_4$ (36.4 K), ${\mathrm{ErH}}_{15}$ (31.5 K), and ${\mathrm{LuH}}_{12}$ (6.7 K) [34].

Figure 4

(a) Calculated electronic band structures and density of states (DOS) of ${\mathrm{YbH}}_{10}$ at 250 GPa. (b) Phonon dispersion curves, phonon density of states (PHDOS) projected on Yb and H atoms, and Eliashberg spectral function ${\alpha }^2\mathrm{F}(\omega$) together with the electron-phonon integral $\lambda (\omega$). (c)–(f) The Fermi surface sheets of ${\mathrm{YbH}}_{10}$.

Figure 5

(a) Crystal structure of $Immm-{\mathrm{LuH}}_8$ at 300 GPa. (b) Fermi surface sheets of ${\mathrm{LuH}}_8$. (c) Calculated electronic band structures and density of states (DOS) of ${\mathrm{LuH}}_8$. (d) Phonon dispersion curves, phonon density of states (PHDOS) projected on Lu and H atoms, and Eliashberg spectral function ${\alpha }^2\mathrm{F}(\omega$) together with the electron-phonon integral $\lambda (\omega$).