Design Principles for High-Temperature Superconductors with a Hydrogen-Based Alloy Backbone at Moderate Pressure

Hydrogen-based superconductors provide a route to the long-sought goal of room-temperature superconductivity, but the high pressures required to metallize these materials limit their immediate application. For example, carbonaceous sulfur hydride, the first room-temperature superconductor made in a laboratory, can reach a critical temperature ($T_c$) of 288 K only at the extreme pressure of 267 GPa. The next recognized challenge is the realization of room-temperature superconductivity at significantly lower pressures. Here, we propose a strategy for the rational design of high-temperature superconductors at low pressures by alloying small-radius elements and hydrogen to form ternary H-based superconductors with alloy backbones. We identify a “fluorite-type” backbone in compositions of the form $AX{\mathrm{H}}_8$, which exhibit high-temperature superconductivity at moderate pressures compared with other reported hydrogen-based superconductors. The $Fm\overline{3}m$ phase of ${\mathrm{LaBeH}}_8$, with a fluorite-type H-Be alloy backbone, is predicted to be thermodynamically stable above 98 GPa, and dynamically stable down to 20 GPa with a high $T_c\sim 185\mathrm{K}$. This is substantially lower than the synthesis pressure required by the geometrically similar clathrate hydride ${\mathrm{LaH}}_{10}$ (170 GPa). Our approach paves the way for finding high-$T_c$ ternary H-based superconductors at conditions close to ambient pressures.

Figure 1

(a) The crystal structure of ${\mathrm{UH}}_8$ with [${\mathrm{H}}_8$] cubic units. The U ions are shown in black and the H ions in pink. (b) The crystal structure of ${\mathrm{LaH}}_{10}$, in which La ions are shown in green. The backbone in ${\mathrm{LaH}}_{10}$ consists of cubic-unit H atoms (pink) and tetrahedron-center H atoms (gray). (c) The crystal structure of ${\mathrm{UH}}_8$, with [${\mathrm{H}}_8$] cubic centers shown as red balls. (d) The crystal structure of fluorite ${\mathrm{CaF}}_2$, the Ca cations are shown in dark blue, and the F ions in light blue. (e) The crystal structure of ${\mathrm{LaBeH}}_8$. The backbone in ${\mathrm{LaBeH}}_8$ consists of tetrahedral-unit H atoms (pink) and cubic-center Be atoms (blue). (f) The fluorite-type cage of ${\mathrm{LaBeH}}_8$.

Figure 2

Calculated enthalpy of fluorite-type hydrides $AX{\mathrm{H}}_8$. (a) The radius of atom $A$ is plotted on the $x$ axis and the radius of atom $X$ on the $y$ axis. Dynamically unstable systems are shown as black crosses. Metastable phases are shown as circles, colored according to the calculated enthalpy above the convex hull. Thermodynamically stable phases are shown as carmine squares. (b) Calculated enthalpy as a function of pressure for La-Be-H structures relative to the $Fm\overline{3}m$ phase of ${\mathrm{LaBeH}}_8$, where structures of ${\mathrm{LaH}}_6$, ${\mathrm{BeH}}_2$, and H are from Refs. [9, 10, 11, 38, 54], respectively.

Figure 3

Pressure dependence of $T_c$s for typical superconductors. The orange circles are $T_c$s of fluorite-type backbone hydrides at the lowest pressure where they become dynamically stable. The red circle is at the lowest pressure where ${\mathrm{LaBeH}}_8$ becomes thermodynamically stable (98 GPa), and the suggested synthesis pressure range for cubic ${\mathrm{LaBeH}}_8$ is highlighted in yellow. The blue squares are $T_c$s of clathrate binary hydrides at the lowest pressures reported in Refs. [6, 9, 10, 39, 55]. The purple stars are $T_c$s of well-known superconductors from experiment [7, 12, 24, 55]. The background is shaded according to the figure of merit $S=(T/\sqrt{P^2+T_{{\mathrm{MgB}}_2}^2})$ used to evaluate the significance of a particular superconductor [55]. The dotted line is the pressure limit of Kawai-type multianvil presses (KMAPs) [56].

Figure 4

(a) The polarization vectors of $\mathrm{H}─\mathrm{S}$ bonds in [${\mathrm{H}}_3\mathrm{S}$] backbone; in these bonds the positive charge is located at H atoms (pink) and negative charge is located at S atoms (yellow). (b) The polarization vectors of $\mathrm{Be}─\mathrm{H}$ bonds in [${\mathrm{BeH}}_8$] backbone converge, leading to a concentration of charge at the hydrogen atoms. In these bonds the positive charge is located at Be atoms (green) and the negative charge is located at H atoms (pink).