Tellurium Hydrides at High Pressures: High-Temperature Superconductors

Observation of high-temperature superconductivity in compressed sulfur hydrides has generated an irresistible wave of searches for new hydrogen-containing superconductors. We herein report the prediction of high-$T_c$ superconductivity in tellurium hydrides stabilized at megabar pressures identified by first-principles calculations in combination with a swarm structure search. Although tellurium is isoelectronic to sulfur or selenium, its heavier atomic mass and weaker electronegativity makes tellurium hydrides fundamentally distinct from sulfur or selenium hydrides in stoichiometries, structures, and chemical bondings. We identify three metallic stoichiometries of ${\mathrm{H}}_4\mathrm{Te}$, ${\mathrm{H}}_5{\mathrm{Te}}_2$, and ${\mathrm{HTe}}_3$, which are not predicted or known stable structures for sulfur or selenium hydrides. The two hydrogen-rich ${\mathrm{H}}_4\mathrm{Te}$ and ${\mathrm{H}}_5{\mathrm{Te}}_2$ phases are primarily ionic and contain exotic quasimolecular ${\mathrm{H}}_2$ and linear ${\mathrm{H}}_3$ units, respectively. Their high-$T_c$ (e.g., 104 K for ${\mathrm{H}}_4\mathrm{Te}$ at 170 GPa) superconductivity originates from the strong electron-phonon couplings associated with intermediate-frequency H-derived wagging and bending modes, a superconducting mechanism which differs substantially with those in sulfur or selenium hydrides where the high-frequency H-stretching vibrations make considerable contributions.

Figure 1

(a) Formation enthalpies ($\mathrm{\Delta }H$) of various H-Te compounds with respect to decomposition into constituent elemental solids at 100–300 GPa. Data points located on the convex hull (solid lines) represent stable species against any type of decomposition. The results of H-S [9] (open circles at 250 GPa) and H-Se [10] (open squares at 300 GPa) systems are shown for comparison. (b) Pressure ranges in which the corresponding structures of different stoichiometries are stabilized. The phases I ($P{3}_{1}21$), V ($\mathrm{Im}-3m$), VI ($I4/mmm$), and VII ($Fm-3m$) of Te [37], and the $P{6}_{3}m$ and $C2/c$ structures of solid ${\mathrm{H}}_2$ [38] are used for calculating $\mathrm{\Delta }H$. The hull data remain essentially unchanged with the inclusion of zero-point energies (see the Supplemental Material [33]).

Figure 2

Structures of stable H-Te compounds at high pressures derived from the CALYPSO structure search: (a),(b) ${\mathrm{H}}_4\mathrm{Te}$ in the $P6/mmm$ and $R\text{−}3m$ structures, respectively; (c) ${\mathrm{H}}_5{\mathrm{Te}}_2$ in the $C2/m$ structure; (d),(e) HTe in the $P4/nmm$ and $P{6}_3/mmc$ structures, respectively; (f) ${\mathrm{HTe}}_3$ in the $C2/c$ structure. Small and large spheres represent H and Te atoms. Solid lines depict the unit cells of the structures. See the Supplemental Material [33] for more detailed structural information.

Figure 3

(a) Electronic band structure of ${\mathrm{H}}_4\mathrm{Te}$ in the $P6/mmm$ structure at 200 GPa. The red dashed lines represent the band structure of the H sublattice with a uniform compensated background charge. (b) Projected density of states for ${\mathrm{H}}_4\mathrm{Te}$ and ${\mathrm{H}}_5{\mathrm{Te}}_2$ in the $C2/m$ structure at 200 GPa. (c)–(e) Fermi surfaces of ${\mathrm{H}}_4\mathrm{Te}$.

Figure 4

Calculated projected phonon density of states (lower panels), Eliashberg EPC spectral function ${\alpha }^{2}F(\omega )$ and its integral $\lambda (\omega )$ (upper panels) of (a) ${\mathrm{H}}_4\mathrm{Te}$ ($P6/mmm$) at 200 GPa, (b) ${\mathrm{H}}_4\mathrm{Te}$ ($R\text{−}3m$) at 300 GPa, and (c) ${\mathrm{H}}_5{\mathrm{Te}}_2$ ($C2/m$) at 300 GPa.