What superconducts in sulfur hydrides under pressure and why

The recent discovery of superconductivity at 190 K in highly compressed ${\mathrm{H}}_2\mathrm{S}$ is spectacular not only because it sets a record high critical temperature, but because it does so in a material that appears to be, and we argue here that it is, a conventional strong-coupling BCS superconductor. Intriguingly, superconductivity in the observed pressure and temperature range was predicted theoretically in a similar compound, ${\mathrm{H}}_3\mathrm{S}.$ Several important questions about this remarkable result, however, are left unanswered: (1) Does the stoichiometry of the superconducting compound differ from the nominal composition, and could it be the predicted ${\mathrm{H}}_3\mathrm{S}$ compound? (2) Is the physical origin of the anomalously high critical temperature related only to the high H phonon frequencies, or does strong electron-ion coupling play a role? We show that at experimentally relevant pressures ${\mathrm{H}}_2\mathrm{S}$ is unstable, decomposing into ${\mathrm{H}}_3\mathrm{S}$ and S, and that ${\mathrm{H}}_3\mathrm{S}$ has a record high $T_c$ due to its covalent bonds driven metallic, which make this compound rather similar to ${\mathrm{MgB}}_2$, but unlike most other good conventional superconductors.

Figure 1

Formation enthalpy of ${\mathrm{H}}_x{\mathrm{S}}_{1-x}$ as a function of H concentration at $P=150$ GPa (red $\times$'s) and 200 GPa (black squares). Upper axis tick marks indicate compositions equivalent to ${\mathrm{H}}_n\mathrm{S}$ for integer $n.$ All compounds above the convex hull (lines) are unstable with respect to decomposition into the two adjacent phases on the convex hull. At both pressures the only stable compound is ${\mathrm{H}}_3\mathrm{S}$. Pure S structures are taken from Refs. [16, 17], and pure H from Ref. [18]. The crystallographic description of these structures is given in the supplemental material [20].

Figure 2

Band structure of the ${\mathrm{H}}_3\mathrm{S}Im\overline{3}m$ structure at $P=200$ GPa, calculated using fplo. Weights of the three most important atomic orbitals are shown with the symbols of the corresponding sizes, and arrows indicate fplo on-site energies of each orbital. The large contribution of H orbitals to the $S\text{−}s$ derived states at the bottom of the band indicates strong covalency.

Figure 3

The main pocket of the Fermi surface of ${\mathrm{H}}_3\mathrm{S}$ at $P=200$ GPa, colored according to the local Fermi velocity (the scale is in arbitrary units). Note the heavy bands near the van Hove singularities. Two small hole pockets near $\Gamma$ and an electron pocket near $H$ contribute little to the total DOS, and are omitted from the picture.