Role of carbon in modifying the properties of superconducting hydrogen sulfide

We examine the role of adding carbon to influence the superconducting properties of hydrogen sulfide. We consider a number of unique structures employing a simulation cell containing carbon, hydrogen, and sulfur atoms with randomized atomic coordinates. We also reproduced some structures reported in the literature. In general, we find the presence of carbon atoms does not raise the superconducting transition temperature of hydrogen sulfide compounds. We discuss the origin of this trend through a detailed examination of structural and electronic properties of carbon-hydrogen-sulfur materials.

Figure 1

Enthalpy of formation (eV) of ${\mathrm{H}}_{\mathrm{x}}\mathrm{CS}$ systems as a function of hydrogen proportion, defined in Eq. (1). Blue circles show the results obtained from the small cells while red squares at $x=8.1$ show the enthalpy of the large cell with the composition of ${\mathrm{H}}_{48}{\mathrm{C}}_8\mathrm{S}$. The chemical potential of hydrogen is taken as the enthalpy of the $Cmca$-12 structure of hydrogen. The zero in the plot is taken as the enthalpy of the lowest enthalpy structure of ${\mathrm{H}}_6\mathrm{CS}$.

Figure 2

Enthalpy of formation (eV) of ${\mathrm{H}}_x{\mathrm{C}}_2$ structures as a function of hydrogen proportion. The chemical potential of hydrogen is taken as $Cmca$-12 hydrogen structure. The zero of the plot is taken as the enthalpy of the lowest enthalpy structure of ${\mathrm{H}}_6{\mathrm{C}}_2$.

Figure 3

Eliashberg spectral function (red solid lines) and cumulative electron-phonon coupling strength λ (blue dashed lines) as a function of phonon frequency (meV). Top, middle, and bottom panels correspond to ${\mathrm{H}}_6\mathrm{CS}$ with $T_C$ of 137 K, ${\mathrm{H}}_6{\mathrm{C}}_2$ with $T_C$ of 172 K, and $R3m {\mathrm{H}}_7\mathrm{CS}$ with $T_C$ of 149 K, respectively.

Figure 4

Ball-and-stick model structures of (a) dynamically unstable but high $T_C {\mathrm{H}}_6\mathrm{CS}$, (b) dynamically stable ${\mathrm{H}}_9\mathrm{CS}$, and (c) another unstable but high $T_C {\mathrm{H}}_{10}\mathrm{CS}$. The structures of (d) insulating ${\mathrm{H}}_6{\mathrm{C}}_2$, (e) metallic ${\mathrm{H}}_6{\mathrm{C}}_2$, and (f) insulating ${\mathrm{H}}_{10}{\mathrm{C}}_2$ are also illustrated. White, brown, and yellow spheres represent hydrogen, carbon, and sulfur atoms, respectively. The vesta software is used to generate images [40]. The lattice parameters and atomic coordinates of these structures are provided in Supplemental Material [41].

Figure 5

Fully optimized ball-and-stick model structure of ${\mathrm{H}}_{48}{\mathrm{C}}_6\mathrm{S}$ with the lowest enthalpy among 10 structures. Atoms outside the cell are also illustrated when these atoms form bonds with the atoms inside the cell. White, brown, and yellow spheres represent hydrogen, carbon, and sulfur atoms, respectively. The lattice parameters and atomic coordinates of this structures are provided in Supplemental Material [41].