Theoretical calculations based on the BCS phonon-mediated theory of superconductivity indicate that highly compressed solid hydrogen and main group hydrogen-rich materials can possess high T_c in predicted high pressure metallic states due to the existence of hydrogen-dominated vibrations. This proposal has motivated the search for superconductivity in these materials using both theoretical and experimental approaches.

Hydrogen sulfides have recently attracted a great deal of attention due to the record high T_c of 203 K observed on compression of H₂S [A. P. Drozdov et al., Nature 525, 73-76 (2015)]. In recent work at Carnegie, a joint theoretical and experimental study has been carried out to characterize the dissociation products of compressed H₂S.  This information is essential for an understanding of the complex superconducting states observed in the hydrogen-sulfur system.

In simulations, it is found that H₂S partially decomposes into S+H₃S+H₄S₃ above 27 GPa, and H₄S₃ emerges as the major component at around 66 GPa. X-ray diffraction (XRD) measurements reveal a small fraction of H₃S and residual H₂S at least up to 140 GPa, which are believed to be responsible for the two superconducting states observed in experiments. This work provides the first XRD evidence on the existence of H₃S at high pressure from the decomposition of H₂S. 

Calculated T_c values for H₄S₃, H₂S, and H₃S are compared to experimental data measured in compressed H₂S, where T_c values have been obtained for samples prepared at low (L-T_c) and high (H-T_c) temperatures (Fig. 1).  Although the value of T_c for Im-3m structured H₃S calculated within the harmonic approximation is much higher than the observed H-T_c, the inclusion of anharmonic effects reproduces the H-T_c data above 180 GPa very well. The predicted T_c for R3m-H₃S increases with pressure, in stark contrast to the experimental observation of a decrease in H-T_c. Further study is required to understand the steep increase of L-T_c above 160 GPa and the high value of H-T_c at around 150 GPa.

Recently, two possible candidate structures for compressed PH₃ have been elucidated using first-principles electronic structure methods (Fig. 2).  Both the calculated values for T_c  as well as the pressure dependence of T_c based on BCS theory agree well with experiment, further supporting proposals that high critical temperatures can be realized by a phonon-mediated mechanism.  In a related study [A. Shamp et al., J. Am. Chem. Soc. 138, 1884-1892 (2016)], similar results were obtained for a PH₂ composition, obtained by the decomposition of PH₃ to PH₂ and molecular hydrogen at high pressure [H. Liu et al., J. Phys. Chem. C 120, 3458-3461 (2016)].