- Department of Applied Physics, University of Tokyo
^{1} - CEMS, RIKEN
^{2} - Department of Physics, Tohoku University
^{3} - Dipartimento di Fisica, UniversitÃ di Roma La Sapienza
^{4}

Recently, it has been reported that room-temperature superconducticity with *T*_{c} ~ 280 K emerges in cabonaceous sulfur hydride (C-S-H) systems under high pressure up to 270 GPa [1]. Since their atomic configuration is still not determined, we explore a variety of crystal structures in a C-S-H convex hull and discuss the stability of candidate structures of C-S-H ternary compounds [2].

Meanwhile, based on *ab initio* calculations using the McMillan-Allen-Dynes formula, it has been recently shown that carbon-doped H_{3}S with a doping level of around 5% could be a promising candidate for the room-temperature superconductor [3,4]. While the McMillan-Allen-Dynes is based on the constant DOS approximation, in this work we perform *ab initio* Migdal-Eliashberg calculation considering the significant energy dependence of the van Hove singulartiy around the Fermi level [5].

Our conclusions include (i) the absence of a dominant low-enthalpy stoichiometry and crystal structure in the ternary phase diagram. (ii) Only the thermodynamics of C-doping phases appears to be marginally competing in enthalpy against H_{3}S. (iii) Accurate results of the transition temperature given by *ab initio* Migdal-Eliashberg calculations differ by more than 110K from recent theoretical claims explaining the room-temperature superconductivitiy in carbonaceous hydrogen sulfide. An unconventional mechanims of superconductivity or a breakdown of current theories in this system is possibly behind the disagreement.

Fig. 1. C-S-H convex hull of the formation enthalpy calculated for selected stoichiometries at 250 GPa. Different stoichiometries are colored according to their formation enthalpy.

Reference:

[1] E. Snider, N. Dasenbrock-Gammon, R. Mcbride, M. Debessai, H. Vindana, K. Vencatasamy, K. V. Lawler, A. Salamat and R. P. Dias, Nature 586, 373-377 (2020)

[2] T. Wang, M. Hirayama, T. Nomoto, T. Koretsune, Ryotaro Arita and J. A. Flores-Livas, Phys. Rev. B 104, 064510 (2021)

[3] Y. Ge, F. Zhang, R. P. Dias, R. J. Hemley and Y. Yao, Materials Today Physics 15, 100330 (2020)

[4] S. X. Hu, R. Paul, V. V. Karasiev and R. P. Dias, arXiv:2012.10259

[5] T. Wang, T. Nomoto, Y. Nomura, H. Shinaoka, J. Otsuki, T. Koretsune and R. Arita, Phys. Rev. B 102, 134503 (2020)

Keywords: room-temperature superconductivity, hydride superconductors, pressure effects, dopants