We investigate the ${ \rm H_3S}$ phase of sulphur hydride under high pressure $\simeq$ 200 GPa by means of { \it ab-initio} calculations within the framework of the density-functional theory (DFT) with the PBE0 hybrid exchange-correlation ($E_{ \rm xc}$) approximation. The choice of $E_{ \rm xc}$ has the largest effect on the calculated electron-phonon coupling (EPC) matrix elements; the high pressure equation of state and phonon frequencies are only slightly modified. Mode-dependent EPC correction factors are determined from PBE0 using a frozen-phonon supercell approach, while standard density-functional perturbation theory is used to determine the EPC with PBE generalized-gradient approximation $E_{ \rm xc}$. Our principle finding is that the calculated PBE0 $T_c$ is enhanced by 25\% compared to PBE. This is similar in magnitude, but in opposite direction, to the proposed suppression of $T_c$ by anharmonic effects [Errea { \em et al., Phys. Rev. Lett.} { \bf 114}, 157004 (2015)]. Our calculations demonstrate the importance of considering exchange-correlation approximations for calculations of superconducting properties for this class of materials.
Categories: cond-mat.supr-con cond-mat.str-el