High-T${}_c$ superconductivity in H${}_3$S: Pressure effects on superconducting critical temperature and Cooper-Pairs Distribution Function

Abstract

We use first-principles calculations to study pressure effects on the vibrational and superconducting properties of H${}_3$S in the cubic $Im\bar{3}m$ phase for the pressure range where the superconducting critical temperature (T${}_c$) was measured (155-225 GPa). The pressure effects were incorporated using the Functional Derivative Method (FDM). In this paper, we present for the first time, the Cooper-Pairs Distribution Functions D${}_{cp}$($\omega ,T_c$) for H${}_3$S, which will allow to identify the spectral regions where Cooper-Pairs formation at temperature T${}_c$ is more favorable. We analyzed in detail the pressure effects on the electron-phonon spectral density function ${\alpha }^2$F$(\omega )$ and phonon density of states (PhDOS) and their relationship with T${}_c$. The FDM manages to reproduce the trend of the pressure dependence of critical temperature, in good agreement with experimental data in the range of 155 to 190 GPa. The $D_{cp}(\omega ,T_c)$ suggests that the low-frequency vibration region is where Cooper-Pairs are possible, which means that S-vibrations have an important role in the H${}_3$S superconductivity properties.

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