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We use first-principles calculations to study pressure effects on the vibrational and superconducting properties of H 3 S in the cubic Im3m 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 (ω, 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 α 2 F(ω) and phonon density of states (PhDOS) and its relationship with the pressure dependence of the T c . Our results show a good agreement with the experiment. The D cp (ω, T c ) suggests that low frequency vibration region is where Cooper-Pairs are possible, which means that S-vibration have an important role in the H 3 S superconductivity properties. The increase in pressure leads to a reduction in the coupling constant λ and an increase in Coulomb pseudopotential µ * which induces a consistent correlation with T c , in good agreement with the Migdal-Eliashberg theory.

From photoacoustic (PA) experiments we determine the nonradiative carrier lifetime in direct band-gap semiconductors. We use the Rosencwaig and Gerscho model to calculate the PA signal in semiconductors taking into account the distinction between non-radiative and radiative carrier lifetimes. We have assumed that for our high quality crystalline samples, the main contribution to the non-radiative processes comes from CHCC and CHSH Auger recombination for n and p-type materials, respectively. For GaAs, InSb and GaSb samples, the experimental data obtained by means of an open photoacoustic cell were fitted to the theoretical model and we show that the values we determined for the non-radiative recombination lifetime agree well with those reported in the literature.

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The Eliashberg kernels a 2 (w)F(to) obtained from tunne6ng experiments for a series of weak to strong coupling TI-Pb-Bi alloys are used to calculate numerically on the imaginary axis the thermodynamic properties of these alloys in the superconducting state. The functional derivatives of Tc and Hc with respect to changes in the kernel are also calculated.