Cooper-pair distribution function D_cp (, T_c) for superconducting D₃S and H₃S

Cooper-pair distribution function, D-cp (omega, T-c), is a recent theoretical proposal that reveals information about the superconductor state through the determination of the spectral regions where Cooper pairs are formed. This is built from the well-established Eliashberg spectral function and phonon density of states, calculated by first-principles. From this function is possible to obtain the N-cp parameter, which is proportional to the total number of Cooper pairs formed at a critical temperature T-c. Herein, we reported D-cp (omega, T-c)function of the compressed D3S and H3S high-T-c conventional superconductors, including the effect of stable sulfur isotopes in H3S. D-cp (omega, T-c) suggests that the vibration energy range of 10-70 meV is where the Cooper pairs are possible for these superconductors, pointing out the possible importance of the low-energy region on the electron-phonon superconductivity. This has been confirmed by the fact that a simple variation in the low-frequency region induced for the substitution of S atoms in H3S by its stable isotopes can lead to important changes in T-c. The results also show proportionality between N-cp parameter and experimental or theoretical T-c values.