Cooper-pair distribution function D_cp(ω, T_c) for superconducting D ₃S and H ₃S

Cooper-pair distribution function, D_cp(ω, 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(ω, 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(ω, 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.