Temperature effects on the calculation of the functional derivative of Tc with respect to α2F(ω).

The functional derivative of the superconducting transition temperature Tc with respect to the electron-phonon coupling function [Formula: see text] permits identifying the frequency regions where phonons are most effective in raising Tc. This work presents an analysis of temperature effects on the calculation of the δTc/δα2F(ω) and µ* parameters. The results may permit establishing that the variation of the temperature in the δTc/δα2F(ω) and µ* parameter allows establishing patterns and conditions that are possibly related to the physical conditions in the superconducting state, with implications on the theoretical estimation of the Tc.

Cooper-pair distribution function [Formula: see text] for superconducting [Formula: see text] and [Formula: see text].

Cooper-pair distribution function, [Formula: see text], 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 [Formula: see text] parameter, which is proportional to the total number of Cooper pairs formed at a critical temperature [Formula: see text]. Herein, we reported [Formula: see text] function of the compressed [Formula: see text] and [Formula: see text] high-[Formula: see text] conventional superconductors, including the effect of stable sulfur isotopes in [Formula: see text]. [Formula: see text] 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 [Formula: see text] by its stable isotopes can lead to important changes in [Formula: see text]. The results also show proportionality between [Formula: see text] parameter and experimental or theoretical [Formula: see text] values.

Cooper Pairs Distribution function for bcc Niobium under pressure from first-principles.

In this paper, we report Cooper Pairs Distribution function [Formula: see text] for bcc Niobium under pressure. This function reveals information about the superconductor state through the determination of the spectral regions for Cooper-pairs formation. [Formula: see text] is built from the well-established Eliashberg spectral function and phonon density of states, calculated by first-principles. [Formula: see text] for Nb suggests that the low-frequency vibration region [Formula: see text] is where Cooper-pairs are possible. From [Formula: see text], it is possible to obtain the [Formula: see text] parameter, which is proportional to the total number of Cooper-Pairs formed at a temperature [Formula: see text]. The [Formula: see text] parameter allows an approach to the understanding of the Nb [Formula: see text] anomalies, measured around 5 and 50 GPa.

The higher superconducting transition temperatureTcand the functional derivative ofTcwithα2F(ω) for electron-phonon superconductors.

This work presents an analysis of the functional derivative of the superconducting transition temperatureTcwith respect to the electron-phonon coupling functionα2F(ω) [δTc/δα2F(ω)] andα2F(ω) spectrum of H3S (Im3̄m), in the pressure range where the high-Tcwas measured (155-225 GPa). The calculations are done in the framework of the Migdal-Eliashberg theory. We find for this electron-phonon superconductor, a correlation between the maximums ofδTc/δα2F(ω) andα2F(ω) with its higherTc. We corroborate this behavior in other electron-phonon superconductors by analyzing data available in the literature, which suggests its validity in this type of superconductors. The correlation observed could be considered as a theoretical tool that in an electron-phonon superconductor, allows describing qualitatively the proximity to its highestTc, and determining the optimal physical conditions (pressure, alloying or doping concentration) that lead to the superconductor reaching its highestTcpossible.