Cooper-pair distribution function $$D_{cp}(\omega ,T_c)$$ for superconducting $$\hbox {D}_3\hbox {S}$$ and $$\hbox {H}_3\hbox {S}$$

Abstract

Cooper-pair distribution function, $$D_{cp}(\omega ,T_c)$$ 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 $$N_{cp}$$ N cp parameter, which is proportional to the total number of Cooper pairs formed at a critical temperature $$T_c$$ T c . Herein, we reported $$D_{cp}(\omega ,T_c)$$ D cp ( ω , T c ) function of the compressed $$D_3S$$ D 3 S and $$H_3S$$ H 3 S high-$$T_c$$ T c conventional superconductors, including the effect of stable sulfur isotopes in $$H_3S$$ H 3 S . $$D_{cp}(\omega ,T_c)$$ 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 $$H_3S$$ H 3 S by its stable isotopes can lead to important changes in $$T_c$$ T c . The results also show proportionality between $$N_{cp}$$ N cp parameter and experimental or theoretical $$T_c$$ T c values.

Superconductivity in Twisted Bilayer Graphene: Cooper-pairs distribution function analysis

“…Furthermore, from D cp (ω, T c ) it is possible to get an estimate of the total number of Cooper pairs formed at temperature T c through a quantity proportional to it, N cp parameter 12,13 . The comparison of N cp parameters obtained from each D cp (ω, T c ) as a function of an electrical eld, for both angles is shown in Fig.…”

On the use of Monkhorst–Pack scheme to evaluate superconductivity and the issue of umklapp electron–phonon interactions

“…Many opted to exclude umklapp phonons to deal with it. 21–28 We show it enlightens us to find an alternative option in the next section.…”

“…23 Camargo–Martínez and colleagues used the MP scheme to study superconductivity in H 3 S, 24 stating they had knowingly excluded umklapp contributions. 25,26 Du and colleagues used the MP scheme to study transition metallic hydrides 27 and made a similar statement. 28…”

“…In a following publication, 26 González-Pedreros, Camargo-Martínez and Mesa continued to apply the MP scheme to evaluate superconductivity in D 3 H. They cited, 25,50 claiming that “the presence of umklapp process is mainly associated with the electrical resistivity, which is measured in the normal state and not in the superconductor one”. They announced “Our calculations were considered in the superconducting state, and Umklapp processes have not been included”.…”

“…We believe the practice in 21–28 amounts to an answer to the call for reducing phonon contributions to superconductivity to solve a historical difficulty. In the BCS theory, superconductivity arises from the interactions between electrons and phonons.…”