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

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.

Effect of substitution on the superconducting phase of transition metal dichalcogenide Nb(Se$$_{x}$$S$$_{1-x}$$)$$_{2}$$ van der Waals layered structure

By means of first-principles cluster expansion, anisotropic superconductivity in the transition metal dichalcogenide Nb(Se$$_{x}$$ x S$$_{1-x}$$ 1 - x )$$_{2}$$ 2 forming a van der Waals (vdW) layered structure is observed theoretically. We show that the Nb(Se$$_{0.5}$$ 0.5 S$$_{0.5}$$ 0.5 )$$_{2}$$ 2 vdW-layered structure exhibits minimum ground-state energy. The Pnnm structure is more thermodynamically stable when compared to the 2H–NbSe$$_{2}$$ 2 and 2H–NbS$$_{2}$$ 2 structures. The characteristics of its phonon dispersions confirm its dynamical stability. According to electronic properties, i.e., electronic band structure, density of states, and Fermi surface indicate metallicity of Nb(Se$$_{0.5}$$ 0.5 S$$_{0.5}$$ 0.5 )$$_{2}$$ 2 . The corresponding superconductivity is then investigated through the Eliashberg spectral function, which gives rise to a superconducting transition temperature of 14.5 K. This proposes a remarkable improvement of superconductivity in this transition metal dichalcogenide.

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

In this paper, we report Cooper Pairs Distribution function $${D}_{cp}(\omega ,{T}_{c})$$ D cp ( ω , T c ) for bcc Niobium under pressure. This function reveals information about the superconductor state through the determination of the spectral regions for Cooper-pairs formation. $${D}_{cp}(\omega ,{T}_{c})$$ D cp ( ω , T c ) is built from the well-established Eliashberg spectral function and phonon density of states, calculated by first-principles. $${D}_{cp}(\omega ,{T}_{c})$$ D cp ( ω , T c ) for Nb suggests that the low-frequency vibration region $$\left(\omega <6 \,{\text{meV}}\right)$$ ω < 6 meV is where Cooper-pairs are possible. From $${D}_{cp}(\omega ,{T}_{c})$$ D cp ( ω , T c ) , it is possible to obtain the $${N}_{cp}$$ N cp parameter, which is proportional to the total number of Cooper-Pairs formed at a temperature $${T}_{c}$$ T c . The $${N}_{cp}$$ N cp parameter allows an approach to the understanding of the Nb $${T}_{c}$$ T c anomalies, measured around 5 and 50 GPa.