# Strong-Coupling Behavior of the Critical Temperature of Pb/Ag, Pb/Cu and Pb/Al Nanocomposites Explained by Proximity Eliashberg Theory

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## Abstract

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## 1. Introduction

## 2. Model: Proximity Eliashberg Equations

## 3. Results and Discussion

## 4. Conclusions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(Color online) Case $Pb-Ag$. Theoretical critical temperature calculated by solving the Eliashberg equations with ${N}_{Ag}\left(0\right)\ne {N}_{Pb}\left(0\right)$ (dark blue solid line) and with ${N}_{Ag}\left(0\right)={N}_{Pb}\left(0\right)$ (red solid line) is shown in function of the rate ${P}_{S}/{P}_{N}$. The experimental data (full red circles) are from ref [22]. In the insert, the electron–phonon spectral functions of lead (green solid line) and silver (orange solid line) are shown.

**Figure 2.**(Color online) Case $Pb-Cu$. Theoretical critical temperature calculated by solving the Eliashberg equations with ${N}_{Cu}\left(0\right)\ne {N}_{Pb}\left(0\right)$ (dark blue solid line) and with ${N}_{Cu}\left(0\right)={N}_{Pb}\left(0\right)$ (red solid line) is shown in function of the rate ${P}_{S}/{P}_{N}$. The experimental data (full red circles) are from ref [23]. In the inset, the electron–phonon spectral functions of lead (green solid line) and copper (orange solid line) are shown.

**Figure 3.**(Color online) Case $Pb-Al$. Theoretical critical temperature calculated by solving the Eliashberg equations with ${N}_{Al}\left(0\right)\ne {N}_{Pb}\left(0\right)$ (dark blue solid line) and with ${N}_{Al}\left(0\right)={N}_{Pb}\left(0\right)$ (red solid line) is shown in function of the rate ${P}_{S}/{P}_{N}$. The experimental data (full red circles) are from ref [5]. In the inset, the electron–phonon spectral functions of lead (green solid line) and aluminum (orange solid line) are shown.

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**MDPI and ACS Style**

Ummarino, G.A.
Strong-Coupling Behavior of the Critical Temperature of Pb/Ag, Pb/Cu and Pb/Al Nanocomposites Explained by Proximity Eliashberg Theory. *Condens. Matter* **2023**, *8*, 45.
https://doi.org/10.3390/condmat8020045

**AMA Style**

Ummarino GA.
Strong-Coupling Behavior of the Critical Temperature of Pb/Ag, Pb/Cu and Pb/Al Nanocomposites Explained by Proximity Eliashberg Theory. *Condensed Matter*. 2023; 8(2):45.
https://doi.org/10.3390/condmat8020045

**Chicago/Turabian Style**

Ummarino, Giovanni Alberto.
2023. "Strong-Coupling Behavior of the Critical Temperature of Pb/Ag, Pb/Cu and Pb/Al Nanocomposites Explained by Proximity Eliashberg Theory" *Condensed Matter* 8, no. 2: 45.
https://doi.org/10.3390/condmat8020045