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The BCS Critical Temperature at High Density
1IST Austria, Am Campus 1, 3400 Klosterneuburg, Austria.
Mathematical Physics, Analysis, and Geometry
|February 7, 2022
Summary
We derived a formula for BCS critical temperature in high-density systems, confirming previous findings and identifying conditions for superconducting domes. This research advances understanding of superconductivity in dense matter.
Area of Science:
- Condensed Matter Physics
- Quantum Mechanics
Background:
- The Bardeen-Cooper-Schrieffer (BCS) theory describes conventional superconductivity.
- Understanding critical temperature () in high-density systems is crucial for materials science.
Purpose of the Study:
- To derive an asymptotic formula for BCS critical temperature () in the high-density limit.
- To rigorously confirm the behavior of at high densities.
- To identify conditions leading to superconducting domes.
Main Methods:
- Asymptotic analysis of the BCS critical temperature formula.
- Investigation of the interaction potential's behavior on the Fermi surface.
Main Results:
- An asymptotic formula for was derived, dependent on the interaction potential near the Fermi surface.
- Rigorous confirmation of previously proposed high-density behavior of .
- Precise conditions for the emergence of superconducting domes were identified.
Conclusions:
- The derived formula provides new insights into superconductivity in high-density systems.
- The study confirms theoretical predictions and clarifies conditions for superconducting dome formation.
- This work contributes to the fundamental understanding of BCS superconductivity.
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