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The BCS Energy Gap at High Density.

Joscha Henheik1, Asbjørn Bækgaard Lauritsen1

  • 1IST Austria, Am Campus 1, 3400 Klosterneuburg, Austria.

Journal of Statistical Physics
|August 3, 2022
PubMed
Summary
This summary is machine-generated.

We derived a formula for the BCS energy gap in high-density systems. This finding, combined with critical temperature research, proves the universal ratio between the energy gap and critical temperature.

Keywords:
BCS theoryEnergy gapSuperconductivity

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Statistical Mechanics

Background:

  • The Bardeen-Cooper-Schrieffer (BCS) theory describes superconductivity.
  • Understanding the energy gap and critical temperature in high-density systems is crucial.

Purpose of the Study:

  • Derive an asymptotic formula for the BCS energy gap at high densities.
  • Investigate the dependence of the energy gap on the interaction potential strength.
  • Prove the universality of the ratio between the energy gap and critical temperature.

Main Methods:

  • Asymptotic analysis of the BCS energy gap equation.
  • Utilizing a previously derived formula for the critical temperature at high densities.

Main Results:

  • An asymptotic formula for the BCS energy gap was derived.
  • The formula shows a strong dependence on the interaction potential strength at the Fermi surface.
  • The universality of the energy gap to critical temperature ratio is proven.

Conclusions:

  • The derived formula provides new insights into superconductivity at high densities.
  • The universality of the gap-to-temperature ratio holds true in this regime.
  • This work unifies understanding of fundamental superconducting properties.