• Corpus ID: 235313550

The BCS Energy Gap at High Density

@inproceedings{Henheik2021TheBE,
  title={The BCS Energy Gap at High Density},
  author={Joscha Henheik and Asbjorn Baekgaard Lauritsen},
  year={2021}
}
We study the BCS energy gap Ξ in the high–density limit and derive an asymptotic formula, which strongly depends on the strength of the interaction potential V on the Fermi surface. In combination with the recent result by one of us (arXiv:2106.02015) on the critical temperature Tc at high densities, we prove the universality of the ratio of the energy gap and the critical temperature. 
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The BCS Critical Temperature at High Density
  • Joscha Henheik
  • Physics
    Mathematical physics, analysis, and geometry
  • 2022
We investigate the BCS critical temperature $$T_c$$ T c in the high-density limit and derive an asymptotic formula, which strongly depends on the behavior of the interaction potential V on the…

References

SHOWING 1-10 OF 22 REFERENCES
The BCS Critical Temperature at High Density
  • Joscha Henheik
  • Physics
    Mathematical physics, analysis, and geometry
  • 2022
We investigate the BCS critical temperature $$T_c$$ T c in the high-density limit and derive an asymptotic formula, which strongly depends on the behavior of the interaction potential V on the…
The critical temperature for the BCS equation at weak coupling
For the BCS equation with local two-body interaction λV(x), we give a rigorous analysis of the asymptotic behavior of the critical temperature as γ»0. We derive necessary and sufficient conditions…
Critical Temperature and Energy Gap for the BCS Equation
We derive upper and lower bounds on the critical temperature Tc and the energy gap � (at zero temperature) for the BCS gap equation, describing spin 1/2 fermions interacting via a local two- body…
The BCS Functional for General Pair Interactions
The Bardeen-Cooper-Schrieffer (BCS) functional has recently received renewed attention as a description of fermionic gases interacting with local pairwise interactions. We present here a rigorous…
The BCS Critical Temperature for Potentials with Negative Scattering Length
We prove that the critical temperature for the BCS gap equation is given by $${T_c = \mu \left( \frac 8\pi {\rm e}^{\gamma -2} + o(1) \right) {\rm e}^{\pi/(2\sqrt \mu a)}}$$ in the low density limit…
Theory of Superconductivity
IN two previous notes1, Prof. Max Born and I have shown that one can obtain a theory of superconductivity by taking account of the fact that the interaction of the electrons with the ionic lattice is…
CONTRIBUTION TO THE THEORY OF SUPER-FLUIDITY IN AN IMPERFECT FERMI GAS
The Cooper effect is studied in a low density Fermi gas. The transition temperature to the superfluid state is determined. (auth)
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We review recent results concerning the mathematical properties of the Bardeen–Cooper–Schrieffer (BCS) functional of superconductivity, which were obtained in a series of papers, partly in…
Ubiquity of Superconducting Domes in the Bardeen-Cooper-Schrieffer Theory with Finite-Range Potentials.
TLDR
It is demonstrated that any well-defined nonlocal potential leads to a "superconducting dome," i.e., a nonmonotonic T_{c}(n) exhibiting a maximum value at finite doping and going to zero for large n, which proves that, contrary to conventional wisdom, the presence of a superconducting Dome is not necessarily an indication of competing orders, nor of exotic superconductivity.
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We study the eigenvalues of Schrödinger type operators T + λV and their asymptotic behavior in the small coupling limit λ → 0, in the case where the symbol of the kinetic energy, T (p), strongly…
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