Universal behavior of the BCS energy gap

  • Joscha Henheik

    Institute of Science and Technology Austria, Klosterneuburg, Austria
  • Asbjørn Bækgaard Lauritsen

    Institute of Science and Technology Austria, Klosterneuburg, Austria; CNRS &CEREMADE, Université Paris–Dauphine, PSL University, Paris, France
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Abstract

We consider the BCS energy gap (essentially given by , the BCS order parameter) at all temperatures up to the critical one, , and show that, in the limit of weak coupling, the ratio is given by a universal function of the relative temperature . On the one hand, this recovers a recent result by Langmann and Triola [Phys. Rev. B 108 (2023), no. 10, article no. 104503] on three-dimensional -wave superconductors for temperatures bounded uniformly away from . On the other hand, our result lifts these restrictions, as we consider arbitrary spatial dimensions , discuss superconductors with non-zero angular momentum (primarily in two dimensions), and treat the perhaps physically most interesting (due to the occurrence of the superconducting phase transition) regime of temperatures close to .

Cite this article

Joscha Henheik, Asbjørn Bækgaard Lauritsen, Universal behavior of the BCS energy gap. J. Spectr. Theory 15 (2025), no. 1, pp. 305–352

DOI 10.4171/JST/540