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Enhanced superconductivity in proximity to peaks in densities of states

Joshua Althüser*, Ilya M. Eremin†, and Götz S. Uhrig‡

  • *Contact author: joshua.althueser@tu-dortmund.de
  • †Contact author: ilya.eremin@ruhr-uni-bochum.de
  • ‡Contact author: goetz.uhrig@tu-dortmund.de
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Phys. Rev. Research 8, 033291 – Published 8 September, 2026

DOI: https://doi.org/10.1103/xbsf-8l6q

Abstract

For the BCS theory of superconductivity, the electron-phonon interaction is transformed to an attractive electron-electron interaction in the vicinity of the Fermi energy only. At the same time, its formal derivation using a unitary transformation reveals that the electrons attract one another whenever their energies do not differ by more than the phonon energy ωD, independent of closeness to the Fermi energy. Consequently, the order parameter becomes finite even away from the Fermi level. Yet, for small interactions, its magnitude is usually small and can be safely ignored, justifying the BCS approximation. Intriguingly, we find that an accumulation of density of states at an energy ɛpeak in proximity to the Fermi energy induces a significant order parameter magnitude around ɛpeak, which exceeds the one at EF for moderate coupling strengths. This strong enhancement is heralded by the softening of an additional collective mode, which resembles a second phase transition. We predict measurable signatures in the thermodynamic and spectroscopic responses to this unexpected phenomenon, guiding future experimental searches for it. Finally, we demonstrate that these signatures remain robust upon including a phenomenological Coulomb repulsion, indicating that the enhancement is not an artifact of the idealized model.

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Phys. Rev. Research 8, 033291– Published 8 September, 2026
  • Received 12 December 2025
  • Accepted 21 August 2026
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