---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '22290'
abstract:
- lang: eng
  text: We introduce a multi-band BCS free energy functional and prove that for a
    multi-band superconductor the effect of inter-band coupling can only increase
    the critical temperature, irrespective of its attractive or repulsive nature and
    its strength. Further, for weak coupling and weaker inter-band coupling, we prove
    that the dependence of the increase in critical temperature on the inter-band
    coupling is (1) linear, if there are two or more equally strongly superconducting
    bands, or (2) quadratic, if there is only one dominating band.
acknowledgement: 'We would like to thank J. Lenells and R. Seiringer for their interest
  and helpful discussions, E. Babaev and Y. Yerin for useful comments about the literature,
  and the anonymous referee for their comments. J.H. gratefully acknowledges partial
  financial support by the ERC Advanced Grant “RMTBeyond” No. 101020331 and the ERC
  Consollidator Grant “ProbQuant” (jointly with the Swiss State Secretariat for Education,
  Research and Innovation). E.L. gratefully acknowledges support from the Swedish
  Research Council, Grant No. 2023-04726. A.B.L. gratefully acknowledges partial financial
  support by the Austrian Science Fund (FWF) through grant DOI: 10.55776/I6427 (as
  part of the SFB/TRR 352) and by the French State support managed by ANR under the
  France 2030 program through the MaQuI CNRS Risky and High-Impact Research programme
  (RI)^2 (grant agreement ANR-24-RRII-0001). Open access funding provided by Royal
  Institute of Technology.'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Sven Joscha
  full_name: Henheik, Sven Joscha
  id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
  last_name: Henheik
  orcid: 0000-0003-1106-327X
- first_name: Edwin
  full_name: Langmann, Edwin
  last_name: Langmann
- first_name: Asbjørn Bækgaard
  full_name: Lauritsen, Asbjørn Bækgaard
  id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1
  last_name: Lauritsen
  orcid: 0000-0003-4476-2288
citation:
  ama: Henheik SJ, Langmann E, Lauritsen AB. Multi-band superconductors have enhanced
    critical temperatures. <i>Annales Henri Poincaré</i>. 2026. doi:<a href="https://doi.org/10.1007/s00023-026-01706-y">10.1007/s00023-026-01706-y</a>
  apa: Henheik, S. J., Langmann, E., &#38; Lauritsen, A. B. (2026). Multi-band superconductors
    have enhanced critical temperatures. <i>Annales Henri Poincaré</i>. Springer Nature.
    <a href="https://doi.org/10.1007/s00023-026-01706-y">https://doi.org/10.1007/s00023-026-01706-y</a>
  chicago: Henheik, Sven Joscha, Edwin Langmann, and Asbjørn Bækgaard Lauritsen. “Multi-Band
    Superconductors Have Enhanced Critical Temperatures.” <i>Annales Henri Poincaré</i>.
    Springer Nature, 2026. <a href="https://doi.org/10.1007/s00023-026-01706-y">https://doi.org/10.1007/s00023-026-01706-y</a>.
  ieee: S. J. Henheik, E. Langmann, and A. B. Lauritsen, “Multi-band superconductors
    have enhanced critical temperatures,” <i>Annales Henri Poincaré</i>. Springer
    Nature, 2026.
  ista: Henheik SJ, Langmann E, Lauritsen AB. 2026. Multi-band superconductors have
    enhanced critical temperatures. Annales Henri Poincaré.
  mla: Henheik, Sven Joscha, et al. “Multi-Band Superconductors Have Enhanced Critical
    Temperatures.” <i>Annales Henri Poincaré</i>, Springer Nature, 2026, doi:<a href="https://doi.org/10.1007/s00023-026-01706-y">10.1007/s00023-026-01706-y</a>.
  short: S.J. Henheik, E. Langmann, A.B. Lauritsen, Annales Henri Poincaré (2026).
das_tickbox: '1'
dataavailabilitystatement: Data sharing is not applicable to this article as no new
  data were created or analyzed in this study.
date_created: 2026-07-13T09:42:22Z
date_published: 2026-06-29T00:00:00Z
date_updated: 2026-07-13T11:34:08Z
day: '29'
ddc:
- '500'
department:
- _id: LaEr
- _id: RoSe
doi: 10.1007/s00023-026-01706-y
ec_funded: 1
external_id:
  arxiv:
  - '2409.17297'
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.1007/s00023-026-01706-y
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
  call_identifier: H2020
  grant_number: '101020331'
  name: Random matrices beyond Wigner-Dyson-Mehta
- _id: bda63fe5-d553-11ed-ba76-a16e3d2f256b
  grant_number: I06427
  name: Mathematical Challenges in BCS Theory of Superconductivity
publication: Annales Henri Poincaré
publication_identifier:
  eissn:
  - 1424-0661
  issn:
  - 1424-0637
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
related_material:
  record:
  - id: '19550'
    relation: earlier_version
    status: public
researchdata_availability: not applicable
scopus_import: '1'
status: public
supplementarymaterial: not applicable
title: Multi-band superconductors have enhanced critical temperatures
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2026'
...