Multi-band superconductors have enhanced critical temperatures Henheik, Sven Joscha ; https://orcid.org/0000-0003-1106-327X Langmann, Edwin Lauritsen, Asbjørn Bækgaard ; https://orcid.org/0000-0003-4476-2288 ddc:500 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. Springer Nature 2026 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/22290 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> eng info:eu-repo/semantics/altIdentifier/doi/10.1007/s00023-026-01706-y info:eu-repo/semantics/altIdentifier/issn/1424-0637 info:eu-repo/semantics/altIdentifier/e-issn/1424-0661 info:eu-repo/semantics/altIdentifier/arxiv/2409.17297 info:eu-repo/semantics/openAccess