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 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. 2024 info:eu-repo/semantics/preprint doc-type:preprint text http://purl.org/coar/resource_type/c_816b https://research-explorer.ista.ac.at/record/19550 Henheik SJ, Langmann E, Lauritsen AB. Multi-band superconductors have enhanced critical temperatures. <i>arXiv</i>. doi:<a href="https://doi.org/10.48550/arXiv.2409.17297">10.48550/arXiv.2409.17297</a> eng info:eu-repo/semantics/altIdentifier/doi/10.48550/arXiv.2409.17297 info:eu-repo/semantics/altIdentifier/arxiv/2409.17297 https://creativecommons.org/licenses/by/4.0/ info:eu-repo/semantics/openAccess