{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2026-06-29T00:00:00Z","_id":"22290","has_accepted_license":"1","quality_controlled":"1","type":"journal_article","publication_status":"epub_ahead","month":"06","oa_version":"Published Version","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."}],"author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X"},{"last_name":"Langmann","first_name":"Edwin","full_name":"Langmann, Edwin"},{"first_name":"Asbjørn Bækgaard","last_name":"Lauritsen","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","full_name":"Lauritsen, Asbjørn Bækgaard","orcid":"0000-0003-4476-2288"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)"},"oa":1,"year":"2026","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.","publication_identifier":{"eissn":["1424-0661"],"issn":["1424-0637"]},"article_processing_charge":"Yes (via OA deal)","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s00023-026-01706-y"}],"scopus_import":"1","ddc":["500"],"language":[{"iso":"eng"}],"day":"29","related_material":{"record":[{"id":"19550","relation":"earlier_version","status":"public"}]},"article_type":"original","publisher":"Springer Nature","supplementarymaterial":"not applicable","PlanS_conform":"1","date_created":"2026-07-13T09:42:22Z","status":"public","OA_type":"hybrid","arxiv":1,"title":"Multi-band superconductors have enhanced critical temperatures","date_updated":"2026-07-13T11:34:08Z","doi":"10.1007/s00023-026-01706-y","publication":"Annales Henri Poincaré","dataavailabilitystatement":"Data sharing is not applicable to this article as no new data were created or analyzed in this study.","das_tickbox":"1","external_id":{"arxiv":["2409.17297"]},"citation":{"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.","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>.","short":"S.J. Henheik, E. Langmann, A.B. Lauritsen, Annales Henri Poincaré (2026).","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>","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>.","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>"},"department":[{"_id":"LaEr"},{"_id":"RoSe"}],"ec_funded":1,"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d"},{"name":"Mathematical Challenges in BCS Theory of Superconductivity","grant_number":"I06427","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b"}],"OA_place":"publisher","researchdata_availability":"not applicable"}