article epub_ahead yes Sven Joscha Henheik author 31d731d7-d235-11ea-ad11-b50331c8d7fb0000-0003-1106-327X Edwin Langmann author Asbjørn Bækgaard Lauritsen author e1a2682f-dc8d-11ea-abe3-81da9ac728f10000-0003-4476-2288 LaEr department RoSe department Random matrices beyond Wigner-Dyson-Mehta project Mathematical Challenges in BCS Theory of Superconductivity project 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 Nature2026 eng 1424-0637 1424-0661 2409.1729710.1007/s00023-026-01706-y https://research-explorer.ista.ac.at/record/19550 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>. S.J. Henheik, E. Langmann, A.B. Lauritsen, Annales Henri Poincaré (2026). Henheik SJ, Langmann E, Lauritsen AB. 2026. Multi-band superconductors have enhanced critical temperatures. Annales Henri Poincaré. S. J. Henheik, E. Langmann, and A. B. Lauritsen, “Multi-band superconductors have enhanced critical temperatures,” <i>Annales Henri Poincaré</i>. Springer Nature, 2026. 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> 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>. 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> 222902026-07-13T09:42:22Z2026-07-13T11:34:08Z