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Hybrid systems of superconductors and magnets display several intriguingproperties, both from a fundamental physics point of view and with practicalapplications. Promising applications in superconducting spintronics motivate asearch for systems where superconductivity can survive larger in-plane criticalmagnetic fields than the conventional limit. The Chandrasekhar-Clogston (CC)limit applies to thin-film conventional superconductors with in-plane magneticfields such that orbital effects may be ignored. For a magnetic field strengthcomparable to the superconducting gap at zero temperature and zero field, aspin-split normal state attains lower free energy than the superconductingstate. A multiband superconductor with a flat band placed just below the Fermisurface has been shown to surpass the CC limit using weak-coupling theory.Since the dimensionless coupling determining the critical temperature scaleswith the density of states, it is natural to anticipate corrections fromstrong-coupling theory in flat-band systems, owing to the large density ofstates of the flat bands. We derive Eliashberg equations and the free energyfor a multiband superconductor in a magnetic field. First, we show that the CClimit can be exceeded by a small amount in one-band strong-couplingsuperconductors due to self-energy renormalization of the magnetic field. Next,we consider a two-band system with one flat band and find that the CC limit canbe exceeded by a large amount also in strong-coupling theory, even whenincluding hybridization between bands that intersect.

Exceeding the Chandrasekhar-Clogston limit in flat-band superconductors: A multiband strong-coupling approach