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The Mielke checkerboard is known to be one of the simplest two-band latticemodels exhibiting an energetically flat band that is in touch with aquadratically dispersive band in the reciprocal space, i.e., its flat band isnot isolated. Motivated by the growing interest in understanding the origins offlat-band superfluidity in various contexts, here we provide an in-depthanalysis showing how the mean-field BCS correlations prevail in this particularmodel. Our work reveals the quantum-geometric origin of flat-band superfluiditythrough uncovering the leading role by a band-structure invariant, i.e., theso-called quantum metric tensor of the single-particle bands, in the inverseeffective mass tensor of the Cooper pairs.

Origin of flat-band superfluidity on the Mielke checkerboard lattice