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To explore whether a flat-band system can accommodate superconductivity, weconsider repulsively interacting fermions on the diamond chain, a simplestquasi-one-dimensional system that contains a flat band. Exact diagonalizationand the density-matrix renormalization group (DMRG) are used to show that wehave a significant binding energy of a Cooper pair with a long-tailed pair-paircorrelation in real space when the total band filling is slightly below $1/3$,where the dispersive band interacts with the flat band that is empty but closeto $E_F$. Pairs selectively formed across the outer sites of the diamond chainare responsible for the pairing correlation. At exactly $1/3$-filling aninsulating phase emerges, where the entanglement spectrum indicates theparticles on the outer sites are highly entangled and topological. These comefrom a peculiarity of the flat band in which "Wannier orbits" are notorthogonalizable.

Superconductivity in repulsively interacting fermions on a diamond chain: flat-band induced pairing