We analyze the properties of flat-band superconductor junctions that behave differently from ordinary junctions containing only metals with Fermi surfaces. In particular, we show how in the tunneling limit the critical Josephson current between flat-band superconductors is inversely proportional to the pair potential, how the quantum geometric contribution to the supercurrent appears even in the normal state of a flat-band weak link, and how Andreev reflection is strongly affected by the presence of bound states. Our results are relevant for analyzing the superconducting properties of junctions involving electronic systems with flat bands.

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• Andreev bound states
• Andreev reflection
• Flat bands
• Proximity effect
• Josephson junctions
• Superconductors
• Landau-Ginzburg theory
• Lattice models in condensed matter