Superconducting junctions with flat bands

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 contributes 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 magic-angle twisted bilayer graphene as well as other electronic systems with flat bands.
Comment: 15 pages