  We study non-equilibrium transport through a superconducting flat-band
lattice in a two-terminal setup with the Schwinger-Keldysh method. We find that
quasiparticle transport is suppressed and coherent pair transport dominates.
For superconducting leads, the AC supercurrent overcomes the DC current which
relies on multiple Andreev reflections. With normal-normal and
normal-superconducting leads, the Andreev reflection and normal currents
vanish. Flat band superconductivity is thus promising not only for high
critical temperatures but also for suppressing unwanted quasiparticle
processes.
