  Quantum physics in flat-band (FB) systems embodies a variety of exotic
phenomenon and even counter intuitive features. The quantum transport in
several graphene based compounds that exhibit a flat band and a tunable gap is
investigated. Despite the localized nature of the FB states and a zero group
velocity, a super-metallic (SM) phase at the FB energy is revealed. The SM
phase is robust against the inelastic scattering strength and controlled only
by the inter-band transitions between the FB and the dispersive bands. The SM
phase appears insensitive and quasi independent of the gap amplitude and nature
of the lattice (disordered or nano-patterned). The universal nature of the
unconventional FB transport is illustrated with the case of electrons in the
Lieb lattice.
