  The ground state and transport properties of the Lieb lattice flat band in
the presence of an attractive Hubbard interaction are considered. It is shown
that the superfluid weight can be large even for an isolated and strictly flat
band. Moreover the superfluid weight is proportional to the interaction
strength and to the quantum metric, a band structure invariant obtained from
the flat-band Bloch functions. These predictions are amenable to verification
with ultracold gases and may explain the anomalous behaviour of the superfluid
weight of high-Tc superconductors.
