  The discovery of superconductivity in twisted bilayer graphene has triggered
a resurgence of interest in flat-band superconductivity. Here, we investigate
the square-octagon lattice, which also exhibits two perfectly flat bands when
next-nearest neighbour hopping or an external magnetic field are added to the
system. We calculate the superconducting phase diagram in the presence of
on-site attractive interactions and find two superconducting domes, as observed
in several types of unconventional superconductors. The critical temperature
shows a linear dependence on the coupling constant, suggesting that
superconductivity might reach high temperatures in the square-octagon lattice.
Our model could be experimentally realized using photonic or ultracold atoms
lattices.
