  Dispersionless energy bands are a peculiar property gathering increasing
attention for the emergence of novel photonic, magnetic and electronic
properties. Here we report the first observation of a graphene superstructure
n-doped up to the Lifshitz transition and exhibiting a flat band, obtained by
ordered Erbium intercalation between a single layer graphene and SiC(0001). STM
experiments reveal large graphene areas characterized by a long-range ordered
hexagonal superstructure with a lattice parameter of 1.40 nm, rotated by 19
degrees with respect to the original lattice. Angle Resolved Photoelectron
Spectroscopy measurements show that this graphene structure exhibits Dirac
cones with perfect linear dispersion, and a Dirac point at -1.72 eV +/- 0.02
under the Fermi level, which is one of the highest doping levels ever obtained
solely by intercalation. Fermi surface measurements show that the Lifshitz
transition has been reached, and that a wide flat band is generated around the
M point. We propose that this modification of the band structure is the effect
of an induced spin-orbit coupling. This system provides a playground to study
the interaction between a novel magnetic order mediated by pi-band states, and
a divergent density of states at the Fermi level.
