  The potential of graphene to impact the development of the next generation of
electronics has renewed interest in its growth and structure. The
graphitization of hexagonal SiC surfaces provides a viable alternative for the
synthesis of graphene, with wafer-size epitaxial graphene on SiC(0001) now
possible. Despite this recent progress, the exact nature of the graphene-SiC
interface and whether the graphene even has a semiconducting gap remain
controversial. Using scanning tunneling microscopy with functionalized tips and
density functional theory calculations, here we show that the interface is a
warped carbon sheet consisting of three-fold hexagon-pentagon-heptagon
complexes periodically inserted into the honeycomb lattice. These defects
relieve the strain between the graphene layer and the SiC substrate, while
still retaining the three-fold coordination for each carbon atom. Moreover,
these defects break the six-fold symmetry of the honeycomb, thereby naturally
inducing a gap: the calculated band structure of the interface is
semiconducting and there are two localized states near K below the Fermi level,
explaining the photoemission and carbon core-level data. Nonlinear dispersion
and a 33 meV gap are found at the Dirac point for the next layer of graphene,
providing insights into the debate over the origin of the gap in epitaxial
graphene on SiC(0001). These results indicate that the interface of the
epitaxial graphene on SiC(0001) is more than a dead buffer layer, but actively
impacts the physical and electronic properties of the subsequent graphene
layers.
