  The quantum-Hall-effect (QHE) occurs in topologically-ordered states of
two-dimensional (2d) electron-systems in which an insulating bulk-state
coexists with protected 1d conducting edge-states. Owing to a unique
topologically imposed edge-bulk correspondence these edge-states are endowed
with universal properties such as fractionally-charged quasiparticles and
interference-patterns, which make them indispensable components for QH-based
quantum-computation and other applications. The precise edge-bulk
correspondence, conjectured theoretically in the limit of sharp edges, is
difficult to realize in conventional semiconductor-based electron systems where
soft boundaries lead to edge-state reconstruction. Using scanning-tunneling
microscopy and spectroscopy to follow the spatial evolution of bulk
Landau-levels towards a zigzag edge of graphene supported above a graphite
substrate we demonstrate that in this system it is possible to realize
atomically sharp edges with no edge-state reconstruction. Our results single
out graphene as a system where the edge-state structure can be controlled and
the universal properties directly probed.
