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The quantum-Hall-effect (QHE) occurs in topologically-ordered states oftwo-dimensional (2d) electron-systems in which an insulating bulk-statecoexists with protected 1d conducting edge-states. Owing to a uniquetopologically imposed edge-bulk correspondence these edge-states are endowedwith universal properties such as fractionally-charged quasiparticles andinterference-patterns, which make them indispensable components for QH-basedquantum-computation and other applications. The precise edge-bulkcorrespondence, conjectured theoretically in the limit of sharp edges, isdifficult to realize in conventional semiconductor-based electron systems wheresoft boundaries lead to edge-state reconstruction. Using scanning-tunnelingmicroscopy and spectroscopy to follow the spatial evolution of bulkLandau-levels towards a zigzag edge of graphene supported above a graphitesubstrate we demonstrate that in this system it is possible to realizeatomically sharp edges with no edge-state reconstruction. Our results singleout graphene as a system where the edge-state structure can be controlled andthe universal properties directly probed.

Evolution of Landau Levels into Edge States at an Atomically Sharp Edge in Graphene