We studied experimentally and theoretically the electronic local density of states (LDOS) near single step edges at the surface of exfoliated graphite. In scanning tunneling microscopy measurements, we observed the $(sqrt{3} times sqrt{3}) R 30^{circ}$ and honeycomb superstructures extending over 3$-$4 nm both from the zigzag and armchair edges. Calculations based on a density-functional derived non-orthogonal tight-binding model show that these superstructures can coexist if the two types of edges admix each other in real graphite step edges. Scanning tunneling spectroscopy measurements near the zigzag edge reveal a clear peak in the LDOS at an energy below the Fermi energy by 20 meV. No such a peak was observed near the armchair edge. We concluded that this peak corresponds to the edge state theoretically predicted for graphene ribbons, since a similar prominent LDOS peak due to the edge state is obtained by the first principles calculations.
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