First-principles calculation of highly asymmetric structure in scanning-tunneling-microscopy images of graphite

Using a first-principles calculation, we have computed the charge density for states near $E_F$ that is related to the current density observable in scanning-tunneling-microscopy experiments for surfaces of hexagonal, rhombohedral, and a model stage-1 intercalated graphite. In hexagonal and rhombohedral graphite, the tunneling current is predicted to be considerably smaller at surface atomic sites which have nearest neighbors directly below them than at sites with no such neighbors. This asymmetry is explained by the particular symmetry of the wave functions at the Fermi surface of graphite near K¯ in the surface Brillouin zone. The calculated asymmetry is nearly independent of the polarity and decreases with increasing magnitude of the bias voltage. Our results show that no asymmetry is expected on surfaces of stage-1 AA stacked intercalated graphite. The dependence of the asymmetry on the tip-to-surface separation has also been evaluated using a tight-binding model for different bias voltages. For the surface of hexagonal graphite, our predictions have been confirmed by recent experiments.