  We study the Kondo effect of a single magnetic adatom on the surface of
graphene. It was shown that the unique linear dispersion relation near the
Dirac points in graphene makes it more easy to form the local magnetic moment,
which simply means that the Kondo resonance can be observed in a more wider
parameter region than in the metallic host. The result indicates that the Kondo
resonance indeed can form ranged from the Kondo regime, to the mixed valence,
even to the empty orbital regime. While the Kondo resonance displays as a sharp
peak in the first regime, it has a peak-dip structure and/or an anti-resonance
in the remaining two regimes, which result from the Fano resonance due to the
significant background leaded by dramatically broadening of the impurity level
in graphene. We also study the scanning tunneling microscopy (STM) spectra of
the adatom and they show obvious particle-hole asymmetry when the chemical
potential is tuned by the gate voltages applied to the graphene. Finally, we
explore the influence of the direct tunneling channel between the STM tip and
the graphene on the Kondo resonance and find that the lineshape of the Kondo
resonance is unaffected, which can be attributed to unusual large asymmetry
factor in graphene. Our study indicates that the graphene is an ideal platform
to study systematically the Kondo physics and these results are useful to
further stimulate the relevant experimental studies on the system.
