  We have studied the graphene/gold interface by means of density functional
theory (DFT) and scanning tunneling spectroscopy (STS). Weak interaction
between graphene and the underlying gold surface leaves unperturbed Dirac cones
in the band-structure, but they can be shifted with respect to the Fermi level
of the whole system, which results in effective doping of graphene. DFT
calculations revealed that the interface is extremely sensitive to the
adsorption distance and to the structure of metal's surface, in particular
strong variation in doping can be attributed to the specific rearrangements of
substrate's atoms, such as the change in the crystallographic orientation,
relaxation or other modifications of the surface. On the other hand, STS
experiments have shown the presence of energetic heterogeneity in terms of the
changes in the local density of states (LDOS) measured at different places on
the sample. Randomly repeated regions of zero-doping and p-type doping have
been identified from parabolic shape characteristics and from well defined
Dirac points, respectively. The doping domains of graphene on gold seem to be
related to the presence of various types of the surface structure across the
sample. DFT simulations for graphene interacting with Au have shown large
differences in doping induced by considered structures of substrate, in
agreement with experimental findings. All these results demonstrate the
possibility of engineering the electronic properties of graphene, especially
tuning the doping across one flake which can be useful for applications of
graphene in electronic devices.
