  Recent advances in experimental techniques emphasize the usefulness of
multiple scanning probe techniques when analyzing nanoscale samples. Here, we
analyze theoretically dual-probe setups with probe separations in the nanometer
range, i.e., in a regime where quantum coherence effects can be observed at low
temperatures. In a dual-probe setup the electrons are injected at one probe and
collected at the other. The measured conductance reflects the local transport
properties on the nanoscale, thereby yielding information complementary to that
obtained with a standard one-probe setup (the local density-of-states). In this
work we develop a real space Green's function method to compute the
conductance. This requires an extension of the standard calculation schemes,
which typically address a finite sample between the probes. In contrast, the
developed method makes no assumption on the sample size (e.g., an extended
graphene sheet). Applying this method, we study the transport anisotropies in
pristine graphene sheets, and analyze the spectroscopic fingerprints arising
from quantum interference around single-site defects, such as vacancies and
adatoms. Furthermore, we demonstrate that the dual-probe setup is a useful tool
for characterizing the electronic transport properties of extended defects or
designed nanostructures. In particular, we show that nanoscale perforations, or
antidots, in a graphene sheet display Fano-type resonances with a strong
dependence on the edge geometry of the perforation.
