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 reg
ime 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 Greens 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.
Experimental advances allow for the inclusion of multiple probes to measure the transport properties of a sample surface. We develop a theory of dual-probe scanning tunnelling microscopy using a Greens Function formalism, and apply it to graphene. Sa
mpling the local conduction properties at finite length scales yields real space conductance maps which show anisotropy for pristine graphene systems and quantum interference effects in the presence of isolated impurities. The spectral signatures of the Fourier transform of real space conductance maps include characteristics that can be related to different scattering processes. We compute the conductance maps of graphene systems with different edge geometries or height fluctuations to determine the effects of non-ideal graphene samples on dual-probe measurements.
