UC Riverside

Graphene consists of a monolayer of carbon atoms arranged in a honeycomb lattice and has been intensively studied due to its fascinating physical properties. We investigate transport in mesoscopic graphene systems, in particular, conductance oscillations due to interference of the Dirac electrons in phase-coherent transport. We consider a measurement set-up with two STM tips. We calculate the Green's functions for pure graphene in the tight-binding model, self-energy corrections due to the presence of the leads (STM tips), and $S$-matrices for the two tips, to obtain the overall $S$-matrix and the conductance using the Landauer-B"{u}ttiker formalism. We map the oscillations in the conductance as a function of position of the tips. For fixed tip positions, we find a non-monotonic dependence of the conductance on the coupling between the tips and graphene. Regular Bloch oscillations are obtained, where the wavelength is determined by the energy. Depending on the lattice orientation, an additional fast oscillation is obtained and its origin elucidated. Richer structures arise when the presence of an impurity is considered.

Moreover, we extend our research to voltage probing with multiple STM tips, specifically, three-tips configuration (two tips act as the current source and sink, the third tip serves as a voltage probe) was considered. Voltage profile has a unique expression for different separation of the fixed two tips, along with oscillations appears when the separation distance is bigger. Voltage profile express different when impurity introduced, which may be used for sensor.