We have studied the dependence of the conductance profile of a sheet of graphene w.r.t. two conduction leads to gather insight into the charge flow, which can in turn be used to analyze the transport mechanism of graphene. Moreover, we simulated scanning probe microscopy (SPM) measurements for the same devices, which can visualize the flow of charge inside the device, thus complementing the transport calculations. From our simulations, we found that both the conductance profile and SPM measurements are excellent tools to assess the transport mechanism differentiating ballistic and diffusive graphene systems. (Phys. Rev. B 88, 125415 (2013))

This figure shows SPM conductance maps simulations for disordered systems. (Left) Graphene sample with disordered edges and (middle, right) devices with bulk disorder. While the interference pattern survives in devices with edge disorder, it is not present in systems with bulk disorder.

In a similar study, we examined the conductance fluctuations (CF) and the sensitivity of the conductance to the motion of a single scatterer in two-dimensional massless Dirac systems. Our extensive numerical study found limits to the predicted universal value of CF. In particular, we found that CF are suppressed for ballistic systems near the Dirac point and approach the universal value at sufficiently strong disorder. The conductance of massless Dirac fermions is sensitive to the motion of a single scatterer. CF of order e2/h result from the motion of a single impurity by a distance comparable to the Fermi wavelength. This result applies to graphene systems with a broad range of impurity strength and concentration while the dependence on the Fermi wavelength can be explored via gate voltages. Our prediction can be tested by comparing graphene samples with varying amounts of disorder and can be used to understand interference effects in mesoscopic graphene devices.

We are currently studying the generation of Raman spectra of graphene from time-dependant semiclassical techniques in order to gauge the importance of non-adiabatic dynamics.