Theory of Electron Imaging in Small Devices
The research in this program involved theoretical investigations of the transport of charge in graphene and small heterostructure devices. There is an important trend toward imaging electronic systems in real space, with the goal of understanding the specifics of individual samples rather than settling for ensemble and statistical descriptions. For example one of our goals has been the understanding of scanning probe microscopy (SPM) imaging of systems in which the motion of the carriers is restricted to two degrees of freedom, such as in grapheme and the two dimensional electron (and hole) gas (2DEGs and 2DHGs) in GaAs/AlGaAs heterostructures, or when the motion is restricted to one degree of freedom as in nanowires. SPM imaging uses the tip of a movable charged probe to alter the electrons locally, depleting or alternatively increasing the amount of charges in the electron gas just below the tip results in a change to the flow pattern of the charge. The focus of this research was on understanding how the tunable tip affects functional aspects of the device that can be used to understand electronic and transport properties. For instance, scanning over the device while measuring the conductance results in conductance maps, an imaging of the charge transport. This imaging is often semi-direct and requires theory and interpretation to extract all that can be deduced about the underlying physical quantities.