Modeling the Appearance of Viscous Electron Flow in Graphene Using a Scanning Probe Microscope

Graphene is an allotrope of carbon comprised of a single layer of carbon atoms bound in a hexagonal crystalline structure exhibiting two-dimensional characteristics. The effect of these characteristics includes the scattering of electrons that are seen in metals; therefore, graphene has the ability to be much more conductive than commonly used conductors — such as copper. Furthermore, in graphene — at a certain range of temperature and electron density — electrons begin interacting with each other in concert as a viscous fluid. To model and analyze this behavior, Navier-Stokes equations for an incompressible fluid will be implemented. The goal is to construct the best geometry and determine suitable boundary conditions for the walls and circular barrier that show the signature of viscous electron flow. The walls act as the edge of the graphene strip, and the circular barrier acts as the tip perturbation of a scanning probe microscope. By counting the number of particles reaching the drain from the source vs position of the circular barrier, we obtain the map of electron flow through the sample. Mapping the flow of electrons in hydrodynamic regime will shed light on the physics of interacting electrons in graphene and pave way for applications in electronics and optics.