Signature of Viscous Electron Flow in Graphene Using a Scanning Probe Microscope

Graphene is a single layer of carbon atoms held together in a hexagonal crystalline structure. Graphene has shown great promise in electronics and photonics because of its two-dimensional properties. These properties reduce the scattering of electrons that are seen in metals, and thus graphene has the ability to be much more conductive than commonly used conductors such as copper. In graphene, at certain range of temperature and electron density, electrons begin interacting with each other in such a way that they start acting together as a viscous fluid. The purpose of this paper is to model the viscous flow of electrons in graphene and analyze the fluid behavior. The model of an incompressible fluid using the Navier-Stokes equations will be created to examine this behavior. The goal is to construct the best geometry and determine suitable boundary conditions for the walls and circular obstacle. The walls act as the edge of the graphene strip, and the circular obstacle acts as the tip perturbation of a scanning probe microscope. The objective is to obtain a suitable geometry showing signature of viscous electron flow.