Hydrodynamic electrons in Graphene: a viscous boundary-layer description

Abstract: In this paper we dwell over the study of the boundary layer problem in a hydrodynamical description of the electrons in gated graphene. It has been verified experimentally that this fluid can display non-Poiseuille like flow as reproduced in our numerical simulation. In fact, the velocity profile displays a maximum value close to the boundary and then decreases as it approaches the bulk of the graphene layer. This work aims to present a satisfactory theoretical description of the boundary layer problem in graphene. We found that by using the fluid equations and following a method similar to that for deriving Blasius' equation, a non-linear model can be obtained whose solutions display the maximum values of velocity near the edges of the graphene layer. We argue that such a non-monotonic model and behaviour can shed some light on the subject of non-topological edge currents in graphene.