Current in conventional conductors is characterized by electron-impurity and electron-phonon scattering. However, recent breakthroughs in fabrication of 2D materials with very low impurity has led to the realization of a new regime of transport, namely, the hydrodynamic regime, where electron-electron Coulomb interaction dominates. A lot of work has been done recently on hydrodynamic transport but they mainly focus on high carrier densities where electrons can be described by a Fermi liquid. In graphene near charge neutrality, the situation is different as both electrons and holes contribute to the current. Some recent work (e.g, G. Wagner, D. X. Nguyen, S. H. Simon, Phys. Rev. Lett. 124, 026601 (2020)) approach this problem by considering a two fluid model with interactions between electrons and holes. However, their analysis is restricted to uniform currents where viscous effects do not arise.
In this talk, I will discuss non-uniform two carrier flow in graphene near charge neutrality. Specifically, we derive a two fluid model with appropriate interactions between electrons and holes that can model this type of flow. Our work is of importance when explaining magneto-resistance in geometries like the Corbino where a simple non-viscous transport theory breaks down.