On the Ballistic Flow of Two-Dimensional Electrons in a Magnetic Field

In conductors with a very low defect density, electrons at low temperatures collide mainly with the sample edges; therefore, the ballistic transport of charge and heat is implemented. An applied perpendicular magnetic field significantly modifies ballistic transport. For the case of two-dimensional electrons, in magnetic fields at which the diameter of cyclotron trajectories is smaller than the sample width, the hydrodynamic transport regime forms. In this regime, the flow is mainly controlled by rare electron-electron collisions, which determine the viscosity effect. In this work, we study the ballistic flow of two-dimensional electrons in long samples in magnetic fields up to the critical field of the transition to the hydrodynamic regime. By solving the kinetic equation, we obtain analytical formulas for the current density and the Hall electric field far and close to the ballistic-hydrodynamic transition, as well as for the longitudinal and Hall resistances in these ranges. Our theoretical results apparently describe the observed longitudinal resistance of pure graphene samples in the magnetic-field range below the ballistic-hydrodynamic transition.