Nonnegative magnetoresistance in hydrodynamic regime of electron fluid transport in two-dimensional materials

Electron transport in ultraclean two-dimensional materials has received much attention. However, the sign of the magnetoresistance effect in various electron flow regimes remains controversial. In this work, the complete electron Boltzmann transport equation is numerically solved with the discrete ordinate method in the real space to clarify the condition of the negative magnetoresistance effect under a weak magnetic field. It turns out from the numerical results that this effect occurs only within the ballistic regime under a low electric field rather than the hydrodynamic regime. It is noteworthy that the existence of momentum-conserving scattering dramatically reverses the sign of magnetoresistance in the ballistic regime. When the electric field becomes strong enough compared to the magnetic field, its effect on the deflection of the electrons is not negligible and will lead to positive magnetoresistance in the whole parameter domain. The possible influence of boundary conditions and internal electric field models on the sign of magnetoresistance is also discussed. Our work provides insight into electron fluid transport under electromagnetic fields.