Electron-hole drag viscosity and magnetotransport in semimetals

In clean two-dimensional materials exposed at intermediate temperatures, interparticle collision dominates over momentum-relaxing collisions such from impurities and phonons. 

In this situation, electrons obey hydrodynamic principles where particles relax quickly among themselves, and local equilibrium distribution that conserves particle number, momentum and energy can be defined. We are interested in a multi-fluid system in which the momentum of one fluid can be transferred to the other without exchanging particle numbers or known as the drag effect. This can simply be realized in semimetals where electron and hole fluids coexist. Under applied magnetic fields, the Navier-Stokes equation shows three components of viscosity, namely particle viscosity (electron or hole), Hall viscosity, and electron-hole drag viscosity. In a viscous regime, it is known that the resistivity of materials is determined by viscosity. In this work, we highlight the interplay of these three viscosities and their role in the magnetoresistance of viscous electron-hole liquids.