Hydrodynamic magnetotransport in two-dimensional electron systems with macroscopic obstacles
P. S. Alekseev, А. П. Дмитриев
Abstract
In high-quality conductors, the hydrodynamic regime of electron transport has recently been realized. In this paper, we theoretically investigate magnetotransport of a viscous electron fluid in samples with electron-impermeable obstacles. We use two approaches to describe the fluid flow. The first one is based on the equations of hydrodynamics of a charged fluid, which assume that the kinetic equation considers the two harmonics of the electron distribution function. The second approach is based on the equations that are obtained by considering three harmonics of the distribution function (quasihydrodynamics). Within the hydrodynamic approach, we consider the cases of the rough and smooth edges of disks, on which the electron scattering is diffusive or specular, respectively. The longitudinal magnetoresistivity turns out to be strong and negative, the same for both the rough and smooth disk edges up to small corrections. For rough disks, the Hall resistivity is equal to its standard value. For smooth disks, the Hall resistance acquires a small correction to the standard value, proportional to the Hall viscosity. In the quasihydrodynamic approach, we consider the case of smooth disks and small magnetic fields. In the regime when the flow is substantially different from the hydrodynamic one, the longitudinal resistivity does not depend on the shear stress relaxation time (but depends on the relaxation time of the third angular harmonic), while the correction to the standard Hall resistivity does not depend on both the relaxation times. We compare the results of the hydrodynamic calculation of the longitudinal resistance with the experimental data on magnetotransport in high-quality GaAs quantum wells with macroscopic defects. Agreement between theory and experiment evidences in favor of the realization of the hydrodynamic transport regime in such systems.