Manifestations of classical size effect and electronic viscosity in the magnetoresistance of narrow two-dimensional conductors: Theory and experiment

Magnetohydrodynamics and electro-electron interaction of massless Dirac fermions

“…Thus, comparison with theory turned out to be possible when the temperature changes by one order of magnitude. These values are very different from the values obtained for a 2D electron Fermi system in GaAs well, which are in order of 5-7 [1,27,41,42]. Parameters C obtained from the experiment coincide in order of magnitude with the results of calculation, if we assume the dimensionless parameter r s ∼ 0.1 − 0.15 which is very different from graphene (r s ≈ 0.7) due to high dielectric constant.…”

“…The index 2 in the e-e scattering time subscript τ 2,ee means that the viscosity coefficient is determined by the relaxation of the second harmonic of the distribution function [1]. The hydrodynamic regime requires l/l 2,ee ≫ 1 and l 2,ee /W ≪ 1, where l = v F τ is the electron transport mean free path related to momentum relaxation time (τ ) brought about by scattering on defects and phonons, v F is the Fermi velocity, W is the channel width, and l 2,ee = v F τ 2,ee is the mean free path for shear viscosity relaxation [7]- [41]. In the presence of the perpendicular magnetic field B the shear viscosity becomes a tensor depending on B, which leads to giant negative magnetoresistance with a Lorentzian profile in narrow channel devices [15].…”

“…[27][28][29][30] for high-mobility GaAs quantum wells with parabolic spectrum. The study of the temperature dependence of viscosity allows one to distinguish between the electron hydrodynamics and ballistic transport [41] and explain the difference between e-e scattering in a single well and in a bilayer [42].…”

“…( 2), we can derive a temperature-independent characteristic time τ 2,imp = 0.65 × 10 −12 s. The hydrodynamic approach is associated with a substantial relaxation of the m-th harmonic of the distribution function due to disorder scattering with the rates τ m,imp [1]. It is usually argued that τ = τ 1,imp [1,41] and τ 2,imp are of the same order of magnitude. In our sample we obtain τ 1,imp = 4.2 × 10 −12 s > τ 2,imp .…”

Anti-Poiseuille flow in neutral graphene

“…The possibility for an electronic system to exhibit the Poiseuille flow in a narrow wire was first pointed out by Gurzhi [19][20][21]. Recently, similar behavior has been a subject of intense theoretical [22][23][24][25][26][27][28][29][30][31][32][33] and experimental [10][11][12][13]22,[34][35][36][37][38][39][40][41][42][43][44] research in the context of electronic transport in high-mobility 2D materials. In contrast to conventional fluids, the electronic flow is affected not only by viscous effects, but also by weak disorder scattering and is characterized by a typical length scale known as the Gurzhi length [26][27][28][29]33]…”