Stokes flow around an obstacle in viscous two-dimensional electron liquid

Gusev, G. M.; Jaroshevich, A. S.; Levin, A. D.; Kvon, Z. D.; Bakarov, A. K.

doi:10.1038/s41598-020-64807-6

Cited by 49 publications

(27 citation statements)

References 39 publications

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“…In the context of hard condensed matter, recent experimental and theoretical works (Hoyos & Son 2012;Levitov & Falkovich 2016;Holder, Queiroz & Stern 2019) have focused on the hydrodynamic behaviour of electrons in solids. There, sizeable parity-violating viscosities can occur and have been observed when the sample is under a magnetic field (Berdyugin et al 2019) and Stokes flow can be realized by introducing holes in the sample (Gusev et al 2020).…”

Section: Discussionmentioning

confidence: 99%

Stokes flows in three-dimensional fluids with odd and parity-violating viscosities

et al. 2022

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The Stokes equation describes the motion of fluids when inertial forces are negligible compared with viscous forces. In this article, we explore the consequence of parity-violating and non-dissipative (i.e. odd) viscosities on Stokes flows in three dimensions. Parity-violating viscosities are coefficients of the viscosity tensor that are not invariant under mirror reflections of space, while odd viscosities are those which do not contribute to dissipation of mechanical energy. These viscosities can occur in systems ranging from synthetic and biological active fluids to magnetized and rotating fluids. We first systematically enumerate all possible parity-violating viscosities compatible with cylindrical symmetry, highlighting their connection to potential microscopic realizations. Then, using a combination of analytical and numerical methods, we analyse the effects of parity-violating viscosities on the Stokeslet solution, on the flow past a sphere or a bubble and on many-particle sedimentation. In all the cases that we analyse, parity-violating viscosities give rise to an azimuthal flow even when the driving force is parallel to the axis of cylindrical symmetry. For a few sedimenting particles, the azimuthal flow bends the trajectories compared with a traditional Stokes flow. For a cloud of particles, the azimuthal flow impedes the transformation of the spherical cloud into a torus and the subsequent breakup into smaller parts that would otherwise occur. The presence of azimuthal flows in cylindrically symmetric systems (sphere, bubble, cloud of particles) can serve as a probe for parity-violating viscosities in experimental systems.

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Section: Discussionmentioning

confidence: 99%

Stokes flows in three-dimensional fluids with odd and parity-violating viscosities

et al. 2022

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“…It makes purely hydrodynamic description of the valley accumulation inapplicable, in general. Particularly, in the decomposition of S ϕ (x) over the angular harmonics of ϕ S ϕ (x) = S 0 (x) + cos ϕ S 1 (x) + cos 2ϕ S 2 (x), (49) cf. Eq.…”

Section: Hydrodynamic Regimementioning

confidence: 99%

“…Recent progress in nanotechnology has made it possible to create two-dimensional electron systems with ultrahigh mobility where the electron mean free path l exceeds by far the width of the channel w [40][41][42][43][44][45][46][47][48][49]. In this case, the electron momentum dissipation takes place mainly at the channel edges.…”

Section: Introductionmentioning

confidence: 99%

Valley and spin accumulation in ballistic and hydrodynamic channels

Glazov

2021

Preprint

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A theory of the valley and spin Hall effects and resulting accumulation of the valley and spin polarization is developed for ultraclean channels made of two-dimensional semiconductors where the electron mean free path due to the residual disorder or phonons exceeds the channel width. Both ballistic and hydrodynamic regimes of the electron transport are studied. The polarization accumulation is determined by interplay of the anomalous velocity, side-jump and skew scattering effects. In the hydrodynamic regime, where the electron-electron scattering is dominant, the valley and spin current generation and dissipation by the electron-electron collisions are taken into account. The accumulated polarization magnitude and its spatial distribution depend strongly on the transport regime. The polarization is much larger in the hydrodynamic regime as compared to the ballistic one. Significant valley and spin polarization arises in the immediate vicinity of the channel edges due to the side-jump and skew scattering mechanisms.

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“…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]…”

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confidence: 99%