Nonlocal transport and the Hall viscosity of two-dimensional hydrodynamic electron liquids

Pellegrino, Francesco; Torre, Iacopo; Polini, Marco

doi:10.1103/physrevb.96.195401

Cited by 143 publications

(129 citation statements)

References 57 publications

(75 reference statements)

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“…Remarkably, it has been of little relevance for these studies of the Hall viscosity whether the system is assumed to be non-interacting and thus not amenable to hydrodynamic relations. With the advent of clean materials with high mobility, attention was directed to classical electron flow in non-quantizing magnetic fields, with the hope to find a route to measure the Hall viscosity directly [8][9][10][11][12][13]. In this case, it is necessary to restrict the discussion to viscous flow with electron-electron interactions strong enough to justify the applicability of the hydrodynamic approach.…”

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confidence: 99%

Unified Description of the Classical Hall Viscosity

2019

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In absence of time-reversal symmetry, viscous electron flow hosts a number of interesting phenomena, of which we focus here on the Hall viscosity. Taking a step beyond the hydrodynamic definition of the Hall viscosity, we derive a generalized relation between Hall viscosity and transverse electric field using a kinetic equation approach. We explore two different geometries where the Hall viscosity is accessible to measurement. For hydrodynamic flow of electrons in a narrow channel, we find that the viscosity may be measured by a local probe of the transverse electric field near the center of the channel. Ballistic flow, on the other hand, is dominated by boundary effects. In a Corbino geometry viscous effects arise not from boundary friction but from the circular flow pattern of the Hall current. In this geometry we introduce a viscous Hall angle which remains well defined throughout the crossover from ballistic to hydrodynamic flow, and captures the bulk viscous response of the fluid.Introduction.-In a breakthrough insight, Avron et al.[1] demonstrated the presence of a quantized observable second to the Hall conductivity in incompressible Quantum Hall states. This observable is the Hall viscosity, the antisymmetric and dissipationless part of the viscosity tensor in 2d. Since then, a lot of activity concentrated on working out the properties of this quantity in the gapped state [2][3][4][5][6][7]. Remarkably, it has been of little relevance for these studies of the Hall viscosity whether the system is assumed to be non-interacting and thus not amenable to hydrodynamic relations. With the advent of clean materials with high mobility, attention was directed to classical electron flow in non-quantizing magnetic fields, with the hope to find a route to measure the Hall viscosity directly [8][9][10][11][12][13]. In this case, it is necessary to restrict the discussion to viscous flow with electron-electron interactions strong enough to justify the applicability of the hydrodynamic approach. A first measurement of the Hall viscosity in Graphene was reported recently [14].

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confidence: 99%

Unified Description of the Classical Hall Viscosity

2019

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“…which combines both scalar functions in the Stokes equation into a single one. Real life experiments are usually sensitive to the electrochemical potential rather than electric voltage or chemical potential alone 11,46 . Taking that into account, the Stokes equation D1 is effectively incompressible, and the gradient of electrochemical potential can be decoupled from the system.…”

Section: Appendix D: Stream Function Formulation and Electrochemical mentioning

confidence: 99%

Boundary-condition and geometry engineering in electronic hydrodynamics

et al. 2019

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We analyze the role of boundary geometry in viscous electronic hydrodynamics. We address the twin questions of how boundary geometry impacts flow profiles, and how one can engineer boundary conditions -in particular the effective slip parameter -to manipulate the flow in a controlled way. We first propose a micropatterned geometry involving finned barriers, for which we show by an explicit solution that one can obtain effectively no-slip boundary conditions regardless of the detailed microscopic nature of the channel surface. Next we analyse the role of mesoscopic boundary curvature on the effective slip length, in particular its impact on the Gurzhi effect. Finally we investigate a hydrodynamic flow through a circular junction, providing a solution, which suggests an experimental set-up for determining the slip parameter. We find that its transport properties differ qualitatively from the case of ballistic conduction, and thus presents a promising setting for distinguishing the two.

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“…The finite electron viscosity leads to several physical consequences, such as a negative nonlocal resistance [4] and super-ballistic transport through point contacts (PCs) [7,18]. These developments have spurred on a great deal of research, including proposals for measuring the Hall viscosity [19][20][21] and connections to strong-coupling predictions from string theory [22].…”

Section: Introductionmentioning

confidence: 99%

Spin–vorticity coupling in viscous electron fluids

Polini

Duine

2019

J. Phys. Mater.

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We consider spin-vorticity coupling-the generation of spin polarization by vorticity-in viscous two-dimensional electron systems with spin-orbit coupling. We first derive hydrodynamic equations for spin and momentum densities in which their mutual coupling is determined by the rotational viscosity. We then calculate the rotational viscosity microscopically in the limits of weak and strong spin-orbit coupling. We provide estimates that show that the spin-orbit coupling achieved in recent experiments is strong enough for the spin-vorticity coupling to be observed. On the one hand, this coupling provides a way to image viscous electron flows by imaging spin densities. On the other hand, we show that the spin polarization generated by spin-vorticity coupling in the hydrodynamic regime can, in principle, be much larger than that generated, e.g. by the spin Hall effect, in the diffusive regime.

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Nonlocal transport and the Hall viscosity of two-dimensional hydrodynamic electron liquids

Cited by 143 publications

References 57 publications

Unified Description of the Classical Hall Viscosity

Unified Description of the Classical Hall Viscosity

Boundary-condition and geometry engineering in electronic hydrodynamics

Spin–vorticity coupling in viscous electron fluids

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