Two-dimensional electron hydrodynamics in a random array of impenetrable obstacles: Magnetoresistivity, Hall viscosity, and the Landauer dipole

Abstract

We formulate a general framework to study the flow of the electron liquid in two dimensions past a random array of impenetrable obstacles in the presence of a magnetic field. We derive a linear-response formula for the resistivity tensor $\hat{\rho }$ in hydrodynamics with obstacles, which expresses $\hat{\rho }$ in terms of the vorticity and its harmonic conjugate, both on the boundary of obstacles. In the limit of rare obstacles, in which we calculate $\hat{\rho }$, the contributions of the flow-induced electric field to the dissipative resistivity from the area covered by the liquid and the area inside obstacles are shown to be equal to each other. We demonstrate that the averaged electric fields outside and inside obstacles are rotated by Hall viscosity from the direction of flow. For the diffusive boundary condition on the obstacles, this effect exactly cancels in $\hat{\rho }$. By contrast, for the specular boundary condition, the total electric field is rotated by Hall viscosity, which means the emergence of a Hall-viscosity-induced effective -- proportional to the obstacle density -- magnetic field. Its effect on the Hall resistivity is particularly notable in that it leads to a deviation of the Hall constant from its universal value. We show that the applied magnetic field enhances hydrodynamic lubrication, giving rise to a strong negative magnetoresistance. We combine the hydrodynamic and electrostatic perspectives by discussing the distribution of charges that create the flow-induced electric field around obstacles. We provide a connection between the tensor $\hat{\rho }$ and the disorder-averaged electric dipole induced by viscosity at the obstacle. This establishes a conceptual link between the resistivity in hydrodynamics with obstacles and the notion of the Landauer dipole. We show that the viscosity-induced dipole is rotated from the direction of flow by Hall viscosity.

arXiv comment30 pages

References in corpus (78)

• Negative local resistance caused by viscous electron backflow in graphene
• Observation of the Dirac fluid and the breakdown of the Wiedemann-Franz law in graphene
• Evidence for hydrodynamic electron flow in PdCoO${}_2$
• Viscosity of Quantum Hall Fluids
• Superballistic flow of viscous electron fluid through graphene constrictions
• Hydrodynamics of electrons in graphene
• Electron Viscosity, Current Vortices and Negative Nonlocal Resistance in Graphene
• Imaging viscous flow of the Dirac fluid in graphene
• Odd viscosity in chiral active fluids
• Hydrodynamic electron flow in high-mobility wires
• Hall Viscosity and Electromagnetic Response
• Measuring Hall Viscosity of Graphene's Electron Fluid
• Visualizing Poiseuille flow of hydrodynamic electrons
• Hall viscosity, orbital spin, and geometry: paired superfluids and quantum Hall systems
• Kubo formulas for viscosity: Hall viscosity, Ward identities, and the relation with conductivity
• Electrical and Thermal Transport at the Planckian Bound of Dissipation in the Hydrodynamic Electron Fluid of WP2
• Non-local transport and the hydrodynamic shear viscosity in graphene
• Odd Viscosity and Odd Elasticity
• Hydrodynamic description of transport in strongly correlated electron systems
• Nonequilibrium phenomena in high Landau levels
• Higher-Than-Ballistic Conduction of Viscous Electron Flows
• Negative magnetoresistance in viscous flow of two-dimensional electrons
• Fluidity Onset in Graphene
• Electrically tunable transverse magnetic focusing in graphene
• Electromagnetic and gravitational responses of two-dimensional non-interacting electrons in background magnetic field
• Imaging Magnetic Focusing of Coherent Electron Waves
• Bulk and shear viscosities of the 2D electron liquid in a doped graphene sheet
• Imaging phonon-mediated hydrodynamic flow in WTe2
• Non-local transport and the Hall viscosity of 2D hydrodynamic electron liquids
• The boundary conditions of viscous electron flow
• Odd viscosity in two-dimensional incompressible fluids
• Hydrodynamic approach to electronic transport in graphene
• The Elasticity of an Electron Liquid
• Electron hydrodynamics dilemma: whirlpools or no whirlpools
• Quasiclassical negative magnetoresistance of a 2D electron gas: interplay of strong scatterers and smooth disorder
• Magnetoresistance in a High Mobility Two-Dimensional Electron Gas
• A Corbino disk viscometer for 2D quantum electron liquids
• Viscous transport and Hall viscosity in a two-dimensional electron system
• Observation of a cyclotron harmonic spike in microwave-induced resistances in ultraclean GaAs/AlGaAs quantum wells
• Hydrodynamic approach to two-dimensional electron systems
• Transport signatures of Hall viscosity
• Electronic hydrodynamics in graphene
• Swimming at Low Reynolds Number in Fluids with Odd (Hall) Viscosity
• Giant negative magnetoresistance in high-mobility 2D electron systems
• Geometric control of universal hydrodynamic flow in a two dimensional electron fluid
• Colossal negative magnetoresistance in a 2D electron gas
• Hall viscosity, topological states and effective theories
• Hydrodynamic theory of an electron gas
• Vorticity induced negative nonlocal resistance in viscous two-dimensional electron system
• Giant microwave photoresistivity in a high-mobility quantum Hall system
• Hydrodynamic and ballistic transport over large length scales in GaAs/AlGaAs
• Linking Spatial Distributions of Potential and Current in Viscous Electronics
• Stokes paradox in electronic Fermi liquids
• Tomographic Dynamics and Scale-Dependent Viscosity in Two-Dimensional Electron Systems
• Kinetic theory of transport for inhomogeneous electron fluids
• Viscosity of two-dimensional electrons
• Magnetoresistance Induced by Rare Strong Scatterers in a High Mobility 2DEG
• The Hierarchy of Excitation Lifetimes in Two-Dimensional Fermi Gases
• Stokes flow around an obstacle in viscous two-dimensional electron liquid
• Unified description of the classical Hall viscosity
• Directional ballistic transport in the two-dimensional metal PdCoO2
• Particle Collisions and Negative Nonlocal Response of Ballistic Electrons
• Phenomenology of non-relativistic parity-violating hydrodynamics in 2+1 dimensions
• Hydrodynamics beyond local equilibrium: application to electron gas
• Dissipative and Hall viscosity of a disordered 2D electron gas
• Conductivity of the classical two-dimensional electron gas
• Viscous magnetoresistance of correlated electron liquids
• Imaging ballistic carrier trajectories in graphene using scanning gate microscopy
• Hall and dissipative viscosity effects on edge magnetoplasmons
• The Hall Number of Strongly Correlated Metals
• Collective modes in interacting two-dimensional tomographic Fermi liquids
• Hydrodynamic lift of a two-dimensional liquid domain with odd viscosity
• Hydrodynamic charge transport in GaAs/AlGaAs ultrahigh-mobility two-dimensional electron gas
• Equilibrium Formulae for Transverse Magneto-transport of Strongly Correlated Metals
• Anomalously long lifetimes in two-dimensional Fermi liquids
• The longitudinal resistance of a quantum Hall system with a density gradient
• Collinear scattering and long-lived excitations in two-dimensional electron fluids
• Residual bulk viscosity of a disordered 2D electron gas

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