English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We formulate a general framework to study the flow of the electron liquid intwo dimensions past a random array of impenetrable obstacles in the presence ofa magnetic field. We derive a linear-response formula for the resistivitytensor $\hat\rho$ in hydrodynamics with obstacles, which expresses $\hat\rho$in terms of the vorticity and its harmonic conjugate, both on the boundary ofobstacles. In the limit of rare obstacles, in which we calculate $\hat\rho$,the contributions of the flow-induced electric field to the dissipativeresistivity from the area covered by the liquid and the area inside obstaclesare shown to be equal to each other. We demonstrate that the averaged electricfields outside and inside obstacles are rotated by Hall viscosity from thedirection of flow. For the diffusive boundary condition on the obstacles, thiseffect exactly cancels in $\hat\rho$. By contrast, for the specular boundarycondition, the total electric field is rotated by Hall viscosity, which meansthe emergence of a Hall-viscosity-induced effective -- proportional to theobstacle density -- magnetic field. Its effect on the Hall resistivity isparticularly notable in that it leads to a deviation of the Hall constant fromits universal value. We show that the applied magnetic field enhanceshydrodynamic lubrication, giving rise to a strong negative magnetoresistance.We combine the hydrodynamic and electrostatic perspectives by discussing thedistribution of charges that create the flow-induced electric field aroundobstacles. We provide a connection between the tensor $\hat\rho$ and thedisorder-averaged electric dipole induced by viscosity at the obstacle. Thisestablishes a conceptual link between the resistivity in hydrodynamics withobstacles and the notion of the Landauer dipole. We show that theviscosity-induced dipole is rotated from the direction of flow by Hallviscosity.

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