# Stokes paradox in electronic Fermi liquids

@article{Lucas2016StokesPI, title={Stokes paradox in electronic Fermi liquids}, author={Andrew Lucas}, journal={Physical Review B}, year={2016}, volume={95}, pages={115425} }

The Stokes paradox is the statement that in a viscous two dimensional fluid, the "linear response" problem of fluid flow around an obstacle is ill-posed. We present a simple consequence of this paradox in the hydrodynamic regime of a Fermi liquid of electrons in two-dimensional metals. Using hydrodynamics and kinetic theory, we estimate the contribution of a single cylindrical obstacle to the global electrical resistance of a material, within linear response. Momentum relaxation, present in any…

## 31 Citations

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

- PhysicsScientific Reports
- 2020

By tuning the temperature, an electronic analog of the Stokes flow around a disc immersed in a two-dimensional viscous liquid is studied and the transport signatures of the ballistic and hydrodynamic regimes on the length scale of disc size are observed.

### Hydrodynamic-to-ballistic crossover in Dirac fluid

- Physics
- 2017

We develop an exactly solvable classical kinetic model of transport in Dirac materials accounting for strong electron-electron (e-e) and electron-hole (e-h) collisions. We use this model to track the…

### Hydrodynamic and ballistic AC transport in two-dimensional Fermi liquids

- PhysicsPhysical Review B
- 2019

Electron transport in clean 2D systems with weak electron-phonon (e-ph) coupling can transition from an Ohmic to a ballistic or a hydrodynamic regime. The ballistic regime occurs when…

### Kinetic theory of transport for inhomogeneous electron fluids

- Physics
- 2018

The interplay between electronic interactions and disorder is neglected in the conventional Boltzmann theory of transport, yet can play an essential role in determining the resistivity of…

### Hydrodynamics of electrons in graphene

- PhysicsJournal of physics. Condensed matter : an Institute of Physics journal
- 2018

A review of recent progress in understanding the hydrodynamic limit of electronic motion in graphene is presented, written for physicists from diverse communities with no prior knowledge of hydrodynamics.

### Pulsating flow and boundary layers in viscous electronic hydrodynamics

- Physics
- 2018

Motivated by experiments on a hydrodynamic regime in electron transport, we study the effect of an oscillating electric field in such a setting. We consider a long two-dimensional channel of width…

### Magnetosonic Waves in a Two-Dimensional Electron Fermi Liquid

- PhysicsSemiconductors
- 2019

The properties of highly viscous fluids at high frequencies become similar to those of amorphous solids. In particular, the propagation of not only longitudinal acoustic waves (plasmons in the case…

### Hall effect in a ballistic flow of two-dimensional interacting particles

- PhysicsPhysical Review B
- 2019

In high-quality solid-state systems at low temperatures, the hydrodynamic or the ballistic regimes of heat and charge transport are realized in the electron and the phonon systems. In these regimes,…

### Ballistic flow of two-dimensional interacting electrons

- PhysicsPhysical Review B
- 2018

In ultra-high quality two-dimensional (2D) materials the mean free paths of phonons and electrons relative to all mechanisms of scattering can be much greater than a size of a sample. In this case…

### Boundary conditions of viscous electron flow

- PhysicsPhysical Review B
- 2019

The sensitivity of charge, heat, or momentum transport to the sample geometry is a hallmark of viscous electron flow. Therefore, hydrodynamic electronics requires the detailed understanding of…

## References

SHOWING 1-10 OF 38 REFERENCES

### Bulk and shear viscosities of the two-dimensional electron liquid in a doped graphene sheet

- Physics
- 2016

Hydrodynamic flow occurs in an electron liquid when the mean free path for electron-electron collisions is the shortest length scale in the problem. In this regime, transport is described by the…

### Transport in inhomogeneous quantum critical fluids and in the Dirac fluid in graphene

- Physics
- 2016

We develop a general hydrodynamic framework for computing direct current thermal and electric transport in a strongly interacting finite temperature quantum system near a Lorentz-invariant quantum…

### Viscosity of a two-dimensional Fermi liquid

- Physics
- 2008

Shear viscosity of a two-dimensional Fermi liquid is found to be a nonanalytic function of temperature. In contrast to the quasiparticle lifetime that is determined by the forward-scattering…

### Hydrodynamic description of transport in strongly correlated electron systems.

- PhysicsPhysical review letters
- 2011

A hydrodynamic description of the resistivity and magnetoresistance of an electron liquid in a smooth disorder potential that is valid when the electron-electron scattering length is sufficiently short is developed.

### Negative Magnetoresistance in Viscous Flow of Two-Dimensional Electrons.

- PhysicsPhysical review letters
- 2016

It is concluded that 2D electrons in those structures in moderate magnetic fields should be treated as a viscous fluid, which is responsible for the giant negative magnetoresistance recently observed in the ultrahigh-mobility GaAs quantum wells.

### Higher-than-ballistic conduction of viscous electron flows

- PhysicsProceedings of the National Academy of Sciences
- 2017

It is shown that in viscous flows, interactions facilitate transport, allowing conductance to exceed the fundamental Landauer’s ballistic limit Gball, and a theory of the ballistic-to-viscous crossover is developed using an approach based on quasi-hydrodynamic variables.

### Observation of the Dirac fluid and the breakdown of the Wiedemann-Franz law in graphene

- PhysicsScience
- 2016

Employing high-sensitivity Johnson noise thermometry, an order of magnitude increase in the thermal conductivity and the breakdown of the Wiedemann-Franz law is reported in the thermally populated charge-neutral plasma in graphene, a signature of the Dirac fluid and constitutes direct evidence of collective motion in a quantum electronic fluid.

### Hydrodynamic Model for Conductivity in Graphene

- PhysicsScientific reports
- 2013

The model, which predicts the conductivity as a function of the impurity fraction of the sample, is supported by extensive simulations for different values of ε, the dimensionless strength of the electric field, and provides excellent agreement with experimental data.

### Nonlocal transport and the hydrodynamic shear viscosity in graphene

- Physics
- 2015

Motivated by recent experimental progress in preparing encapsulated graphene sheets with ultrahigh mobilities up to room temperature, we present a theoretical study of dc transport in doped graphene…

### Corbino disk viscometer for 2D quantum electron liquids.

- PhysicsPhysical review letters
- 2014

A Corbino disk device is proposed, which allows a determination of the viscosity of a quantum electron liquid from the dc potential difference that arises between the inner and the outer edge of the disk in response to an oscillating magnetic flux.