Strongly coupled electron fluids in the Poiseuille regime

Johanna Erdmenger, Ioannis Matthaiakakis, René Meyer, and David Rodríguez Fernández
Phys. Rev. B 98, 195143 – Published 30 November 2018

Abstract

In the context of describing electrons in solids as a fluid in the hydrodynamic regime, we consider a flow of electrons in a channel of finite width, i.e., a Poiseuille flow. The electrons are accelerated by a constant electric field. We develop the appropriate relativistic hydrodynamic formalism in 2+1 dimensions and show that the fluid has a finite dc conductivity due to boundary-induced momentum relaxation, even in the absence of impurities. We use methods involving the AdS/CFT correspondence to examine the system in the strong-coupling regime. We calculate and study velocity profiles across the channel, from which we obtain the differential resistance dV/dI. We find that dV/dI decreases with increasing current I as expected for a Poiseuille flow, also at strong coupling and in the relativistic velocity regime. Moreover, we vary the coupling strength by varying η/s, the ratio of shear viscosity over entropy density. We find that dV/dI decreases when the coupling is increased. We also find that strongly coupled fluids are more likely to become ultrarelativistic and turbulent. These conclusions are insensitive to the presence of impurities. In particular, we predict that in channels which are clearly in the hydrodynamic regime already at small currents, the DC channel resistance strongly depends on η/s.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
5 More
  • Received 9 July 2018
  • Revised 31 October 2018

DOI:https://doi.org/10.1103/PhysRevB.98.195143

©2018 American Physical Society

Physics Subject Headings (PhySH)

Fluid DynamicsNonlinear DynamicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Johanna Erdmenger, Ioannis Matthaiakakis, René Meyer, and David Rodríguez Fernández

  • Institute for Theoretical Physics and Astrophysics, Julius-Maximilians-Universität Würzburg, 97074 Würzburg, Germany

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 98, Iss. 19 — 15 November 2018

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review B

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×