Strongly coupled electron fluids in the Poiseuille regime

TL;DR

This paper investigates relativistic electron fluid flow in narrow channels using hydrodynamic theory and AdS/CFT methods, revealing how strong coupling and boundary effects influence resistance and flow behavior.

Contribution

It develops a relativistic hydrodynamic formalism for electron fluids in 2+1 dimensions and explores the impact of strong coupling on flow profiles and resistance.

Findings

$dV/dI$ decreases with increasing current, consistent with Poiseuille flow.

Increasing coupling (lower $ ext{η/s}$) reduces differential resistance.

Strongly coupled fluids tend to become ultra-relativistic and turbulent.

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 $\eta/s$, 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 ultra-relativistic 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 $\eta/s$.