Dragging of electric current by hydrodynamic flow at charge neutrality

Abstract

We develop a theory of drag in graphene double layers near charge neutrality. We work in the regime of electron hydrodynamics and account for interlayer correlations of charge puddle disorder. The drag resistivity is expressed in terms of the viscosity, intrinsic conductivity of the electron liquid, and the correlation function of the puddle disorder. The contributions of the interlayer transfer of momentum and energy to drag have opposite signs. This leads to a nonmonotonic dependence of the drag resistivity on the carrier density. For layer-symmetric doping, the drag resistivity changes sign as a function of the carrier density. At interlayer separations shorter than the disorder correlation length, the transconductivity saturates to the disorder-induced enhancement of the intralayer conductivity. We provide quantitative estimates of the effect for Dirac electron liquids in monolayer graphene and bilayer graphene double-layer devices.

Figures (2)

• Figure 1: Setup for the EDL device with interlayer separation $d$. The color map in each layer represents electron-hole puddles modeled for a checkerboard potential with the correlation radius $\xi$. The positive/negative densities, $\delta n(\bm{r})$, are shown in yellow/blue, respectively. The driving electric field $\bm{E}_1$ induces temperature modulations and a vortical flow in the active layer. The transfer of momentum induces a co-moving vortical flow in the passive later as shown by the closed stream lines. The interlayer heat transfer caused by temperature modulations is indicated by broken dashed lines. It drives counter-propagating longituninal flows in the two layers, shown by open blue lines.
• Figure 2: Density dependence of the normalized drag resistivity of a bilayer system for the matched electron-electron and electron-hole densities subjected to a perfectly correlated long-range disorder. The value of the drag resistivity at dual neutrality point is sent by the disorder-induced enhancement of conductivity characterized by the parameter $\chi_\sigma$ (on the plot $\chi_{\sigma}=0.1$ and $p=1/3$). The density is plotted in the dimensionless units of $x=en_{0}/\sqrt{k\sigma_{0}}$.