Visualizing Poiseuille flow of hydrodynamic electrons

Abstract

Hydrodynamics is a general description for the flow of a fluid, and is expected to hold even for fundamental particles such as electrons when inter-particle interactions dominate. While various aspects of electron hydrodynamics were revealed in recent experiments, the fundamental spatial structure of hydrodynamic electrons, the Poiseuille flow profile, has remained elusive. In this work we provide the first real-space imaging of Poiseuille flow of an electronic fluid, as well as visualization of its evolution from ballistic flow. Utilizing a scanning nanotube single electron transistor, we image the Hall voltage of electronic flow through channels of high-mobility graphene. We find that the profile of the Hall field across the channel is a key physical quantity for distinguishing ballistic from hydrodynamic flow. We image the transition from flat, ballistic field profiles at low temperature into parabolic field profiles at elevated temperatures, which is the hallmark of Poiseuille flow. The curvature of the imaged profiles is qualitatively reproduced by Boltzmann calculations, which allow us to create a 'phase diagram' that characterizes the electron flow regimes. Our results provide long-sought, direct confirmation of Poiseuille flow in the solid state, and enable a new approach for exploring the rich physics of interacting electrons in real space.

Quantum aspects of hydrodynamic transport from weak electron-impurity scattering

“…Introduction -Recent experimental reports of peculiar transport phenomena in ultraclean graphene [1][2][3][4][5] and other materials [6][7][8] have generated much excitement regarding the role of hydrodynamic transport in these experiments. Nevertheless, because of the lack of microscopic understanding on the hydrodynamic transport of electrons, experiments have been interpreted largely through analogy with classical fluids.…”

Vorticity of viscous electronic flow in graphene

“…(B1). This quantity was recently measured within the hydrodynamic temperature window in graphene 11 to be ζ ≈ 500 nm. To describe the mutual effect of disorder and viscosity on the electronic flow we introduce a "Gurzhi number"…”

“…Nevertheless, using realistic parameters (with the values borrowed from the experiments of Refs. 11,13,15,20) we obtain values of order mΩ (measurable in a modern laboratory).…”

“…The obtained values of ξ for different widths W (shown in the legend) roughly agree with the estimate ξ = W/π based on the van der Pauw method 24,39 .tion indicating a viscous flow. Later on it became clear that negative nonlocal resistance may appear in multiterminal measurements on ballistic (and perhaps even diffusive 24 ) electronic systems 11,15 such that additional measurements were necessary to ensure that one observes indeed the hydrodynamic behavior.We have solved the hydrodynamic equation (1) with the slip boundary conditions 11,36 in a somewhat longer Hall bar (in comparison to the experimental samples of Refs. 14,15,20).…”

“…Recently two breakthrough experiments demonstrated two distinct imaging techniques allowing to "observe" the electronic flow directly 7,11,12 . This makes it possible to study a distinct feature of the hydrodynamic flow -vorticity -in laboratory experiments.…”