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Visualizing Poiseuille flow of hydrodynamic electrons

In a theory-experiment collaboration, Professor Thomas Scaffidi and colleagues observed for the first time a completely new regime of transport in which the electrons behave like a viscous fluid, flowing down the wire. The story was also featured in a News and Views in Nature.
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The experiments were done at the Weizmann institute in the group of Shahal Ilani, and the theoretical calculations were performed at the University of Toronto in the group of Thomas Scaffidi.

Hydrodynamics, which generally describes the flow of a fluid, is expected to hold even for fundamental particles such as electrons when inter-particle interactions dominate. Although various aspects of electron hydrodynamics have been revealed in recent experiments, the fundamental spatial structure of hydrodynamic electrons—the Poiseuille flow profile—has remained elusive. Here we provide direct imaging of the Poiseuille flow of an electronic fluid, as well as a visualization of its evolution from ballistic flow. Using a scanning carbon nanotube single-electron transistor 12 , 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 temperatures 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 direct confirmation of Poiseuille flow in the solid state, and enable exploration of the rich physics of interacting electrons in real space.

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