Visualizing Poiseuille flow of hydrodynamic electrons

Joseph A. Sulpizio, Lior Ella, Asaf Rozen, John Birkbeck, David J. Perello, Debarghya Dutta, Moshe Ben-Shalom, Takashi Taniguchi, Kenji Watanabe, Tobias Holder, Raquel Queiroz, Alessandro Principi, Ady Stern, Thomas Scaffidi, Andre K. Geim and Shahal Ilani ()
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Joseph A. Sulpizio: Weizmann Institute of Science
Lior Ella: Weizmann Institute of Science
Asaf Rozen: Weizmann Institute of Science
John Birkbeck: University of Manchester
David J. Perello: University of Manchester
Debarghya Dutta: Weizmann Institute of Science
Moshe Ben-Shalom: University of Manchester
Takashi Taniguchi: National Institute for Materials Science
Kenji Watanabe: National Institute for Materials Science
Tobias Holder: Weizmann Institute of Science
Raquel Queiroz: Weizmann Institute of Science
Alessandro Principi: University of Manchester
Ady Stern: Weizmann Institute of Science
Thomas Scaffidi: University of California
Andre K. Geim: University of Manchester
Shahal Ilani: Weizmann Institute of Science

Nature, 2019, vol. 576, issue 7785, 75-79

Abstract: Abstract Hydrodynamics, which generally describes the flow of a fluid, is expected to hold even for fundamental particles such as electrons when inter-particle interactions dominate1. Although various aspects of electron hydrodynamics have been revealed in recent experiments2–11, 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 transistor12, 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.

Date: 2019
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DOI: 10.1038/s41586-019-1788-9

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