# Visualizing Poiseuille flow of hydrodynamic electrons

## TL;DR

This paper presents the first real-space imaging of Poiseuille flow in an electronic fluid within high-mobility graphene, demonstrating the transition from ballistic to hydrodynamic flow and providing direct confirmation of Poiseuille flow in solids.

## Contribution

It provides the first visualization of Poiseuille flow of electrons and distinguishes it from ballistic flow using Hall voltage imaging in graphene.

## Key findings

- Imaged the transition from ballistic to Poiseuille flow with temperature.
- Identified the Hall field profile as a key indicator of flow regime.
- Created a phase diagram characterizing electron flow regimes.

## 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.

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Source: https://tomesphere.com/paper/1905.11662