Imaging Viscous Flow of Hydrodynamic Electron Fluid in Graphene with Nitrogen Vacancy Centers in Diamond

Collective behavior due to strong electron-electron interactions can lead to transport resembling that of a hydrodynamic fluid. Novel flow patterns, for example parabolic velocity profile known as the Poiseuille flow, arise due to viscosity in such electron fluids. In this work, we directly observe viscous Poiseuille flow in hBN-encapsulated graphene channels via imaging the associated stray magnetic field with nitrogen-vacancy (NV) centers in diamond. With wide-field magnetic imaging, we obtain diffraction-limited 2D image of the stray field generated by current flow in a graphene device on a diamond surface. The measured current density across the channel strongly deviates from the profile of a uniform flow and instead matches that of a viscous fluid. We then employ scanning NV microscopy to image the stray field with ~50 nm resolution. As a benchmark, we demonstrate the ability to image the uniform Ohmic flow in a thin metallic wire. In the case of a graphene channel, we observe a parabolic current profile corresponding to viscous Poiseuille flow. Our measurement establishes the viscous flow of a hydrodynamic electron fluid in graphene at room temperature.