In a conducting material, electrical resistance arises from electrons scattering off either impurities in the atomic lattice or lattice vibrations called phonons. Electron-impurity and electron–phonon scattering can be measured easily because the momentum of the scattered electrons changes. But electrons in a solid also scatter off one another. Although electron–electron scattering does not affect overall resistance because of conservation of momentum, theory predicts that at some temperatures, the colliding electrons should flow like a viscous liquid. Recent experiments in graphene provide substantial indirect evidence of the formation of fluidlike nonlocal flow of electrons at 50–250 K. Now Joseph Sulpizio, Lior Ella, Asaf Rozen, and Shahal Ilani at the Weizmann Institute of Science in Israel and colleagues have used a novel imaging technique to directly observe electron flow in high-mobility graphene channels, and they show that the flow follows the hydrodynamic laws that govern a viscous fluid.

Credit: Adapted from J. A. Sulpizio et al., Nature 576, 75 (2019)

To spatially map an electric field, Sulpizio and colleagues constructed a device with a carbon nanotube single-electron transistor as a probe. The device’s extreme sensitivity makes it possible to scan a component of the voltage gradient that is perpendicular to the direction of current flow. Images of that Hall voltage provide information about the flow’s structure as it passes through channels in a graphene sheet. By mapping the voltage, the researchers created a profile of the electron flow traveling through the graphene. At 7.5 K, the flow remained unimpeded, or ballistic, and retained the predicted flat flow profile (as seen in the left graph). But at temperatures of 75–150 K, the profile displayed the parabolic shape (right graph) characteristic of a viscous hydrodynamic flow called Poiseuille flow. The experiments also enabled visualization of the evolution from ballistic to viscous flow.

The study is an important step toward explaining how viscous electron fluids behave inside metallic conductors. The new imaging capability provides a way to image the intricate flows of strongly interacting electrons in materials such as twisted bilayer graphene. (J. A. Sulpizio et al., Nature 576, 75, 2019.)