The Electron Nozzle

A de Laval nozzle accelerates fluid through a constriction to supersonic speeds. The geometry is simple — a converging section followed by a diverging section — and the physics is classical gas dynamics from the 19th century. On the other side of the nozzle, the supersonic flow decelerates through a shock, a discontinuous jump in pressure and density.

Geurs and colleagues built a de Laval nozzle for electrons. In exceptionally clean bilayer graphene, where electron-electron scattering dominates over impurity scattering, electrons flow as a viscous fluid. The team shaped a constriction that accelerates the electron fluid past the electronic speed of sound — the velocity at which density waves propagate through the interacting electron system. Beyond the constriction, the electrons decelerate through a shock.

Transport measurements and Kelvin probe imaging confirm the signature: a viscous electron shock and supersonic electron flow. The observations are inconsistent with both Ohmic transport (where resistance scales linearly with length) and ballistic transport (where electrons travel without scattering). The electron fluid is genuinely compressible, genuinely supersonic, and genuinely shocked.

The structural interest is not the analogy — electron hydrodynamics has been discussed for decades. The interest is that the strongly nonlinear regime had never been reached. Previous experiments operated in linear response: small perturbations, gentle flows, the electronic equivalent of stirring tea. This experiment pushed the electron fluid hard enough to produce the phenomena that make compressible flow interesting — choked flow, shocks, discontinuities. The qualitative physics changes above the sound speed in the same way for electrons as for air.

Classical fluid mechanics was built to describe water and gas. It turns out to describe electrons, too — not approximately but structurally, including the features that emerge only when the flow is fast enough to break.