Supersonic flow and hydraulic jump in an electronic de Laval nozzle

In very clean solid-state systems, where carrier-carrier interactions dominate over any other scattering mechanisms, the flow of electrons can be described within a hydrodynamic framework. In these cases, analogues of viscous fluid phenomena have been experimentally observed. However, experimental studies of electron hydrodynamics have so far been limited to the low velocity, linear response regime. At velocities approaching the speed of sound, the electronic fluid is expected to exhibit compressible behaviour where nonlinear effects and discontinuities such as shocks and choked flow have long been predicted. This compressible regime remains unexplored in electronic systems, despite its promise of strongly nonlinear flow phenomena. Here, we demonstrate compressible electron flow in bilayer graphene through an electronic de Laval nozzle, a structure that accelerates charge carriers past the electronic speed of sound, until they slow down suddenly in a shock. Discontinuities in transport measurements and local flattening of potential in Kelvin probe measurements are consistent with a viscous electron shock front and the presence of supersonic electron flow, and are not consistent with Ohmic or ballistic flow. Breaking the sound barrier in electron liquids opens the door for novel, intrinsically nonlinear electronic devices beyond the paradigm of incompressible flow.