Hydrodynamics of the electronic Fermi liquid: a pedagogical overview

For over a hundred years, electron transport in conductive materials has been primarily described by the Drude model, which assumes that current flow is impeded primarily by momentum-relaxing collisions between electrons and extrinsic objects such as impurities or phonons. In the past decade, however, experiments have increasingly realized ultra-high quality electronic materials that demonstrate a qualitatively distinct method of charge transport called hydrodynamic flow. Hydrodynamic flow occurs when electrons collide much more frequently with each other than with anything else, and in this limit the electric current has long-wavelength collective behaviour analogous to that of a classical fluid. While electron hydrodynamics has long been postulated theoretically for solid-state systems, the plethora of recent experimental realizations has reinvigorated the field. Here, we review recent theoretical and experimental progress in understanding hydrodynamic electrons using the (hydrodynamic) Fermi liquid as our prototypical example.