We have investigated how electric currents flow through FIB-fabricated microconstrictions in ultra-pure crystals of the delafossite PdCoO2. As the channel width becomes narrower and narrower, the sample enters the ballistic regime when it becomes thinner than the bulk mean free path (which is at 20 micron insanely high in this material). In ballistic transport, the dominant source of scattering is boundary scattering, and simple phase space calculations give a clear theoretical prediction how the resistance should scale with channel width in this case, which has been observed in many materials.
Our experiments show clear deviations from this classical scaling, that clearly contradict the expectations for ballistic current flow. The results can be quantitatively explained though if one assumes a viscous contribution to the electron flow arising from electron-electron interactions. It turns out that the electronic liquid in PdCoO2 at 2K has a similar viscosity to that of water at room temperature!