Higher-than-ballistic conduction of viscous electron flows

Strongly interacting electrons can move in a neatly coordinated way, reminiscent of the movement of viscous fluids. Here, we show that in viscous flows, interactions facilitate transport, allowing conductance to exceed the fundamental Landauer's ballistic limit G_ball. The effect is particularly striking for the flow through a viscous point contact, a constriction exhibiting the quantum mechanical ballistic transport at T = 0 but governed by electron hydrodynamics at elevated temperatures. We develop a theory of the ballistic-to-viscous crossover using an approach based on quasi-hydrodynamic variables. Conductance is found to obey an additive relation G = G_ball + G_vis, where the viscous contribution G_vis dominates over G_ball in the hydrodynamic limit. The superballistic, low-dissipation transport is a generic feature of viscous electronics.