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 Gball. 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 Gvis dominates over Gball in the hydrodynamic limit. The super-ballistic, low-dissipation transport is a generic feature of viscous electronics.