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 \(G_{\rm ball}\). 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 \(G=G_{\rm ball}+G_{\rm vis}\), where the viscous contribution \(G_{\rm vis}\) dominates over \(G_{\rm ball}\) in the hydrodynamic limit. We argue that superballistic, low-dissipation transport is a generic feature of viscous electronics.