Higher-Than-Ballistic Conduction of Viscous Electron Flows

TL;DR

This paper demonstrates that viscous electron flows can achieve conductance exceeding the ballistic limit, revealing a superballistic transport regime driven by electron hydrodynamics.

Contribution

It introduces a theory describing the crossover from ballistic to viscous transport, showing conductance as a sum of ballistic and viscous contributions, with viscous effects dominating at higher temperatures.

Findings

Conductance can surpass the Landauer ballistic limit in viscous flows.

The conductance follows an additive relation: G=G_ball+G_vis.

Viscous effects lead to superballistic, low-dissipation transport.

Abstract

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.