Spread and erase -- How electron hydrodynamics can eliminate the Landauer-Sharvin resistance

TL;DR

This paper demonstrates that electron hydrodynamics can eliminate the fundamental Landauer-Sharvin resistance in electronic systems by spreading it throughout the bulk, especially with optimized device geometries, potentially leading to arbitrarily low resistance.

Contribution

It reveals how device geometry and electron hydrodynamics can fully eliminate Landauer-Sharvin resistance, contrasting with traditional ohmic behavior.

Findings

Hydrodynamics allows resistance to be spread and eliminated in the bulk.

Proper device geometry enables complete resistance removal.

Resistance can decrease with device length in hydrodynamic regime.

Abstract

It has long been realized that even a perfectly clean electronic system harbors a Landauer-Sharvin resistance, inversely proportional to the number of its conduction channels. This resistance is usually associated with voltage drops on the system's contacts to an external circuit. Recent theories have shown that hydrodynamic effects can reduce this resistance, raising the question of the lower bound of resistance of hydrodynamic electrons. Here we show that by a proper choice of device geometry, it is possible to spread the Landauer-Sharvin resistance throughout the bulk of the system, allowing its complete elimination by electron hydrodynamics. We trace the effect to the dynamics of electrons flowing in channels that terminate within the sample. For ballistic systems this termination leads to back-reflection of the electrons and creates resistance. Hydrodynamically, the scattering of these electrons off other electrons allows them to transfer to transmitted channels and avoid the resistance. Counter-intuitively, we find that in contrast to the ohmic regime, for hydrodynamic electrons the resistance of a device with a given width can decrease with its length, suggesting that a long enough device may have an arbitrarily small total resistance.