Imaging the breakdown of ohmic transport in graphene

TL;DR

This study uses nitrogen-vacancy center magnetometry to directly visualize how electron transport in graphene transitions from Ohmic to viscous behavior as temperature decreases, revealing the breakdown of classical conduction laws.

Contribution

It provides the first direct imaging of the local breakdown of Ohm's law in graphene, demonstrating a transition from diffusive to viscous electron flow with temperature.

Findings

Ohmic flow is observed at room temperature with current on the edges.

Below 200 K, current concentrates at the constriction center.

The flow pattern change indicates a crossover to viscous electron transport.

Abstract

Ohm's law describes the proportionality of current density and electric field. In solid-state conductors, Ohm's law emerges due to electron scattering processes that relax the electrical current. Here, we use nitrogen-vacancy center magnetometry to directly image the local breakdown of Ohm's law in a narrow constriction fabricated in a high mobility graphene monolayer. Ohmic flow is visible at room temperature as current concentration on the constriction edges, with flow profiles entirely determined by sample geometry. However, as the temperature is lowered below 200 K, the current concentrates near the constriction center. The change in the flow pattern is consistent with a crossover from diffusive to viscous electron transport dominated by electron-electron scattering processes that do not relax current.