[Paper Review] Imaging the breakdown of ohmic transport in graphene

A. Jenkins, S. Baumann+8 more|arXiv (Cornell University)|Feb 12, 2020

Graphene research and applicationsMaterials Science22 citations

TL;DR

This study uses nitrogen-vacancy (NV) center magnetometry to directly image current flow in a graphene constriction, revealing a clear transition from ohmic to viscous electron transport as temperature decreases below 200 K. The observed current concentration shifting from edges to center confirms a crossover from diffusive to hydrodynamic transport dominated by momentum-conserving electron-electron scattering, providing direct evidence for non-ohmic behavior in clean graphene at low temperatures.

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.

Motivation & Objective

• To directly observe the local breakdown of Ohm’s law in graphene at the nanoscale.
• To distinguish between ohmic, ballistic, and hydrodynamic transport regimes in a high-mobility graphene device.
• To probe the transition from diffusive to viscous electron transport driven by electron-electron scattering.
• To resolve the role of electron-electron scattering in suppressing current relaxation in low-disorder, low-density graphene.
• To validate theoretical predictions of electron hydrodynamics in graphene using spatially resolved current imaging.

Proposed method

• Scanning nitrogen-vacancy (NV) center magnetometry is used to map the local magnetic field above a graphene device with a narrow constriction.
• The measured magnetic field shifts are converted to current density profiles via the Biot-Savart law, enabling reconstruction of the underlying current flow.
• The NV probe is positioned at a fixed height above the graphene, with the field response convolved with the finite probe size to correct for spatial broadening.
• Measurements are performed at varying temperatures (from 298 K down to 100 K) and carrier densities to tune the electron-electron scattering length relative to the mean free path.
• Two geometries—slit and channel—are used to compare sensitivity to boundary scattering and to isolate hydrodynamic signatures.
• A parameter-free ohmic model is used to simulate current profiles for comparison with experimental data, validating the observed transport regime.

Experimental results

Research questions

• RQ1 Does the current flow profile in a graphene constriction transition from edge-localized (ohmic) to center-localized (viscous) as temperature is reduced?
• RQ2 Can NV magnetometry resolve the local breakdown of Ohm’s law in a high-mobility graphene device?
• RQ3 What is the role of electron-electron scattering in suppressing current relaxation and enabling hydrodynamic transport?
• RQ4 How do boundary scattering and edge effects influence current flow in different device geometries?
• RQ5 Is the observed transition consistent with a crossover from diffusive to viscous transport dominated by momentum-conserving electron-electron collisions?

Key findings

• At room temperature and near the charge neutrality point, current density exhibits a double-peak structure near the constriction edges, consistent with ohmic transport.
• As temperature is lowered below 200 K, the current density profile evolves from double-peaked to centrally peaked, indicating a transition to viscous flow.
• The observed current profile at 100 K shows a parabolic shape characteristic of Poiseuille-like viscous flow, with current concentrated in the center of the constriction.
• The transition is robust and reproducible across multiple devices, with the slit geometry showing a clear, unambiguous signature of the ohmic-to-viscous crossover.
• The channel geometry exhibits rounded profiles that are insensitive to temperature and carrier density changes, likely due to boundary-enhanced scattering, making it unsuitable for resolving the hydrodynamic transition.
• The results provide direct experimental evidence for a collision-dominated regime in graphene where the electron-electron scattering length is shorter than the mean free path, confirming the onset of electron hydrodynamics.