Imaging of Submicroampere Currents in Bilayer Graphene Using a Scanning Diamond Magnetometer

At a Glance

Metadata	Details
Publication Date	2022-05-05
Journal	Physical Review Applied
Authors	Marius L. Palm, William S. Huxter, Pol Welter, Stefan Ernst, Patrick Scheidegger
Institutions	ETH Zurich, National Institute for Materials Science
Citations	27
Analysis	Full AI Review Included

Technical Documentation & Analysis: Scanning Diamond Magnetometry for 2D Materials

Executive Summary

This research successfully demonstrates advanced nanoscale current imaging in Bilayer Graphene (BLG) using a Single Crystal Diamond (SCD) scanning probe equipped with a Nitrogen-Vacancy (NV) center. The findings validate the critical role of high-quality MPCVD diamond in achieving breakthrough quantum sensing performance for electronic transport studies.

Breakthrough Sensitivity: Achieved exceptional magnetic field sensitivity of 4.6 nT and current density sensitivity of 20 nA/µm at room temperature, significantly improving upon previous limitations.
High Dynamic Range: Introduced advanced AC quantum sensing and Bayesian phase unwrapping techniques, increasing the magnetic field dynamic range by a factor of 6.5x (from ±1 µT to ±6.5 µT).
High Resolution Imaging: Demonstrated spatial resolution between 50 nm and 100 nm, enabling the visualization of subtle, localized current anomalies (e.g., flow channels correlated with hBN encapsulation bubbles).
Non-Invasive Methodology: Successfully mitigated undesired back-action effects (scanning tip, laser, microwave pulses) on the electronic transport properties of the BLG device.
Material Validation: Confirms the necessity of ultra-high-purity, low-strain Single Crystal Diamond (SCD) for creating stable, high-coherence NV centers essential for nT-level magnetometry.
Transport Physics: Provided definitive evidence that current flow in the tested BLG devices is fully in the diffusive regime at room temperature, contrasting with previous monolayer graphene studies.

Technical Specifications

The following hard data points were extracted from the experimental results, highlighting the performance achieved using the SCD NV-center probe:

Parameter	Value	Unit	Context
Magnetic Field Sensitivity (Absolute)	4.6	nT	Achieved with 120s averaging time per pixel
Current Density Sensitivity (Absolute)	20	nA/µm	Achieved with 120s averaging time per pixel
Per-Root-Hertz Sensitivity (B)	51	nT/√Hz	Nominal sensitivity of the NV center tip
Spatial Resolution	50 - 100	nm	Resolution achieved in current density maps
Dynamic Range Improvement	6.5	x	Factor increase using phase unwrapping
Source-Drain Current (High Sensitivity)	0.3	µA	Current used for high-sensitivity imaging (Fig. 5)
AC Modulation Frequency (High Sensitivity)	1.33	MHz	Used to maximize sensitivity
NV Center Standoff Distance (z)	71	nm	Mean distance from NV center to graphene sheet
Electron Hall Mobility (µ)	3.3·10⁴	cm²/(Vs)	Measured on the Bilayer Graphene (BLG) device
Mean Free Path (l_m)	0.4	µm	Measured on the BLG device
Spin Echo Coherence Time (τ₂)	20.5	µs	Used in Bayesian inference protocol

Key Methodologies

The experiment relied on precise material engineering and synchronized quantum control protocols:

Device Fabrication: Bilayer Graphene (BLG) was encapsulated between two layers of hexagonal Boron Nitride (hBN, 11 nm top / 27 nm bottom) and placed on a 4 nm thick graphite back-gate. Electrical contacts were defined using e-beam lithography and Cr/Au deposition.
Diamond Probe Integration: A custom-built scanning magnetometer utilized a Single Crystal Diamond (SCD) probe tip containing a single NV center near the apex. The tip was operated in non-contact mode via a quartz tuning fork.
Quantum Control Synchronization: All analog and digital signals—including the source-drain voltage (V_SD), microwave pulses, laser pulses (520 nm), and back-gate voltage (V_BG)—were synchronized using a multi-channel Arbitrary Waveform Generator (AWG).
AC Quantum Sensing: The current-generated magnetic field (B_ac) was detected using the quantum lock-in amplifier concept, applying a square-wave V_SD (50 kHz - 1.33 MHz) and measuring the NV spin quantum phase (φ) via Photo-Luminescence (PL) intensity.
Dynamical Decoupling: A spin echo sequence, or a dynamical decoupling sequence with up to N = 128 refocusing pulses, was used to extend the coherent precession time (τ up to 48 µs) and maximize sensitivity.
High Dynamic Range Reconstruction: Two phase unwrapping strategies were developed: (1) a variable grid method for local refinement, and (2) a Bayesian inference method that incorporates spatial smoothness priors to recover the magnetic field map and associated current density (J) from wrapped phase data.

6CCVD Solutions & Capabilities

6CCVD is uniquely positioned to supply the advanced diamond materials and customization services required to replicate and extend this cutting-edge scanning diamond magnetometry research. Our MPCVD diamond products meet the stringent purity, thickness, and surface quality demands of quantum sensing applications.

Research Requirement	6CCVD Solution & Capability	Technical Advantage & Sales Pitch
High-Purity NV Center Host Material	Optical Grade Single Crystal Diamond (SCD)	We supply high-purity SCD plates (0.1 µm to 500 µm thick, substrates up to 10 mm) essential for maximizing NV center coherence times (τ₂) and achieving the demonstrated nT-level magnetic sensitivity.
Custom Probe Tip Manufacturing	Custom Dimensions & Precision Laser Cutting	The experiment relies on a specific probe geometry. 6CCVD offers custom laser cutting and shaping services for SCD plates, allowing researchers to define precise tip dimensions and orientations for optimal scanning.
Ultra-Low Surface Roughness	SCD Polishing (Ra < 1 nm)	Achieving a low NV standoff distance (z = 71 nm) is critical for high spatial resolution. Our proprietary polishing techniques guarantee SCD surfaces with Ra < 1 nm, ensuring stable non-contact scanning and maximum magnetic field coupling.
Integration of On-Chip Electronics	Internal Metalization Services (Au, Cr/Au, Ti/Pt/Au)	The BLG devices used Cr/Au contacts. We offer in-house metalization (Au, Pt, Pd, Ti, W, Cu) directly onto diamond substrates, facilitating the integration of microwave transmission lines or complex contact pads for advanced transport experiments.
Large-Area Substrates for 2D Heterostructures	PCD Wafers up to 125 mm Diameter	For scaling up 2D material stacks (BLG/hBN) or integrating multiple devices, 6CCVD provides large-area Polycrystalline Diamond (PCD) substrates up to 125 mm in diameter, polished to Ra < 5 nm.
Material Selection and Optimization	In-House PhD Engineering Support	Our expert team assists researchers in selecting the optimal diamond grade (e.g., low-strain, specific nitrogen concentration) and crystallographic orientation required to maximize NV center performance for specific quantum sensing protocols.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

Nanoscale electronic transport gives rise to a number of intriguing physical\nphenomena that are accompanied by distinct spatial patterns of current flow.\nHere, we report on sensitive magnetic imaging of two-dimensional current\ndistributions in bilayer graphene at room temperature. By combining dynamical\nmodulation of the source-drain current with ac quantum sensing of a\nnitrogen-vacancy center in a diamond probe, we acquire magnetic field and\ncurrent density maps with excellent sensitivities of 4.6 nT and 20 nA/$\mu$m,\nrespectively. The spatial resolution is 50-100 nm. We further introduce a set\nof methods for increasing the technique’s dynamic range and for mitigating\nundesired back-action of magnetometry operation on the electronic transport.\nCurrent density maps reveal local variations in the flow pattern and global\ntuning of current flow via the back-gate potential. No signatures of\nhydrodynamic transport are observed. Our experiments demonstrate the\nfeasibility for imaging subtle features of nanoscale transport in\ntwo-dimensional materials and conductors.\n

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Original Source

DOI: https://doi.org/10.1103/physrevapplied.17.054008