Imaging viscous flow of the Dirac fluid in graphene

At a Glance

Metadata	Details
Publication Date	2020-07-22
Journal	Nature
Authors	Mark J. H. Ku, Tony X. Zhou, Qing Li, Young J. Shin, Jing K. Shi
Institutions	University of Maryland, College Park, Center for Astrophysics Harvard & Smithsonian
Citations	301
Analysis	Full AI Review Included

Technical Documentation: MPCVD Diamond for Quantum Spin Magnetometry in Dirac Fluid Research

Source Paper: Ku et al., “Imaging Viscous Flow of the Dirac Fluid in Graphene Using a Quantum Spin Magnetometer” (arXiv:1905.10791v3)

Executive Summary

This research successfully provides the first direct imaging of viscous electron flow in charge-neutral graphene, establishing the Dirac fluid as a quantum-critical, nearly-ideal fluid at room temperature. The findings rely critically on high-quality MPCVD diamond substrates integrated with Nitrogen Vacancy (NV) centers for nanoscale magnetic sensing.

Core Achievement: Direct observation of viscous Poiseuille flow in the Dirac electron fluid of charge-neutral graphene at 300 K.
Methodology: Nanoscale magnetic imaging performed using quantum spin magnetometers realized with near-surface Nitrogen Vacancy (NV) centers in Single Crystal Diamond (SCD).
Key Material Requirement: Electronic grade SCD substrates with ultra-low surface roughness (Ra < 1 nm) are essential for high-fidelity NV center creation and subsequent van der Waals heterostructure integration (hBN-G-hBN).
Quantified Results: Kinematic viscosity (ν) was bounded between 0.1 and 0.2 m²/s near the Charge Neutrality Point (CNP).
Quantum Criticality: The measured ratio of shear viscosity to entropy density (η/s₀ ≈ 0.3 - 0.8 ħ/k_B) confirms the nearly-ideal fluid nature, consistent with universal values expected at quantum criticality.
Future Implications: The technique paves the way for studying hydrodynamic transport in other quantum critical fluids and imaging electronic turbulence.

Technical Specifications

The following hard data points were extracted from the research, highlighting the stringent material and operational requirements for successful quantum magnetometry in condensed matter physics.

Parameter	Value	Unit	Context
Operating Temperature (T)	300	K	Viscous flow observed robustly at room temperature.
Kinematic Viscosity (ν) Bounds	0.1 - 0.2	m²/s	Extracted near the CNP (median value D_ν/W = 0.5).
Shear Viscosity Ratio (η/s₀)	0.3 - 0.8	ħ/k_B	Observed near the CNP, confirming ideal fluid behavior.
Ideal Fluid Lower Bound	0.08	ħ/k_B	Theoretical minimum for η/s.
Viscous Scattering Time (τ_ν)	5	τ_ħ	Normalized by Planckian time (τ_ħ = h/(k_BT)).
Diamond Surface Roughness (Ra)	< 1	nm	Required for high-quality NV center fabrication and heterostructure deposition.
NV Center Implantation Energy	6	keV	Used for ¹⁵N implantation to achieve near-surface NVs.
NV Center Depth	10 - 20	nm	Optimal depth beneath the diamond surface for magnetic coupling.
NV-Graphene Stand-off Distance (d)	≤ 50	nm	Critical distance determining spatial resolution.
Wide-Field NV Ensemble Density	~10¹²	cm^-2	Resulting density from 2 x 10¹³ cm^-2 dosage.
Graphene Channel Width (W)	1	µm	Device dimension used for wide-field imaging.
Source-Drain Current (I)	100	µA	Current sourced for wide-field vector magnetic imaging.
Applied Voltage Drop (V_sd)	≤ 26	mV	Applied across the graphene channel at T=300 K (≤ k_BT).

Key Methodologies

The experiment relies on the precise fabrication of NV-integrated diamond substrates and subsequent integration with van der Waals materials.

Diamond Substrate Selection: Electronic grade Single Crystal Diamond (SCD) with {110} cut, grown via Chemical Vapor Deposition (CVD), was employed.
Surface Preparation: Atomic Force Microscopy (AFM) was used to ensure the diamond surface roughness was maintained under 1 nm (Ra < 1 nm).
NV Center Creation: Near-surface NV spins were generated using 6 keV ¹⁵N implantation, followed by annealing.
- Wide-Field Imaging: Dosage of 2 x 10¹³ cm^-2 resulting in an ensemble density of ~10¹² cm^-2.
- Scanning Probe: Dosage selected to ensure, on average, one NV spin per diamond nanopillar probe.
Device Fabrication (Heterostructure): A polymer-free assembly method was used to prepare the van der Waals heterostructure (hBN-Graphene-hBN stack) on the diamond or standard SiO₂/Si substrate.
Contact Metalization: Electron-beam evaporation was used to deposit 10 nm Cr (adhesion layer) followed by a minimum of 100 nm Au for electrical contacts and bond pads.
Magnetic Imaging: Current flow was mapped using two complementary modalities:
- Scanning single-spin NV magnetometry (high spatial resolution, d ≤ 50 nm).
- Wide-field NV ensemble magnetometry (2D vector field mapping, resolution ~420 nm).
Current Reconstruction: Current density J(x, y) was reconstructed from the measured stray magnetic field B(x, y, z=d) by inverting the Biot-Savart law, confirming the parabolic Poiseuille profile characteristic of viscous flow.

6CCVD Solutions & Capabilities

The success of this groundbreaking research hinges on the availability of ultra-high quality, customized diamond substrates. 6CCVD is uniquely positioned to supply the materials and engineering services required to replicate and advance this work in quantum sensing and condensed matter physics.

Applicable Materials

To replicate the high-fidelity quantum sensing platform used in this study, researchers require the highest quality SCD substrates.

Material Requirement	6CCVD Material Solution	Technical Advantage
Electronic Grade Diamond	Optical Grade SCD (Single Crystal Diamond)	Guaranteed high purity and low strain, essential for maximizing NV spin coherence time (T₂) and stability.
Ultra-Smooth Surface	Precision Polished SCD	Achieved roughness of Ra < 1 nm, meeting or exceeding the strict requirement for reliable near-surface NV creation and seamless integration of 2D materials (hBN/Graphene).
Custom Substrate Geometry	Custom SCD Plates/Wafers	Available in custom dimensions and orientations (e.g., {110} or {100} cuts) up to 125mm, enabling scaling from research chips to commercial sensor arrays.

Customization Potential

6CCVD offers comprehensive post-growth services critical for advanced quantum device fabrication, eliminating the need for multiple vendors.

Metalization Services: The paper utilized Cr/Au contacts (10 nm Cr / 100 nm Au). 6CCVD offers internal metalization capabilities including Au, Pt, Pd, Ti, W, and Cu deposition, allowing researchers to receive ready-to-use substrates with specified contact geometries.
Custom Thickness Control: We provide SCD substrates with precise thickness control, ranging from 0.1 µm to 500 µm (for active layers) and up to 10 mm (for bulk substrates), supporting both thin-film NV layers and robust bulk sensor platforms.
Laser Cutting and Shaping: 6CCVD provides custom laser cutting and shaping services to produce specialized diamond nanopillars or micro-structures required for scanning probe magnetometry, ensuring compatibility with conventional AFM technology.

Engineering Support

The complexity of integrating NV centers, 2D materials, and electronic transport measurements demands expert material consultation.

Quantum Sensing Expertise: 6CCVD’s in-house PhD team specializes in MPCVD growth optimization for quantum applications. We can assist researchers in selecting the optimal SCD grade and orientation to maximize NV center yield and coherence for similar Quantum Spin Magnetometry projects.
Surface Chemistry Consultation: We provide guidance on surface termination and cleaning protocols necessary for achieving the ultra-low roughness and chemical inertness required for high-quality van der Waals heterostructure deposition.

Call to Action: For custom specifications, material consultation, or to discuss scaling your quantum sensing platform, visit 6ccvd.com or contact our engineering team directly. We ship globally (DDU default, DDP available).

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Original Source

DOI: https://doi.org/10.1038/s41586-020-2507-2