Imaging viscous flow of the Dirac fluid in graphene
At a Glance
Section titled āAt a Glanceā| 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 | Harvard University Press, Harvard University |
| Citations | 301 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled āExecutive SummaryāThis research provides the first direct, local observation (āsmoking gunā) of viscous hydrodynamic electron flow in charge-neutral graphene, establishing the materialās electron-hole plasma as a nearly-ideal quantum critical fluid at room temperature.
- Direct Imaging of Viscosity: Viscous flow (Dirac fluid) in graphene was directly imaged via measurement of the flow-induced stray magnetic field using quantum spin magnetometers (Nitrogen Vacancy, NV, centers in diamond).
- Confirmation of Poiseuille Flow: Both scanning single-spin and wide-field NV magnetometry revealed a distinct parabolic Poiseuille profile for electron current density near the charge neutrality point (CNP), contrasting sharply with the uniform profile characteristic of conventional Ohmic transport.
- Quantum Criticality Established: The measured transport quantities, including kinematic viscosity (Ī½) and scattering rates, are comparable to universal values expected at quantum criticality.
- Near-Ideal Fluid Status: The ratio of shear viscosity to entropy density (Ī·/s0) was measured to be approximately 0.3 - 0.8 ħ/kB near the CNP, placing it within an order of magnitude of the theoretical āideal fluidā lower bound (0.08 ħ/kB).
- Robust Room Temperature Effect: Viscous flow was found to be robust at room temperature (300 K), both near and far from the CNP, challenging the conventional use of Drude conductivity models for graphene characterization at elevated temperatures.
- Methodological Advance: The work highlights the capability of NV quantum spin magnetometers for probing correlated-electronic phenomena and hydrodynamic transport at the nanoscale.
Technical Specifications
Section titled āTechnical Specificationsā| Parameter | Value | Unit | Context |
|---|---|---|---|
| Operating Temperature (T) | 300 | K | All primary measurements (Room Temperature). |
| Kinematic Viscosity (Ī½) | 0.1 to 0.2 | m2/s | Extracted away from the CNP. |
| Shear Viscosity Ratio (Ī·/s0) | 0.3 - 0.8 | ħ/kB | Observed near the CNP. |
| Ideal Fluid Lower Bound (Ī·/s) | 0.08 | ħ/kB | Theoretical quantum critical limit (1/(4Ļ) ħ/kB). |
| Viscous Scattering Time (ĻĪ½) | ~5 | Ļħ | Normalized by Planckian time (Ļħ = ħ/(kBT)). |
| Graphene Channel Width (W) | 1.0 or 0.8 | Āµm | Device dimensions used for imaging. |
| Stand-off Distance (d) | ā¤ 50 | nm | NV sensor to graphene distance (Scanning NV). |
| Wide-field Resolution | ~400 | nm | 2D magnetic imaging resolution (diffraction limit). |
| NV Implantation Depth | 10 - 20 | nm | Depth of near-surface NV spins beneath diamond. |
| Typical Current (Scanning NV) | ā¤ 2 | ĀµA | Used near CNP in linear response regime. |
| Source-Drain Current (Wide-field) | 100 | ĀµA | Used for 2D vector current mapping. |
| Carrier Density Range (n) | Up to 1.5 x 1012 | cm-2 | Range tested for viscous flow dependence. |
| Gate Dielectric (hBN) Thickness | 13(1) and 27(1) | nm | Graphene-on-diamond device. |
| Gate Dielectric (SiO2) Thickness | 385 | nm | Standard substrate devices. |
| Fermi Velocity (vF) | 106 | m/s | Characteristic velocity of Dirac electrons. |
Key Methodologies
Section titled āKey MethodologiesāThe experiment relies on two complementary NV magnetometry modalities combined with van der Waals heterostructure fabrication.
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Device Fabrication (hBN-G-hBN):
- Monolayer graphene (G) flakes were encapsulated in hexagonal boron nitride (hBN) using a polymer-free assembly method.
- Devices were fabricated on standard SiO2/p-doped Si substrates (for scanning NV) or on macroscopic diamond chips (for wide-field NV).
- For the graphene-on-diamond device, a graphite top gate (TG) was used, insulated from the graphene by hBN and hydrogen silsesquioxane (HSQ).
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NV Center Creation:
- Electronic grade single crystal diamonds ({110} cut) were used, ensuring surface roughness < 1 nm.
- Near-surface NV spins were created via 15N implantation at 6 keV, followed by annealing, resulting in NV depths of 10-20 nm.
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Scanning NV Magnetic Microscopy (Single Spin):
- A diamond nanopillar probe containing a single near-surface NV spin was used, achieving a stand-off distance of ā¤ 50 nm.
- Measurement utilized NV spin-echo AC magnetometry to measure the projected stray magnetic field (B||) with high signal-to-noise ratio.
- A 1D scan across the channel width (x-direction) was performed to obtain the current density profile Jy(x).
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Wide-field NV Magnetic Imaging (Ensemble):
- A high-density ensemble of near-surface NV spins was used to image a 5 Āµm diameter area.
- Optically Detected Magnetic Resonance (ODMR) measurements were performed across four NV orientations to reconstruct the full 2D vector magnetic field (Bx and By).
- This modality allowed verification of current conservation (ā Ā· J = 0) and provided 2D flow maps with ~400 nm resolution.
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Current Density Reconstruction:
- Wide-field: Current density J(x, y) was reconstructed by direct inversion of the Biot-Savart law in Fourier space.
- Scanning: Current density Jy(x) was obtained by minimizing a cost function (Ļ2) comparing measured B|| to calculated B|| from a parameterized current profile, incorporating regularization to handle high-frequency noise amplification.
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Transport Analysis:
- Conductivity (Ļ) was measured using a lock-in amplifier (17.77 Hz).
- Kinematic viscosity (Ī½) was extracted by fitting the measured conductivity and current profile to the electronic Navier-Stokes equation (Eq. 2), assuming no-slip boundary conditions.
Commercial Applications
Section titled āCommercial ApplicationsāThe methodologies and findings presented have significant implications for several high-tech fields:
- Quantum Sensing and Metrology: The use of NV centers in diamond for nanoscale magnetic field imaging is a core technology for quantum sensing, enabling high-resolution mapping of current flow in complex electronic devices.
- Advanced Electronic Materials Characterization: Provides a non-invasive, local method for characterizing transport mechanisms (hydrodynamic vs. Ohmic) in 2D materials and heterostructures, crucial for optimizing device performance.
- Low-Dissipation Electronics: Understanding and harnessing hydrodynamic electron flow, which minimizes momentum-relaxing scattering, is key for designing future high-speed, low-power electronic devices.
- Strongly-Correlated Quantum Matter Research: The technique serves as a benchmark for testing many-body theories by allowing direct extraction of fundamental parameters like viscosity Ī½(n, T) in quantum critical fluids, relevant to high-Tc superconductors and strange metals.
- Topological Materials: The magnetic imaging techniques can be deployed to study current flow patterns in exotic states, such as topological transport in the quantum spin Hall effect.