Sensing at the Nanoscale Using Nitrogen-Vacancy Centers in Diamond - A Model for a Quantum Pressure Sensor

At a Glance

Metadata	Details
Publication Date	2024-04-12
Journal	Nanomaterials
Authors	Hari P. Paudel, Gary R. Lander, Scott Crawford, Yuhua Duan
Institutions	National Energy Technology Laboratory, Defense Logistics Agency
Citations	5
Analysis	Full AI Review Included

Executive Summary

This research presents a computational model for a highly sensitive quantum pressure sensor (Quantum Manometer) utilizing the Nitrogen-Vacancy (NV^-) center in diamond.

Core Value Proposition: The model predicts ultra-high stress sensitivity by manipulating the ground-state electronic spin levels of the NV^- center, enabling measurements in harsh, high-pressure environments.
Predicted Sensitivity: The calculated pressure sensitivity (ngs) is 0.32 MPa/√Hz, comparable to state-of-the-art experimental results (0.6 MPa/√Hz).
Methodology: A combined approach using first-principles Density Functional Theory (DFT) and a low-energy Hamiltonian model was employed to quantify spin level shifts and splitting under uniaxial strain.
Quantum Advantage: Quantum sensing based on spin manifold manipulation was shown to be superior to traditional optical sensing (based on band edge shifting) by approximately four orders of magnitude in terms of frequency shift per unit pressure.
Operating Range: The diamond host material provides excellent mechanical strength, allowing the sensor to operate under extreme pressure limits, potentially up to 60 GPa (simulated) and applicable in research environments up to 200 GPa.
Key Finding: Stress applied along the crystal symmetry axis (p || [111]) results in a constant energy level shift without splitting, simplifying measurement in specific orientations.

Technical Specifications

Parameter	Value	Unit	Context
Predicted Pressure Sensitivity (ngs)	0.32	MPa/√Hz	Calculated using T₂* ≈ 10 µs and C ≈ 0.05.
Zero-Field Splitting (D₀)	2.88	GHz	Ground state (³A) separation between ms=0 and ms=±1 sublevels.
Spin Dephasing Time (T₂*)	10	µs	Measured value used for sensitivity calculation (Room Temperature, nanodiamond ensemble).
Energy Shift per Unit Pressure (Spin Manifold)	3	MHz/GPa	For uniaxial stress p
Energy Shift per Unit Pressure (Optical/Band Edge)	5.88 x 10⁵	MHz/GPa	DFT estimate for conduction band edge shift (Traditional sensing metric).
Maximum Simulated Pressure (Doherty Ref.)	60	GPa	Hydrostatic pressure applied in DAC experiments.
Diamond Unit Cell Lattice Parameter (a)	0.356	nm	Used for DFT simulation setup.
DFT Plane-Wave Cutoff Energy	520	eV	Computational parameter for VASP simulation.
Excited State Splitting (∆E_ex)	Up to 60	meV	Observed under 2% change in longitudinal (c) lattice parameter.

Key Methodologies

The study combined computational and analytical modeling to predict the NV center’s response to stress:

DFT Simulation Setup: First-principles DFT was implemented using the VASP package. A 3 x 3 x 3 diamond supercell (1.07 nm dimensions) containing a single negatively charged NV center (NV^-, q = -1) was modeled.
Functional and Basis Set: The Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) functional and projector augmented wave (PAW) pseudo-potentials were used, with a plane-wave cutoff energy of 520 eV.
Stress Application: Uniaxial and isotropic stresses were introduced by systematically varying the lattice parameters along the longitudinal (c-axis) and transverse (a, b plane) directions, simulating strain up to ±2%.
Band Structure Monitoring: The DFT results tracked the shift and splitting of the defect bands (³A ground state and ³E excited state) and the overall band gap magnitude as a function of applied strain.
Low-Energy Hamiltonian Derivation: A spin-stress coupling Hamiltonian (H) was developed for the S=1 ground state, incorporating the zero-field splitting (D₀) and stress-induced perturbations (M_i and N_i parameters).
Eigenvalue Calculation: Analytical solutions for the Hamiltonian eigenvalues were derived to determine the frequency shift and splitting of the ms=±1 spin manifold per unit stress (MHz/GPa).
Sensitivity Quantification: The predicted stress sensitivity (ngs) was calculated using the derived frequency shift, a typical spin dephasing time (T₂* ≈ 10 µs), and photon collection efficiency (C ≈ 0.05).

Commercial Applications

The proposed quantum manometer model is highly relevant for applications requiring high-resolution pressure sensing in extreme or inaccessible environments.

Industry/Sector	Application	Context/Benefit
Energy & Subsurface	Geological CO₂ Storage Monitoring	Detecting trapped high-pressure CO₂ (pressure greater than 10 MPa) and monitoring co-seismic pulses.
Infrastructure	Pipeline and Mine Monitoring	Ensuring safe operating conditions and uninterrupted service by detecting stress and vibrations.
Geophysics	Subsurface Seismic Vibration Detection	Measuring earth’s subsurface vibrations and monitoring volumetric strain in crystalline rock.
Materials Science	High-Pressure Research	Systematic control and monitoring of pressure in extreme conditions, such as synthesizing metallic hydrogen or studying high-temperature superconductivity (up to 200 GPa).
Quantum Technology	Quantum Metrology Devices	Developing next-generation sensors with sensitivity levels orders of magnitude beyond classical limits for variables like pressure, temperature, and electromagnetic fields.

View Original Abstract

The sensing of stress under harsh environmental conditions with high resolution has critical importance for a range of applications including earth’s subsurface scanning, geological CO2 storage monitoring, and mineral and resource recovery. Using a first-principles density functional theory (DFT) approach combined with the theoretical modelling of the low-energy Hamiltonian, here, we investigate a novel approach to detect unprecedented levels of pressure by taking advantage of the solid-state electronic spin of nitrogen-vacancy (NV) centers in diamond. We computationally explore the effect of strain on the defect band edges and band gaps by varying the lattice parameters of a diamond supercell hosting a single NV center. A low-energy Hamiltonian is developed that includes the effect of stress on the energy level of a ±1 spin manifold at the ground state. By quantifying the energy level shift and split, we predict pressure sensing of up to 0.3 MPa/Hz using the experimentally measured spin dephasing time. We show the superiority of the quantum sensing approach over traditional optical sensing techniques by discussing our results from DFT and theoretical modelling for the frequency shift per unit pressure. Importantly, we propose a quantum manometer that could be useful to measure earth’s subsurface vibrations as well as for pressure detection and monitoring in high-temperature superconductivity studies and in material sciences. Our results open avenues for the development of a sensing technology with high sensitivity and resolution under extreme pressure limits that potentially has a wider applicability than the existing pressure sensing technologies.

Tech Support

Original Source

DOI: https://doi.org/10.3390/nano14080675

References

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