Electronic excitations of the charged nitrogen-vacancy center in diamond obtained using time-independent variational density functional calculations
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2023-07-13 |
| Journal | SciPost Physics |
| Authors | Aleksei V. Ivanov, Yorick L. A. Schmerwitz, Gianluca Levi, Hannes JĂŽnsson |
| Institutions | University of Iceland, Riverlane (United Kingdom) |
| Citations | 20 |
| Analysis | Full AI Review Included |
Technical Documentation & Analysis: Electronic Excitations in NV- Centers
Section titled âTechnical Documentation & Analysis: Electronic Excitations in NV- CentersâThis document analyzes the research paper âElectronic excitations of the charged nitrogen-vacancy center in diamond obtained using time-independent variational density functional calculationsâ and outlines how 6CCVDâs advanced MPCVD diamond materials and processing capabilities directly support the experimental realization and extension of this critical quantum technology research.
Executive Summary
Section titled âExecutive SummaryâThe research validates a computationally efficient method for accurately modeling the electronic structure of the negatively charged Nitrogen-Vacancy ($\text{NV}^-$) center in diamond, a cornerstone defect for solid-state quantum technologies.
- Methodological Validation: Time-independent variational Density Functional Theory (DFT) using meta-Generalized Gradient Approximation (meta-GGA) functionals (specifically $\text{r}^2\text{SCAN}$) provides highly accurate results for $\text{NV}^-$ excited states.
- Accuracy Achieved: Vertical excitation energies and Zero-Phonon Line (ZPL) estimates show deviations of only $\sim$3% compared to computationally intensive beyond-RPA quantum embedding methods.
- Energy Level Ordering: The calculations successfully confirm the experimentally established energy level ordering: $\text{}^3\text{A}_2 < \text{}^1\text{E} < \text{}^1\text{A}_1 < \text{}^3\text{E}$.
- Computational Efficiency: This approach offers a significantly smaller computational effort than high-level many-body methods, accelerating the theoretical characterization of other quantum defects.
- Material Requirement: The successful modeling of isolated defects using large supercells (up to 511 atoms) underscores the necessity of high-purity, low-strain Single Crystal Diamond (SCD) for experimental validation and device fabrication.
- Application Focus: The findings are crucial for optimizing the optical spin initialization mechanism required for diamond-based quantum computing, nanoscale sensing, and single-photon emission.
Technical Specifications
Section titled âTechnical SpecificationsâThe following hard data points were extracted from the computational results, highlighting the precision required for experimental material characterization.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Defect System | $\text{NV}^-$ Center | N/A | Prototypical quantum defect in diamond |
| Computational Method | Variational DFT ($\Delta$SCF) | N/A | Direct orbital optimization |
| Best Functional Used | $\text{r}^2\text{SCAN}$ | N/A | Provides closest agreement to beyond-RPA reference |
| Supercell Size | 511 | Atoms | Used to model isolated defects under PBC |
| Kinetic Energy Cutoff | 600 | eV | Plane-wave basis set parameter |
| Atomic Force Tolerance | < 0.01 | eV/Ă | Criterion for ground state ($\text{}^3\text{A}_2$) optimization |
| Triplet Vertical Excitation ($\text{}^3\text{A}_2 \to \text{}^3\text{E}$) | 2.057 | eV | $\text{r}^2\text{SCAN}$ result |
| Triplet ZPL Excitation ($\text{}^3\text{A}_2 \to \text{}^3\text{E}$) | 1.789 | eV | $\text{r}^2\text{SCAN}$ result (Relaxed excited state) |
| Experimental Triplet ZPL | 1.945 | eV | Reference experimental value |
| Singlet Excitation ($\text{}^3\text{A}_2 \to \text{}^1\text{E}$) | 0.621 | eV | $\text{r}^2\text{SCAN}$ result |
| Singlet ZPL Transition ($\text{}^1\text{E} \leftrightarrow \text{}^1\text{A}_1$) | 1.19 | eV | Experimental value |
Key Methodologies
Section titled âKey MethodologiesâThe theoretical approach relies on precise computational control over the simulated diamond lattice, which translates directly to the required quality and purity of the physical diamond material.
- Supercell Setup: Calculations utilized large supercells (up to 511 atoms) subject to periodic boundary conditions to accurately model the isolated $\text{NV}^-$ defect and minimize finite-size artifacts.
- Lattice Optimization: Initial diamond lattice parameters were optimized using the PBE functional.
- Ground State Optimization: The $\text{NV}^-$ defect was introduced, and the resulting structure was optimized in the ground triplet state ($\text{}^3\text{A}_2$) until the largest atomic force was below 0.01 eV/Ă .
- Excited State Calculation: Vertical excitation energies were obtained using direct orbital optimization methods, converging on saddle points on the electronic energy surface for the excited state determinants ($\text{}^1\Phi_3$ and $\text{}^3\Phi_4$).
- Zero-Phonon Line (ZPL) Calculation: ZPL energies were determined by optimizing the atomic structure in the excited triplet state ($\text{}^3\text{E}$) and calculating the energy difference relative to the relaxed ground state.
- Functional Comparison: Four density functionals were tested (LDA, PBE, TPSS, and $\text{r}^2\text{SCAN}$), confirming that the meta-GGA functionals (TPSS, $\text{r}^2\text{SCAN}$) provided the most accurate excitation energies.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThe accurate theoretical modeling of the $\text{NV}^-$ center demands ultra-high-purity, low-strain diamond material for experimental verification and device scaling. 6CCVD is uniquely positioned to supply the necessary MPCVD diamond substrates.
Applicable Materials
Section titled âApplicable MaterialsâTo replicate and extend this research into functional quantum devices, researchers require diamond with extremely low background nitrogen and controlled defect creation.
| 6CCVD Material | Description & Relevance to NV- Research |
|---|---|
| Optical Grade SCD | Essential. Ultra-low nitrogen content (< 1 ppb) and minimal strain are critical for achieving the long coherence times ($\text{T}_2$) necessary for quantum applications. This material serves as the ideal host for subsequent controlled $\text{NV}^-$ creation (via irradiation/annealing). |
| Custom SCD Thickness | SCD wafers available from 0.1 ”m up to 500 ”m. Allows for precise control over $\text{NV}^-$ depth (e.g., shallow $\text{NV}^-$ for sensing, deep $\text{NV}^-$ for bulk qubits). |
| Polycrystalline Diamond (PCD) | While SCD is preferred for coherence, high-quality PCD (up to 125 mm diameter) can be used for large-area thermal management or high-power optical components related to the quantum setup. |
| Boron-Doped Diamond (BDD) | Available for applications requiring conductive diamond electrodes, potentially useful for controlling the charge state of the $\text{NV}$ center ($\text{NV}^0$ vs. $\text{NV}^-$). |
Customization Potential
Section titled âCustomization Potentialâ6CCVDâs in-house fabrication and processing capabilities ensure that the theoretical models can be translated into practical devices.
- Custom Dimensions: We offer SCD plates and wafers in custom sizes, supporting the scaling of quantum experiments beyond small lab samples. Our PCD capability extends up to 125 mm diameter.
- Precision Polishing: Achieving high-quality optical interfaces is vital for ZPL measurements and optical initialization. 6CCVD guarantees surface roughness of Ra < 1 nm for SCD and Ra < 5 nm for inch-size PCD, ensuring minimal scattering losses.
- Advanced Metalization: For integrating $\text{NV}^-$ centers into microwave or electrical control circuits, 6CCVD provides internal metalization services, including deposition of Ti, Pt, Au, Pd, W, and Cu. This is crucial for creating high-fidelity spin control structures adjacent to the defect.
- Laser Cutting and Shaping: Custom shapes and precise laser cutting services are available to create microstructures (e.g., waveguides, photonic crystal cavities) necessary for enhancing the collection efficiency of single photons emitted by the $\text{NV}^-$ center.
Engineering Support
Section titled âEngineering SupportâThe successful application of this DFT methodology requires deep material knowledge to select the optimal diamond substrate.
6CCVDâs in-house PhD engineering team specializes in MPCVD growth parameters and defect engineering. We offer consultation services to assist researchers in:
- Material Selection: Choosing the appropriate SCD grade (e.g., low-strain, specific crystallographic orientation) to minimize unwanted broadening of the ZPL and maximize $\text{NV}^-$ coherence.
- Defect Creation Strategy: Advising on optimal nitrogen incorporation levels or post-growth irradiation/annealing protocols to achieve the desired $\text{NV}^-$ concentration and charge state stability.
- Interface Optimization: Designing metalization schemes and polishing specifications for integration into complex quantum device architectures (e.g., superconducting circuits or optical resonators).
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
Elucidation of the mechanism for optical spin initialization of point defects in solids in the context of quantum applications requires an accurate description of the excited electronic states involved. While variational density functional calculations have been successful in describing the ground state of a great variety of systems, doubts have been expressed in the literature regarding the ability of such calculations to describe electronic excitations of point defects. A direct orbital optimization method is used here to perform time-independent, variational density functional calculations of a prototypical defect, the negatively charged nitrogen-vacancy center in diamond. The calculations include up to 511 atoms subject to periodic boundary conditions and the excited state calculations require similar computational effort as ground state calculations. Contrary to some previous reports, the use of local and semilocal density functionals gives the correct ordering of the low-lying triplet and singlet states, namely {}^{3}A_2 &lt; {}^{1}E &lt; {}^{1}A_1 &lt; {}^{3}E <mml:math xmlns:mml=âhttp://www.w3.org/1998/Math/MathMLâ display=âinlineâ> <mml:mrow> <mml:msup> <mml:mrow/> <mml:mn>3</mml:mn> </mml:msup> <mml:msub> <mml:mi>A</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo><</mml:mo> <mml:msup> <mml:mrow/> <mml:mn>1</mml:mn> </mml:msup> <mml:mi>E</mml:mi> <mml:mo><</mml:mo> <mml:msup> <mml:mrow/> <mml:mn>1</mml:mn> </mml:msup> <mml:msub> <mml:mi>A</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo><</mml:mo> <mml:msup> <mml:mrow/> <mml:mn>3</mml:mn> </mml:msup> <mml:mi>E</mml:mi> </mml:mrow> </mml:math> . Furthermore, the more advanced meta generalized gradient approximation functionals give results that are in remarkably good agreement with high-level, many-body calculations as well as available experimental estimates, even for the excited singlet state which is often referred to as having multireference character. The lowering of the energy in the triplet excited state as the atom coordinates are optimized in accordance with analytical forces is also close to the experimental estimate and the resulting zero-phonon line triplet excitation energy is underestimated by only 0.15 eV. The approach used here is found to be a promising tool for studying electronic excitations of point defects in, for example, systems relevant for quantum technologies.