| Metadata | Details |
|---|
| Publication Date | 2023-07-13 |
| Journal | SciPost Physics |
| Authors | Aleksei V. Ivanov, Yorick L. A. Schmerwitz, Gianluca Levi, Hannes JĂ´nsson |
| Institutions | University of Iceland, Riverlane (United Kingdom) |
| Citations | 20 |
| Analysis | Full AI Review Included |
- Method Validation: Variational Density Functional Theory (DFT) using direct orbital optimization is validated as an accurate and computationally efficient method for modeling excited electronic states in the negatively charged nitrogen-vacancy (NV-) center in diamond.
- State Ordering Confirmation: DFT calculations, even with local and semilocal functionals, correctly predict the energy ordering of the four lowest-lying states: 3A2 < 1E < 1A1 < 3E, resolving a long-standing controversy in previous DFT literature.
- High Accuracy Achieved: Advanced meta-Generalized Gradient Approximation (meta-GGA) functionals, particularly r2SCAN, yield vertical excitation energies that deviate by less than 0.06 eV from the most accurate theoretical reference (beyond-RPA quantum embedding).
- Computational Efficiency: The variational DFT approach requires computational effort similar to ground state calculations, making it significantly less demanding than high-level many-body methods (e.g., GW+BSE or beyond-RPA).
- Zero-Phonon Line (ZPL) Estimate: The calculated ZPL energy for the critical 3A2 â 3E transition (1.789 eV via r2SCAN) is highly accurate, underestimating the experimental value (1.945 eV) by only 0.15 eV.
- Applicability: This methodology is a promising, cost-effective tool for characterizing electronic excitations and optimizing atomic structures in excited states of quantum defects relevant to quantum technologies.
| Parameter | Value | Unit | Context |
|---|
| Maximum Supercell Size | 511 | atoms | Used for periodic boundary conditions to model isolated defects. |
| Kinetic Energy Cutoff | 600 | eV | Plane-wave basis set cutoff energy. |
| Atomic Force Convergence | 0.01 | eV/A | Maximum force threshold for geometry optimization in the ground state. |
| Triplet Ground State ZPL Energy (Exp.) | 1.945 | eV | Experimental Zero-Phonon Line (ZPL) for 3A2 â 3E transition. |
| r2SCAN ZPL Energy (3A2 â 3E) | 1.789 | eV | Calculated ZPL energy after atomic relaxation in the excited state. |
| r2SCAN Vertical Excitation Accuracy | < 0.06 | eV | Maximum deviation from beyond-RPA reference calculations. |
| Singlet Transition ZPL Energy (Exp.) | 1.19 | eV | Experimental ZPL for 1E â 1A1 transition. |
| Triplet Ground State Splitting (ms=0 vs ms=Âą1) | ~2.88 | GHz | Determined by Electron Paramagnetic Resonance (EPR) (~10-5 eV). |
| Best Performing Functional | r2SCAN | N/A | Meta-GGA functional providing the closest agreement with high-level theory and experiment. |
- System Modeling: The NV- center was represented using large diamond supercells (up to 511 atoms) under periodic boundary conditions to minimize finite-size and surface artifacts.
- Computational Framework: Calculations utilized the GPAW software, Libxc library, and ASE environment, employing a plane-wave basis set with a 600 eV kinetic energy cutoff and the Projector Augmented Wave (PAW) method.
- Ground State Optimization: The atomic structure was optimized in the 3A2 triplet ground state using various density functionals (LDA, PBE, TPSS, r2SCAN) until the largest atomic force was below 0.01 eV/A.
- Excited State Calculation (Variational DFT): Time-independent variational DFT (ÎSCF) was performed using a direct orbital optimization method to find excited electronic states as stationary points (saddle points) on the energy surface.
- Saddle Point Convergence: A limited-memory symmetric rank-one (L-SR1) quasi-Newton algorithm was used to assist convergence on the excited state saddle points, ensuring stability.
- Multideterminant Singlet Energy Derivation: The energies of the multideterminant singlet states (1E and 1A1) were calculated from the energies of optimized single-determinant solutions (mÎŚ2 and 1ÎŚ3) using spin-purification and energy difference formulas (Eqs. 5 and 6).
- Zero-Phonon Line (ZPL) Calculation: ZPL energies for the triplet transition (3A2 â 3E) were obtained by optimizing the atomic coordinates in the excited 3E state and calculating the energy difference relative to the relaxed 3A2 ground state.
- Quantum Sensing and Metrology: NV- centers are primary candidates for nanoscale sensors. Accurate modeling of the electronic states is crucial for optimizing the optical spin initialization cycle, enhancing sensitivity and coherence time in magnetometers and thermometers.
- Solid-State Quantum Bits (Qubits): The NV- center serves as a robust solid-state qubit. This methodology provides the necessary theoretical foundation to predict and control the spin state (ms=0 initialization) via optical excitation, which is fundamental for quantum computing architectures.
- Defect Engineering: The validated DFT approach can be applied to screen and characterize other promising point defects in semiconductors (e.g., SiC, ZnO) that are relevant for quantum technologies, significantly reducing the need for computationally expensive high-level methods.
- Quantum Communication: Supporting the development of diamond-based single-photon emitters by accurately modeling the excited state lifetimes and transition energies required for reliable photon generation.
- Materials Characterization: Providing a reliable, low-cost simulation tool for predicting structural relaxation and vibrational properties (phonons) associated with electronic transitions in quantum materials.
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.