Multiconfigurational study of the negatively charged nitrogen-vacancy center in diamond
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2021-01-25 |
| Journal | Physical review. B./Physical review. B |
| Authors | Churna Bhandari, Aleksander L. Wysocki, Sophia E. Economou, Pratibha Dev, Kyungwha Park |
| Institutions | Howard University, Virginia Tech |
| Citations | 32 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive SummaryâThis study presents a breakthrough in modeling the electronic and magnetic properties of the negatively charged Nitrogen-Vacancy (NV-) center in diamond using advanced multiconfigurational quantum chemistry (QC) methods.
- Validation of QC Methods: Demonstrated that multiconfigurational QC (specifically CASSCF) accurately describes the many-body electronic states of the NV- center, overcoming limitations inherent in standard single-particle Density Functional Theory (DFT).
- Resolution of State Ordering: Correctly predicted the ordering and energy differences of the excited spin-singlet states (1E and 1A1), resolving a long-standing conflict in theoretical predictions and aligning results with recent experimental data.
- Accurate Excitation Energies: Calculated triplet-triplet, singlet-singlet, and triplet-singlet excitation energies that show good to excellent agreement with experimental zero-phonon line (ZPL) and vertical excitation data.
- Zero-Field Splitting (ZFS) Calculation: Achieved the first ab initio calculation of ZFS induced by both Spin-Orbit Coupling (SOC) and Spin-Spin Coupling (SSC) for the NV- center, providing critical magnetic parameters.
- Key Methodological Advance: Success hinged on systematically identifying and including extra unoccupied defect orbitals (beyond the four standard dangling bonds) in the active space to properly account for electron correlation.
- General Screening Tool: The developed numerical procedure is general and can be applied to screen and predict properties of other promising deep defects (color centers) in wide band-gap semiconductors like SiC and complex oxides.
Technical Specifications
Section titled âTechnical SpecificationsâThe following table summarizes key calculated and experimental parameters related to the NV- center electronic structure and magnetic properties.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Ground State ZFS (Calculated, 3A2) | 2.7 | GHz | Total SSC contribution (70-atom cluster) |
| Ground State ZFS (Experimental, 3A2) | 2.88 | GHz | Experimental reference (Ref. 65) |
| Excited State ZFS (Calculated, 3E) | 4.6 to 21.5 | GHz | Range of SOC+SSC splitting levels (70-atom cluster) |
| Excited State ZFS (Experimental, 3E) | 0.47 to 12.62 | GHz | Range of SOC+SSC splitting levels (Ref. 65) |
| Triplet Excitation Energy (3A2 to 3E) | 1.93 - 2.14 | eV | Calculated (70-atom to 162-atom clusters) |
| Triplet Excitation Energy (3A2 to 3E) | 1.945* | eV | Experimental Zero-Phonon Line (ZPL) |
| Singlet-Singlet Energy Gap (1A1 - 1E) | 1.07 - 1.35 | eV | Calculated (70-atom to 162-atom clusters) |
| Singlet-Singlet Energy Gap (1A1 - 1E) | 1.190* | eV | Experimental ZPL (Ref. 31) |
| 3E to 1A1 Energy Gap | 0.52 - 0.54 | eV | Calculated (70-atom to 162-atom clusters) |
| 3E to 1A1 Energy Gap | 0.321 - 0.414 | eV | Experimental range (Ref. 36, 37) |
| DFT-Optimized N-C Bond Length | 2.734 | Angstrom | Nearest carbon atoms to vacancy |
| DFT-Optimized C-C Bond Length | 2.676 | Angstrom | Nearest neighboring carbon atoms |
Key Methodologies
Section titled âKey MethodologiesâThe electronic structure and magnetic properties were determined using a systematic, multi-step quantum chemistry procedure based on the Complete Active Space Self-Consistent Field (CASSCF) method.
- Cluster Preparation and Geometry:
- Initial geometry was obtained from DFT optimization (PBE functional) of a 215-atom cubic supercell containing the NV- center.
- Two hydrogen-passivated clusters (C33H36N- and C85H76N-) were constructed, retaining C3v symmetry.
- Basis Sets and Relativistic Effects:
- Relativistically contracted all-electron correlation-consistent polarized double-zeta basis sets (cc-pVDZ-DK) were used for all atoms.
- Scalar relativistic effects were included via the Douglas-Kroll-Hess Hamiltonian.
- Active Space Determination (CASSCF(6,6)):
- The crucial step involved expanding the active space beyond the four standard dangling bond orbitals (a1N, a1C, ex, ey).
- A systematic CASSCF procedure identified two extra unoccupied defect orbitals (exâ and eyâ) with E IRRep symmetry, leading to the final active space of 6 electrons in 6 orbitals (CASSCF(6,6)).
- Symmetry Maintenance:
- Orbital symmetrization (using
libmsym) and theSUPERSYMMETRYkeyword in OpenMolcas were employed to ensure purely symmetric molecular orbitals and maintain the perfect degeneracy of E IRRep states (accuracy up to ~10 neV).
- Orbital symmetrization (using
- Inclusion of Magnetic Interactions:
- Spin-Orbit Coupling (SOC): Calculated using the Restricted Active Space State Interaction (RASSI) method within the atomic mean-field approximation (OpenMolcas).
- Spin-Spin Coupling (SSC): Calculated as the two-electron direct SSC over the CASSCF(6,6) wave functions using first-order perturbation theory (ORCA).
Commercial Applications
Section titled âCommercial ApplicationsâThe accurate theoretical modeling of deep defects in wide band-gap materials is essential for advancing solid-state quantum technologies.
- Quantum Sensing and Metrology: NV- centers are leading candidates for high-sensitivity magnetic field, temperature, and strain sensing at the nanoscale. Accurate ZFS and excited state modeling is critical for optimizing spin initialization and readout mechanisms.
- Solid-State Quantum Computing: The NV- center spin serves as a robust qubit. The precise understanding of intersystem crossing (transitions between triplet and singlet states) is key to developing high-fidelity spin initialization and readout protocols necessary for quantum computation.
- Materials Screening and Discovery: The developed CASSCF(6,6) methodology provides a reliable, general procedure for screening and characterizing other promising color centers in various wide band-gap semiconductors, including:
- Silicon Vacancies (SiV) and NV centers in Silicon Carbide (SiC).
- Group-IV defects and transition-metal defects in diamond.
- Rare-earth defects in silicon or complex oxides.
- Quantum Communication: Defects like the NV- center are used to realize quantum entanglement over long distances. Accurate modeling of electronic states helps optimize optical transitions for interfacing spins with photons.
- Defect Engineering: Provides theoretical guidance for engineering defects with desirable properties (e.g., long spin coherence times, high radiative efficiency) by predicting the effects of external perturbations like electric fields and strain.
View Original Abstract
Deep defects in wide band gap semiconductors have emerged as leading qubit candidates for realizing quantum sensing and information applications. Due to the spatial localization of the defect states, these deep defects can be considered as artificial atoms/molecules in a solid state matrix. Here we show that unlike single-particle treatments, the multiconfigurational quantum chemistry methods, traditionally reserved for atoms/molecules, accurately describe the many-body characteristics of the electronic states of these defect centers and correctly predict properties that single-particle treatments fail to obtain. We choose the negatively charged nitrogen-vacancy (NV$^-$) center in diamond as the prototype defect to study with these techniques due to its importance for quantum information applications and because its properties are well-known, which makes it an ideal benchmark system. By properly accounting for electron correlations and including spin-orbit coupling and dipolar spin-spin coupling in the quantum chemistry calculations, for the NV$^-$ center in diamond clusters, we are able to: (i) show the correct splitting of the ground (first-excited) triplet state into two levels (four levels), (ii) calculate zero-field splitting values of the ground and excited triplet states, in good agreement with experiment, and (iii) calculate the energy differences between ground and exited spin-triplet and spin-singlet states, as well as their ordering, which are also found to be in good agreement with recent experimental data. The numerical procedure we have developed is general and it can screen other color centers whose properties are not well known but promising for applications.