Photoionization of negatively charged NV centers in diamond - Theory and ab initio calculations
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2021-12-06 |
| Journal | Physical review. B./Physical review. B |
| Authors | Lukas Razinkovas, M. Maciaszek, Friedemann Reinhard, Marcus W. Doherty, Audrius Alkauskas |
| Institutions | Kaunas University of Technology, University of Rostock |
| Citations | 46 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive SummaryâThis study presents the first comprehensive ab-initio calculation of photoionization thresholds and absolute cross sections for the negatively charged Nitrogen-Vacancy (NV-) center in diamond, providing critical data for quantum technology development.
- New Threshold Determined: The photoionization threshold from the excited triplet state (IP(3E)) is calculated to be 1.15 eV, significantly lower than the ground state threshold (2.67 eV).
- Final State Mechanism Revealed: Ionization from the NV- 3E state transitions directly into the metastable NV0 4A2 state, rather than the ground NV0 2E state, correcting previous assumptions.
- Spin Physics Explained: The transition mechanism explains the observed spin polarization in NV0 Electron Spin Resonance (ESR) experiments, showing that NV- spin polarization transfers directly to the NV0 4A2 manifold.
- Cross Sections Quantified: Absolute photoionization cross sections (Ïph) and stimulated emission cross sections (Ïst) are calculated, crucial for optimizing charge-state dynamics in devices.
- Methodological Advance: A novel computational methodology combining dense k-point integration, band unfolding, and hybrid DFT was developed to accurately calculate defect cross sections, overcoming artifacts from the supercell approach.
- Dual-Beam Protocol Validation: The calculated cross section ratios (Ïph/Ïst) consistently explain the high efficiency of spin-to-charge conversion protocols using dual-beam (sub-ZPL) excitation.
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| IP(3A2) Threshold | 2.67 | eV | Photoionization from NV- ground state (3A2). |
| IP(3E) Threshold | 1.15 | eV | Photoionization from NV- excited state (3E). |
| IP(1E) Threshold (Est.) | 2.2 ± 0.1 | eV | Photoionization from NV- singlet state (1E). |
| ZPL Energy (3A2 â 3E) | 1.996 (Calc) / 1.945 (Exp) | eV | Zero-Phonon Line energy for intra-defect transition. |
| NV0 State Energy Difference | 0.48 | eV | Energy difference E(4A2) - E(2E) in neutral NV0. |
| Radiative Lifetime (3E â 3A2) | 12.2 | ns | Calculated radiative lifetime (PBE functional). |
| Diamond Band Gap (HSE) | 5.34 | eV | Calculated bulk diamond band gap (Experimental: 5.46 eV). |
| Lattice Constant (HSE) | 3.548 | A | Calculated diamond lattice constant (Experimental: 3.567 A). |
| Refractive Index (nD) | 2.4 | - | Refractive index of diamond used in cross section calculation. |
| Supercell Size | 4 x 4 x 4 (512 atoms) | - | Used for geometry optimization and self-consistent calculations. |
| k-Point Mesh Density (Integration) | 300 x 300 x 300 | - | Used for Brillouin zone integration of cross sections (primitive cell). |
Key Methodologies
Section titled âKey MethodologiesâThe calculations rely on advanced Density Functional Theory (DFT) methods to accurately model the electronic structure and optical transitions of the NV center embedded in a diamond supercell.
- Electronic Structure and Geometry:
- The Heyd, Scuseria, and Ernzerhof (HSE) hybrid functional was used for geometry optimization and calculating ionization potentials (IPs) and excitation energies.
- A large 4x4x4 supercell (512 atoms) was employed, sampled using a single Î point for geometry relaxation.
- Excited State Energies:
- The delta-self-consistent-field (ASCF) method was used to calculate the energies of the excited triplet (3E) and metastable quartet (4A2) states, ensuring accurate energy differences for the IP calculation.
- Optical Matrix Elements (PBE Approximation):
- Optical matrix elements (transition dipole moments) were calculated using the computationally less expensive PBE functional, justified by showing <10% difference compared to HSE for selected transitions.
- Calculations were performed assuming the neutral (q=0) charge state provides a more accurate approximation for the delocalized conduction band states than the negatively charged (q=-1) state.
- Brillouin Zone Integration Correction:
- To obtain smooth, converged cross sections (Ïph), a dense k-point mesh (14x14x14 for supercell, 300x300x300 for primitive cell) was used in non-self-consistent calculations.
- Band Unfolding: The calculated band structure of the defect supercell was âunfoldedâ onto the primitive diamond Brillouin zone to remove spurious mini-gaps and discontinuities caused by artificial periodicity.
- Rigid Energy Shift: A rigid energy shift was applied to align the calculated Kohn-Sham eigenvalues with the accurate photoionization thresholds obtained from total energy calculations (IPs).
- Vibrational Broadening:
- The effects of electron-phonon coupling were included by replacing the delta functions in the cross section formula with normalized spectral functions A(Δ), calculated using the generating function approach and multi-mode Jahn-Teller treatment.
Commercial Applications
Section titled âCommercial ApplicationsâThe detailed understanding of NV- photoionization mechanisms is critical for optimizing the performance and reliability of diamond-based quantum technologies.
- Quantum Sensing and Metrology:
- Photocurrent Detection of Magnetic Resonance (PDMR): The calculated cross sections enable the design of optimal laser wavelengths and intensities for highly efficient spin readout, potentially achieving read-out rates superior to traditional optical protocols.
- Charge State Control: Precise knowledge of IP(3E) allows engineers to select laser wavelengths that maximize spin-to-charge conversion (e.g., 1.17 eV or 1.93 eV excitation) while minimizing detrimental charge switching in other regimes.
- Quantum Communication and Computing:
- Spin Readout Fidelity: The confirmation that spin polarization transfers from NV- to NV0 4A2 provides a physical basis for designing robust, high-fidelity spin readout protocols based on charge conversion.
- Remote NV Coupling: The data supports protocols requiring excitation to the conduction band, such as spatial stimulated Raman adiabatic passage (STIRAP) for coupling remote NV centers.
- Diamond Laser Technology:
- Stimulated Emission Optimization: Knowledge of the photoionization cross section (Ïph) from the 3E state relative to the stimulated emission cross section (Ïst) is essential for designing diamond lasers based on NV centers, ensuring that photoionization does not compete detrimentally with stimulated emission.
- Materials Science and Defect Engineering:
- Computational Methodology: The advanced DFT methodology (band unfolding, dense k-mesh integration) is directly applicable to calculating optical cross sections for other deep-level quantum defects in wide bandgap semiconductors (e.g., SiC, GaN), accelerating defect discovery and characterization.
View Original Abstract
We present ab-initio calculations of photoionization thresholds and cross\nsections of the negatively charged nitrogen-vacancy (NV) center in diamond from\nthe ground $^{3}\!A_2$ and the excited $^{3}\!E$ states. We show that after the\nionization from the $^{3}\!E$ level the NV center transitions into the\nmetastable $^{4}\!A_2$ electronic state of the neutral defect. We reveal how\nspin polarization of $\mathrm{NV}^{-}$ gives rise to spin polarization of the\n$^{4}\!A_2$ state, providing an explanation of electron spin resonance\nexperiments. We obtain smooth photoionization cross sections by employing dense\n$k$-point meshes for the Brillouin zone integration together with the band\nunfolding technique to rectify the distortions of the band structure induced by\nartificial periodicity of the supercell approach. Our calculations provide a\ncomprehensive picture of photoionization mechanisms of $\mathrm{NV}^{-}$. They\nwill be useful in interpreting and designing experiments on charge-state\ndynamics at NV centers. In particular, we offer a consistent explanation of\nrecent results of spin-to-charge conversion of NV centers.\n