First-Principles Framework for the Prediction of Intersystem Crossing Rates in Spin Defects - The Role of Electron Correlation
At a Glance
Section titled “At a Glance”| Metadata | Details |
|---|---|
| Publication Date | 2025-06-16 |
| Journal | Physical Review Letters |
| Authors | Yu Jin, Jinsoo Park, Malcolm McMillan, Daniel Donghyon Ohm, C. Barnes |
| Institutions | University of Chicago, University of Modena and Reggio Emilia |
| Citations | 1 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled “Executive Summary”This paper presents a rigorous, first-principles computational framework for accurately predicting Intersystem Crossing (ISC) rates in solid-state spin defects, using the Nitrogen-Vacancy (NV-) center in diamond as the primary case study.
- Core Achievement: Developed a scalable framework that successfully integrates Quantum Defect Embedding Theory (QDET) for many-body electronic states with Time-Dependent Density Functional Theory (TDDFT) for electron-phonon (e-ph) interactions.
- Electron Correlation: The methodology accurately captures crucial electron correlation effects, leading to precise calculations of Spin-Orbit Coupling (SOC) parameters (λz and λ1) that significantly differ from previous mean-field approaches.
- ISC Rate Validation: The calculated ISC rates (ΓA1 and ΓE1,2) show excellent agreement with measured experimental values (e.g., ΓA1 = 100.5 ± 3.8 MHz).
- Lifetime Agreement: Theoretical predictions for fluorescence lifetimes match experimental measurements across a broad temperature range (100 K to 600 K), validating the temperature-dependent ISC model.
- Advanced Physics: The framework explicitly incorporates complex vibronic effects, including the Dynamic Jahn-Teller (DJT) effect and the Herzberg-Teller (HT) effect, which are critical for accurate Vibrational Overlap Function (VOF) calculations.
- Scalability: Unlike cluster models, this approach relies on solid-state calculations and is scalable to supercells containing thousands of atoms (up to 13,823 atoms), enabling systematic treatment of finite-size effects.
- Versatility: The framework is general and robust, applicable to studying ISC mechanisms and optimizing the optical spin-polarization cycle in broad classes of spin defects for quantum technologies.
Technical Specifications
Section titled “Technical Specifications”The following table summarizes key calculated and measured parameters related to the NV- center in diamond, focusing on the ISC process.
| Parameter | Value | Unit | Context |
|---|---|---|---|
| ISC Rate (ΓA1) | 100.5 ± 3.8 | MHz | Experimental value (near 0 K) |
| ISC Rate (ΓE1,2) | 52.2 ± 2.0 | MHz | Experimental value (near 0 K) |
| Radiative Decay Rate (ΓRad) | 82.9 | MHz | Used for lifetime calculation (3E state) |
| SOC Parameter (λz) | 23.1 ± 4.3 | GHz | Final QDET result, dilute limit |
| SOC Parameter (λ1) | 29.4 ± 2.8 | GHz | Final QDET result, dilute limit |
| Energy Gap (Δ) | [0.334, 0.375] | eV | Refined 3E to 1A1 energy gap range |
| VOF Onset (FE1,2) | 78 | meV | Confirms e-type phonon-assisted nature of ISC |
| Temperature Range (Validation) | 100 to 600 | K | Fluorescence lifetime validation range |
| Maximum Supercell Size | 13,823 | Atoms | Used for VOF dilute limit extrapolation |
| Effective Phonon Energy (ħωe) | 77.6 | meV | Used in Dynamic Jahn-Teller (DJT) model |
| Ham Reduction Factor (p) | 0.304 | Dimensionless | Used to relate λz to fine structure splitting |
Key Methodologies
Section titled “Key Methodologies”The computational framework integrates several high-level first-principles methods to calculate the ISC rate (Γ) using Fermi’s golden rule (Γ ∝ |λ|2 F(Δ)), where λ is the SOC matrix element and F(Δ) is the Vibrational Overlap Function (VOF).
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Electronic Structure and Correlation (QDET):
- Ground state structure obtained via Density Functional Theory (DFT).
- Many-body electronic states (3A2, 3E, 1E, 1A1) computed using Quantum Defect Embedding Theory (QDET). This method solves the effective Hamiltonian using Full Configuration Interaction (FCI) within the active space, accurately capturing electron correlation.
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Spin-Orbit Coupling (SOC):
- SOC matrix elements (λ) calculated using the many-body SOC operator and QDET wave functions.
- Finite-size effects were systematically addressed by converging λ values with increasing supercell size (up to 1727 atoms) and extrapolating to the dilute limit.
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Excited State Geometry and Phonons (TDDFT):
- Equilibrium atomic geometries for the excited states (3E and 1A1) obtained using spin-conserving and spin-flip Time-Dependent DFT (TDDFT).
- Phonon modes of the 1A1 state calculated using the frozen phonon approach.
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Vibrational Overlap Function (VOF) Calculation:
- VOF (F(Δ)) calculated using the Huang-Rhys (HR) theory, based on the equilibrium geometries and phonon modes.
- The VOF results were extrapolated to the dilute limit using force constant embedding (approximated by a 13,823-atom supercell).
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Vibronic Coupling Effects:
- Dynamic Jahn-Teller (DJT) Effect: Incorporated using an effective Hamiltonian approach to account for coupling between the 3E electronic sublevels and e-type phonon modes, which is necessary to calculate the ΓE1,2 ISC rate.
- Herzberg-Teller (HT) Effect: Included by computing the derivative of the SOC matrix element (λ) with respect to configuration coordinates, accounting for the dependence of λ on atomic vibrations.
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Temperature Dependence:
- Finite-temperature ISC rates (ΓISC(T)) calculated by summing contributions from different vibronic levels of the 3E state, weighted by the Boltzmann factor, effectively capturing phonon-induced orbital averaging.
Commercial Applications
Section titled “Commercial Applications”This first-principles framework provides essential predictive capabilities for engineering and optimizing solid-state spin defects, which are foundational components in emerging quantum technologies.
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Quantum Sensing:
- Application: Designing and optimizing NV- centers and similar defects (e.g., divacancies in SiC) for high-sensitivity quantum sensors (magnetometers, thermometers, strain sensors).
- Value: Accurate ISC rate prediction is crucial for maximizing the optical spin-readout contrast, directly impacting sensor sensitivity.
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Quantum Computing and Communication:
- Application: Development of robust solid-state spin qubits.
- Value: The framework allows for ab initio prediction of the full optical cycle dynamics, enabling targeted material engineering (e.g., strain engineering) to tune the energy gap (Δ) and enhance ISC rates for faster initialization and readout.
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High-Throughput Materials Discovery:
- Application: Screening and discovery of new optically active spin defects in novel quantum materials (e.g., transition metal impurities in solids, defects in 2D materials like hBN).
- Value: Provides a robust, scalable computational tool to predict key optical properties entirely from first principles, accelerating the discovery workflow and reducing reliance on expensive experimental trials.
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Spectroscopy and Defect Engineering:
- Application: Interpreting complex experimental results, particularly under external fields (electric, magnetic, strain).
- Value: The ability to accurately model SOC and e-ph interactions allows engineers to understand how external perturbations affect the spin dynamics and optical properties of the defect.
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Advanced Materials Modeling:
- Application: Calculating phosphorescence rates for transition metal impurities in solids, expanding the framework’s use beyond vacancy-type defects.
- Value: Broadens the applicability of first-principles methods in predicting spin-related phenomena in quantum materials research.
View Original Abstract
Optically active spin defects in solids are promising platforms for quantum technologies. Here, we present a first-principles framework to investigate intersystem crossing processes, which represent crucial steps in the optical spin-polarization cycle used to address spin defects. Considering the nitrogen-vacancy center in diamond as a case study, we demonstrate that our framework effectively captures electron correlation effects in the calculation of many-body electronic states and their spin-orbit coupling and electron-phonon interactions, while systematically addressing finite-size effects. We validate our predictions by carrying out measurements of fluorescence lifetimes, finding excellent agreement between theory and experiments. The framework presented here provides a versatile and robust tool for exploring the optical cycle of varied spin defects entirely from first principles.