An ab initio effective solid-state photoluminescence by frequency constraint of cluster calculation
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2020-12-16 |
| Journal | Journal of Applied Physics |
| Authors | Akib Karim, Igor Lyskov, Salvy P. Russo, Alberto Peruzzo, Akib Karim |
| Institutions | Centre for Quantum Computation and Communication Technology, RMIT University |
| Citations | 11 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive SummaryâThis research introduces a novel ab-initio computational method to accurately simulate the photoluminescence (PL) spectra of solid-state defects, overcoming the limitations of finite-size cluster calculations.
- Core Achievement: Developed a frequency constraint method that uses a low-frequency cutoff to remove spurious vibrational coupling (surface modes) inherent in small nanodiamond cluster simulations.
- Methodology: The cutoff frequency is determined by comparing Partial Huang-Rhys (PHR) factors derived from unconstrained and constrained (fixed outer atoms) excited state geometry optimizations using Time-Dependent Density Functional Theory (TD-DFT).
- Validation: The method was successfully validated on the Nitrogen-Vacancy (NV-) center in a C197NH140 nanodiamond cluster.
- Accuracy: The calculated adiabatic energy (Eadiab) of 1.945 eV matches the experimental Zero-Phonon Line (ZPL) of the bulk NV- center (1.945 eV).
- Engineering Impact: This approach enables the use of more accurate, but computationally expensive, excited state methods (like TD-DFT) for characterizing solid-state emitters, facilitating the prediction and discovery of new quantum materials.
- Spectral Resolution: This work provides the first vibrationally resolved PL spectrum for an NV- defect in a nanodiamond cluster using TD-DFT.
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| Defect System | NV- Center in Diamond | N/A | Most studied defect used for validation. |
| Cluster Composition | C197NH140 | N/A | Nanodiamond size corresponding to third nearest neighbors to the defect. |
| Adiabatic Energy (Eadiab) | 1.945 | eV | Calculated ZPL for C197NH140 nanodiamond. |
| Experimental ZPL (Bulk NV-) | 1.945 | eV | Reference value for solid state NV-. |
| Low Frequency Cutoff (Lower Bound) | 357 | cm-1 | Frequency used to remove spurious surface vibrational modes. |
| Low Frequency Cutoff (Upper Bound) | 469 | cm-1 | Frequency used to remove spurious surface vibrational modes. |
| Simulated Temperature | 300 | K | Used in the correlation function evaluation for the PL spectrum. |
| Gaussian Convolution Width | 200 | cm-1 | Applied to replicate experimental line broadening (FWHM of ZPL). |
| Total Huang-Rhys Constant (S) | 4.32 | (dim-less) | Calculated for C197NH140 with cutoff (Experimental literature value is 3.8). |
| Highest Coupled Mode (PHR Peak) | 532 | cm-1 | Corresponds to the 65 meV peak identified in bulk simulations. |
Key Methodologies
Section titled âKey MethodologiesâThe simulation relies on a modified Displaced Harmonic Oscillator (DHO) model under the Franck-Condon approximation, incorporating a frequency cutoff derived from comparative ab-initio calculations.
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Ground State Geometry Optimization (DFT):
- The C197NH140 cluster geometry is relaxed using DFT (PBE0 functional, def2-SV(P) basis set) with C3v symmetry constraints.
- Normal mode calculations are performed using finite difference (SNF program) to obtain vibrational eigenfrequencies (Evib) and normal coordinates.
-
Excited State Optimization (TD-DFT):
- Unconstrained State: TD-DFT optimization is performed under Cs symmetry to find the relaxed excited state geometry, yielding the adiabatic energy (Eadiab), displacement vector (D), and unconstrained Partial Huang-Rhys (PHR) factors.
- Constrained State: A second TD-DFT optimization is performed where the outermost CH and CH2 groups are fixed (constrained) to mimic the solid-state environment, yielding constrained PHR factors.
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Cutoff Frequency Determination:
- The difference between the constrained and unconstrained PHR spectra is analyzed.
- The cutoff frequency (e.g., 357 cm-1) is chosen as the boundary frequency where the constrained PHR value first drops below or equals the unconstrained value, marking the transition from suppressed surface modes to bulk-like modes.
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Photoluminescence (PL) Spectrum Generation:
- The unconstrained PHR spectrum is modified by applying the calculated low-frequency cutoff.
- This modified PHR spectrum, along with Eadiab, is input into the DHO model (implemented via modified VIBES software) to calculate the time-dependent correlation function.
- The Fourier transform of the correlation function yields the final PL spectrum, simulated at 300 K and convoluted with a 200 cm-1 Gaussian to match experimental broadening.
Commercial Applications
Section titled âCommercial ApplicationsâThis advanced simulation technique is critical for the rapid characterization and prediction of solid-state quantum emitters, particularly those embedded in nanoscale materials.
| Industry/Sector | Application | Relevance to NV- Technology |
|---|---|---|
| Quantum Sensing & Metrology | Designing and optimizing defects for high-sensitivity magnetic field, temperature, and strain sensing. | NV- centers are leading room-temperature solid-state quantum sensors. Accurate PL simulation aids in predicting spectral response under various conditions. |
| Quantum Computing & Photonics | Identifying and engineering deterministic single-photon sources (SPS) with high coherence and minimal decoherence. | The method accurately models coupling to vibrational states, which is the primary limitation for generating high-quality photon emission from nanomaterials. |
| Materials Discovery & Engineering | Predicting electronic and vibrational properties of novel defect centers (beyond NV-) that cannot be solved with previous methods (e.g., defects with the same symmetry in ground and excited states). | The TD-DFT approach used here has fewer symmetry restrictions than older A-SCF methods, broadening the scope of discoverable emitters. |
| Nanodiamond Synthesis | Guiding the synthesis of nanodiamonds to control surface termination and minimize low-frequency surface modes that degrade quantum performance. | The simulation quantifies the effect of surface coupling, providing targets for surface passivation strategies. |
View Original Abstract
Measuring the photoluminescence of defects in crystals is a common experimental technique for analysis and identification. However, current theoretical simulations typically require the simulation of a large number of atoms to eliminate finite-size effects, which discourages computationally expensive excited state methods. We show how to extract the room-temperature photoluminescence spectra of defect centers in bulk from an ab initio simulation of a defect in small clusters. The finite-size effect of small clusters manifests as strong coupling to low frequency vibrational modes. We find that removing vibrations below a cutoff frequency determined by constrained optimization returns the main features of the solid-state photoluminescence spectrum. This strategy is illustrated for the negatively charged nitrogen vacancy defect in diamond (NVâ) presenting a connection between defects in solid state and clusters; the first vibrationally resolved ab initio photoluminescence spectrum of an NVâ defect in a nanodiamond; and an alternative technique for simulating photoluminescence for solid-state defects utilizing more accurate excited state methods.