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An ab initio effective solid-state photoluminescence by frequency constraint of cluster calculation

MetadataDetails
Publication Date2020-12-16
JournalJournal of Applied Physics
AuthorsAkib Karim, Igor Lyskov, Salvy P. Russo, Alberto Peruzzo, Akib Karim
InstitutionsCentre for Quantum Computation and Communication Technology, RMIT University
Citations11
AnalysisFull AI Review Included

This 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.
ParameterValueUnitContext
Defect SystemNV- Center in DiamondN/AMost studied defect used for validation.
Cluster CompositionC197NH140N/ANanodiamond size corresponding to third nearest neighbors to the defect.
Adiabatic Energy (Eadiab)1.945eVCalculated ZPL for C197NH140 nanodiamond.
Experimental ZPL (Bulk NV-)1.945eVReference value for solid state NV-.
Low Frequency Cutoff (Lower Bound)357cm-1Frequency used to remove spurious surface vibrational modes.
Low Frequency Cutoff (Upper Bound)469cm-1Frequency used to remove spurious surface vibrational modes.
Simulated Temperature300KUsed in the correlation function evaluation for the PL spectrum.
Gaussian Convolution Width200cm-1Applied 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)532cm-1Corresponds to the 65 meV peak identified in bulk simulations.

The 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.

  1. 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.
  2. 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.
  3. 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.
  4. 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.

This advanced simulation technique is critical for the rapid characterization and prediction of solid-state quantum emitters, particularly those embedded in nanoscale materials.

Industry/SectorApplicationRelevance to NV- Technology
Quantum Sensing & MetrologyDesigning 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 & PhotonicsIdentifying 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 & EngineeringPredicting 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 SynthesisGuiding 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 (NV−) presenting a connection between defects in solid state and clusters; the first vibrationally resolved ab initio photoluminescence spectrum of an NV− defect in a nanodiamond; and an alternative technique for simulating photoluminescence for solid-state defects utilizing more accurate excited state methods.