The charge cycle of group IV vacancy centers in diamond: From DFT to rate equations

Bart Partoens; Dirk Lamoen; Joshua Claes

REVIEW 4 major objections 5 minor 3 references

The charge cycle of group IV vacancy centers in diamond: From DFT to rate equations

T0 review · 4 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read This paper derives DFT-calibrated rate equations for the charge cycle of group IV vacancy centers in diamond, predicting that below 3.29 eV silicon vacancy centers end entirely in the double-negative charge state and that SiV(0) takes…

desk verdict A genuinely useful systematic DFT-to-kinetics framework for group IV vacancy charge cycling, but the headline SiV prediction is not reproducible because a load-bearing matrix element is never reported. read the letter →

arxiv 2504.19748 v1 pith:C6OMAOW6 submitted 2025-04-28 cond-mat.mtrl-sci physics.atom-phphysics.comp-phphysics.opticsquant-ph

Joshua Claes , Bart Partoens , Dirk Lamoen This is my paper · ORCID

classification cond-mat.mtrl-sciphysics.atom-phphysics.comp-phphysics.opticsquant-ph

keywords groupIVvacancycenterssiliconcenterdiamondchargestatedynamicsphotoionizationonsetenergyrateequationsFermi'sgoldenruledensityfunctionaltheory

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Group IV vacancy centers in diamond — point defects where a silicon, germanium, tin, or lead atom sits between two missing carbon atoms — are leading candidates for quantum technology because their optical and spin properties depend on charge state. This paper builds a closed model of their charge cycle from the -2 to the 0 state, starting from density-functional theory. It computes the photon energies at which each one-step and two-step ionization process turns on, then feeds those onsets, dipole matrix elements, and density-of-states factors into rate equations derived from Fermi's golden rule. The headline result is a prediction for the silicon vacancy center: after long illumination with photon energies below 3.29 eV, the population ends up completely in the double-negative SiV(-2) state; between 3.29 and about 4 eV a mixture appears in which SiV(-1) dominates, with SiV(0) taking over near 4.0 eV. If correct, this gives experimentalists a photon-energy dial for preparing a desired charge state all-optically, without moving the Fermi level by doping.

What carries the argument

The load-bearing machinery is a rate-equation model for charge-state populations built on Fermi's golden rule and Einstein coefficients, with three kinds of input objects: one- and two-step photoionization onset energies computed from DFT formation energies; transition dipole matrix elements between many-electron states, including degeneracy factors from the D3d symmetry; and a medium-corrected density of states shifted so that band edges respect the computed onsets. To keep the system closed, the authors introduce two auxiliary excitonic states — a neutral defect plus a conduction-band electron, and a negative defect plus a valence-band hole — with a relaxation parameter $C_{i,j}$ that returns the system to its ground charge state. Taking $C_{i,j}$ sufficiently large suppresses spontaneous and stimulated emission, leaving photoionization and relaxation as the only channels. The excited neutral state enters as a product Jahn-Teller state, whose wavefunction is used in the two-step ionization dipole moments.

What would settle it

Illuminate diamond containing silicon vacancy centers that start in the neutral charge state at a fixed photon energy between, say, 2.5 and 3.2 eV for a long time and monitor the charge-state population through charge-selective photoluminescence or photoelectric readout; the model predicts the final population is essentially 100% SiV(-2), so any substantial remaining SiV(-1) or SiV(0) rules out the emission-suppression limit or the computed onset energies. The same check across 3.29 to 4.0 eV should show SiV(-1) dominance with SiV(0) rising near 4.0 eV.

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Extended reading notes

Core claim

The authors claim that the full charge cycle among the -2, -1, and 0 charge states for each group IV vacancy center is governed by a closed set of rate equations whose inputs come from hybrid density-functional calculations: optical charge-transition onset energies for ground-state and excited-state photoionization, transition dipole moments, degeneracy factors from group theory, and a scissor-corrected density of states. For silicon vacancy centers, the model reproduces the known requirement of ultraviolet light to reach the neutral state and yields a sharp charge-state map: below 3.29 eV, the final state is entirely SiV(-2); between 3.29 eV and roughly 4.0 eV, SiV(-1) dominates; and near 4.0 eV, SiV(0) rises to take over. For the heavier centers, the lower onset energies make the final charge state less predictable, and the model is used to rationalize observations such as the recovery of GeV(-1) under 3.06 eV illumination through the GeV(-2) to GeV(-1) transition.

Load-bearing premise

The rate-equation predictions assume the temporary electron- or hole-carrying excitonic states relax back to their ground charge states so quickly that spontaneous and stimulated emission are negligible, a regime the paper imposes by taking the relaxation parameter large but never quantifies.

Editorial extensions

If this is right

For silicon vacancy centers, photons below 3.29 eV drive any starting population toward SiV(-2), meaning sub-3.29 eV illumination acts as an all-optical route to the double-negative charge state, even starting from the hard-to-reach neutral state.
In the 3.29 to 4.0 eV window, SiV(-1) becomes the dominant species because SiV(-2) can be re-ionized back to SiV(-1) while SiV(-1) is not yet efficiently ionized to SiV(0); near 4.0 eV, SiV(0) starts to take over.
The two-step ionization path through the first excited state of SiV(-1) has an onset of only 0.45 eV, so a single sub-bandgap pump can gradually accumulate SiV(-2) even though direct ground-state ionization requires 2.17 eV.
For the germanium vacancy, the model explains the experimentally observed recovery of GeV(-1) under 3.06 eV light as the GeV(-2) to GeV(-1) transition, and it predicts that 2.33 eV light should not suffice without assistance from nearby defects or small errors in the computed onset.
Ground-state photoionization onset energies decrease with the mass of the group IV atom, so heavier centers (GeV, SnV, PbV) require lower photon energies than SiV to cycle their charge states.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the fully -2 below 3.29 eV prediction holds, it suggests a simple protocol for deterministic charge-state preparation: use a sub-3.29 eV pump to make SiV(-2), then a second pulse above 3.29 eV tuned to the relevant onset to repump into SiV(-1) or SiV(0).
The model treats the relaxation parameter $C_{i,j}$ as effectively infinite; a quantitative experiment measuring residual emission or deviations from the predicted final populations would pin down the actual relaxation timescales and allow radiative recombination to be included.
The same machinery should transfer directly to other split-vacancy centers with D3d symmetry in different hosts, since only the DFT inputs — onset energies and dipole matrix elements — would need recomputation.
A useful extension would be computing the unknown SiV(-1)* to SiV(-2) matrix element, because the paper shows the transition is energetically allowed at 0.45 eV but leaves its cross section unquantified, and the actual accumulation of SiV(-2) depends on that value.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

The useful core here is the systematic enumeration of one- and two-step photoionization pathways for all four group IV vacancy centers, with degeneracy factors derived from the multi-electron states, and the first rate-equation model of the -2/-1/0 charge cycle for these defects. The formation-energy pipeline is standard (HSE06, Makov-Payne corrections) and the group-theoretic derivations look careful. The comparison with the GeV experiment in Ref. 39 is a genuine forward prediction, which earns this paper more than a desk rejection.

The soft spots are real, though. The stress-test note is on target: the route to SiV(-2) below the 3.29 eV ground-state threshold runs through SiV(-1)* → SiV(-2), and Section 5.2 says the matrix element for that transition is "not yet known." Yet Fig. 6 uses PBE and PBE-1/2 matrix elements to simulate exactly that rate. No value or estimate for that matrix element is reported anywhere, so the headline "completely double negative below 3.29 eV" prediction is not reproducible from the paper as written. If that rate is small, the -2 population collapses. This is distinct from the unquantified C_{i,j} emission-suppression parameter: at least the large-C limit is well-defined, while this matrix element is simply absent.

Two more issues, in proportion. The "below 3.29 eV" claim is overbroad: since the initial condition is SiV(0) and the 0→-1 threshold is 1.72 eV, below 1.72 eV the final state should stay neutral. The C_{i,j} rates are set "sufficiently large" with no sensitivity analysis; if relaxation is not fast, emission channels will repopulate higher charge states. The manuscript also reads like a draft — empty conclusion, typos, several missing numbers — but those are fixable.

The central approach is defensible and the onset-energy diagrams are the most complete set I know for these centers. Experimentalists trying to tune charge state by wavelength will get the most out of those diagrams; theorists will want the rate-equation machinery. With a table of dipole matrix elements (or a stated approximation), a sensitivity scan in C, and a sharper statement of the energy window, this would be a solid contribution. I would send it to peer review and require those additions, not desk-reject it.

Referee Report

4 major / 5 minor

Summary. The manuscript develops a first-principles framework for the photo-induced charge cycling of group IV vacancy centers in diamond. It computes optical charge-transition thresholds from HSE06 formation energies, evaluates transition dipole matrix elements from PBE and PBE-1/2 wavefunctions, derives Einstein-coefficient-based rate equations that include auxiliary 'excitonic' states to model ionization and relaxation, and applies the resulting equations to the silicon vacancy center. The central quantitative claim, in Section 5.3 and Figure 6, is that for photon energies below 3.29 eV the final charge state of SiV is completely the double-negative state, with SiV(-1) and SiV(0) appearing at higher energies. The paper also discusses the Ge vacancy qualitatively, comparing with the experimental dark-state recovery in Ref. [39].

Significance. If fully supported, the paper would provide a closed DFT-calibrated rate-equation description of the entire -2/-1/0 charge cycle, including group-theoretically derived degeneracy factors and forward predictions that are not fitted to experiment. The computed onset energies for all four group IV vacancy centers are a useful output, and the explicit comparison with the GeV experiment of Ref. [39] is an honest forward test. However, the central rate-equation prediction in Figure 6 is currently not reproducible: one key transition matrix element is admitted in Section 5.2 to be unknown, the auxiliary-state relaxation rates C_{i,j} are never quantified, and the underlying densities of states and matrix elements are not tabulated. The framework is promising, but the specific 'completely double-negative' claim is not yet supported by the evidence in the manuscript.

major comments (4)

[Section 5.2 and Figure 6] The headline prediction that SiV is 'completely the double negative charge state' below 3.29 eV rests on the two-step path SiV(0) to SiV(-1), SiV(-1) to SiV(-1)*, and then SiV(-1)* to SiV(-2). Section 5.2 explicitly states that 'the matrix element for this transition is not yet known.' No value, estimate, or bound for this matrix element is given anywhere in the manuscript, and the caption of Figure 6 only says that matrix elements were determined with PBE and PBE-1/2. Since Section 2.3 states that rate equations are formulated for every charge-changing transition in Figure 3, the simulation behind Figure 6 must have used a specific value for this transition. Without that value, the prediction is not reproducible and could depend sensitively on an arbitrary input. The authors should report the matrix element used and, ideally, show that the qualitative outcome is robust when it is varied.
[Section 2.3, Equations (14)-(17)] The relaxation rates C_{i,j} of the auxiliary 'excitonic' states are introduced with the statement 'By choosing C_{i,j} sufficiently large, we recover a regime where emission is effectively suppressed,' but no numerical values are provided and no sensitivity analysis is performed. The final populations in Figure 6 result from the competition between radiative emission and these nonradiative relaxation channels. If the C values are large but finite, or if they differ from transition to transition, the predicted charge-state fractions could change, including the claimed 'completely double negative below 3.29 eV' outcome. Please quantify C_{i,j} (or demonstrate that the large-C limit is reached for all physically plausible values) and test the sensitivity of Figure 6 to this parameter.
[Sections 3 and 5.3] The rate equations require the density of states rho_q(epsilon) for each charge state and the transition dipole matrix elements for all processes in Figure 3. Neither the densities nor the matrix elements (beyond the generic statement 'determined with PBE and PBE-1/2') are tabulated or deposited. This makes the rate-equation results in Figure 6 not independently reproducible and prevents readers from checking the claimed closed set of DFT-calibrated rate equations. Please provide a complete table of the computed matrix elements and densities (or a data repository) so that the calculation can be reproduced.
[Title, Abstract, and Sections 5.2-5.3] The abstract and title state that the charge cycle of group IV vacancy centers is modeled, and Section 5.2 presents onset-energy diagrams for SiV, GeV, SnV, and PbV; however, rate equations and final charge-state populations are computed and shown only for SiV in Figure 6. For the other three centers, Section 5.2 says 'To properly study this we'll need the rate equations,' yet those equations are not provided. If the intended contribution is the method plus a SiV demonstration, the scope should be stated accordingly; if the claim is that the framework captures all four centers, the corresponding rate equations (or at least the input data needed to run them) should be included.

minor comments (5)

[Section 2.3] The sentence 'There a scissor operator is applied such that the density of state respects the onset energy' is grammatically garbled and does not define the scissor shift value or how it is applied to the DFT densities. Please rewrite and specify the shift used for each charge state.
[Section 5.3] The sentence 'we find that the final charge state completely the double negative charge state' is missing a verb; it should read 'is completely the double-negative charge state' or similar.
[Section 3.1.1] The phrase 'where only explicitly write the 4 highest energy eg states' is missing a subject ('we'). Please correct this and similar typos throughout the manuscript (e.g., 'a head' for 'ahead' in Section 2.1).
[Equation (17)] The density-of-states arguments such as rho_0(-epsilon_gamma) and rho_0(0) are not explained in a table or list; please define the sign convention and the meaning of the arguments to make the equation self-contained.
[Figure 6] The caption does not state the values of the relaxation rates C_{i,j} used in the simulation, nor the photon flux and irradiation time beyond the text of Section 5.3. Please add these parameters to the caption or the main text.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the DFT-calibrated rate equations are forward predictions; the unknown SiV(-1)* to SiV(-2) matrix element is a missing input, not a circular fit.

full rationale

The derivation chain is self-contained: onset energies are obtained from HSE06 formation-energy calculations, transition dipole matrix elements from PBE/PBE-1/2 wavefunctions, and the rate equations follow from Fermi's golden rule. No experimental data are fitted, and the comparison with the GeV experiment in Ref. [39] is a genuine forward prediction. The paper itself flags two input gaps: Section 5.2 states 'While the matrix element for this transition is not yet known' for the SiV(-1)* to SiV(-2) transition, and Section 2.3 introduces the unquantified C_{i,j} relaxation parameter to suppress emission. These are missing or assumed inputs that affect reproducibility, but they are not circular reductions: no fitted value is renamed as a prediction, and no step is equivalent to its own input by construction. Citations to [15] and [20] are external works, not self-citations. Therefore no circularity is found.

Assumptions & free parameters 2 free parameters · 7 assumptions · 1 invented entities

The paper's central predictions rest on the reliability of hybrid DFT formation energies, frozen-orbital transition dipoles, an imported Jahn-Teller state, and a model-specific fast-relaxation limit for auxiliary states. Most are standard domain assumptions; the scissor shift and the C-limit are paper-specific modeling choices. No independent benchmark against measured charge transition energies is provided.

free parameters (2)

C_{i,j} relaxation rates = not reported (sufficiently large)
Introduced in Section 2.3 to suppress emission from auxiliary states; the rate-equation results in Figure 6 assume large values that are never quantified.
Scissor operator shift = not reported
Applied in the Section 2.3 footnote so that DFT densities of states respect the calculated onset energies; the shift value is not given and it affects the photoionization rates.

assumptions (7)

domain assumption Hybrid DFT (HSE06) yields accurate formation energies for group IV vacancy centers.
All onset energies in Figures 4 and 5 derive from formation energies computed with this approximation, with no benchmark against measured charge transition energies.
domain assumption Frozen-orbital approximation for transition dipole moments.
Section 3.1.1 states "we assume that all single-electron orbitals are the same in the initial and final state"; this underlies every matrix element r_ij and the degeneracy-factor derivations.
domain assumption The product Jahn-Teller state of Ref. [15] describes the neutral excited state.
Equations (3) and (38) import this state without re-derivation, and the two-step ionization cross section depends on it.
ad hoc to paper Scissor operator aligns DFT densities of states to the calculated onset energies.
Footnote in Section 2.3; the scissor shift is a model adjustment, not an ab initio result, and its value is not reported.
ad hoc to paper Fast nonradiative relaxation of auxiliary states suppresses emission (C_{i,j} large).
Section 2.3, Equations (14)-(17); the charge-state accumulation results in Figure 6 depend on this limit.
domain assumption Phonon broadening prescriptions from Refs. [20-22] transfer to group IV defects.
Section 2.2.1 adopts these prescriptions with no independent validation for G4V centers.
domain assumption Low-lying defect levels do not contribute to photoionization in the energy ranges considered.
Section 5.3 admits that "photo-ionization from lower lying defect levels" is omitted; this is load-bearing for the high-energy (around 4 eV) SiV(0) prediction.

invented entities (1)

Auxiliary excitonic states (neutral defect plus conduction-band electron, negative defect plus valence-band hole)
purpose: Model the brief period after photon absorption during which emission is still possible, then relax to ground charge states with rate C; they allow absorption to be the only net charge-changing channel.
Introduced in Section 2.3 as bookkeeping states; no direct experimental observable is predicted for them and their relaxation rates are not measured.

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Pith. "Pith review of The charge cycle of group IV vacancy centers in diamond: From DFT to rate equations." pith.science (2026). https://pith.science/paper/C6OMAOW6

@misc{pith2026250419748,
  author       = {Pith},
  title        = {Pith review of: The charge cycle of group IV vacancy centers in diamond: From DFT to rate equations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/C6OMAOW6}},
  note         = {Machine review of arXiv:2504.19748}
}

abstract

The silicon vacancy center in diamond is a promising system for quantum technologies due to its exceptional optical and spin properties. This has led to great interest in the silicon-vacancy center as well as in the other group IV vacancy centers. In this work, we model the charge cycle of the group IV vacancy centers from the $-2$ to $0$ charge state. As a first step, we compute the onset energies for all relevant one- and two-step ionization processes. Based on these results, we then derive the rate equations using Fermi's golden rule.

Figures

Figures reproduced from arXiv: 2504.19748 by the authors.

**Figure 2.** The photoionization from the negative charge state to the neutral state (a) and the [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗

**Figure 3.** A scheme of the charge cycle of the SiV, where each an illustration of each calculation [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: The transition energies for the group IV vacancy centers in diamond. [PITH_FULL_IMAGE:figures/full_fig_p013_4.png]

**Figure 5.** Figure 5: Onset energies for the charge cycles of SiV, GeV, SnV, and PbV calculated base on [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]

**Figure 6.** Figure 6: The final concentration of the charge states of SiV for different energies of the [PITH_FULL_IMAGE:figures/full_fig_p015_6.png]

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Works this paper leans on

3 extracted references · 3 canonical work pages

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Reviewed August 16, 2026 · model on record in the stance chip above.

[1] [1]

Indistinguishable photons from separated silicon-vacancy centers in diamond

1A. Sipahigil, K. D. Jahnke, L. J. Rogers, T. Teraji, J. Isoya, A. S. Zibrov, F. Jelezko, and M. D. Lukin, “Indistinguishable photons from separated silicon-vacancy centers in diamond”, Phys. Rev. Lett. 113, 113602 (2014). 2E. Neu, D. Steinmetz, J. Riedrich-M¨ oller, S. Gsell, M. Fischer, M. Schreck, and C. Becher, “Single photon emission from silicon-vac...

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Electron–phonon processes of the silicon-vacancy centre in diamond

Manson, M. D. Lukin, and F. Jelezko, “Electron–phonon processes of the silicon-vacancy centre in diamond”, New Journal of Physics 17, 043011 (2015). 5J. P. Goss, R. Jones, S. J. Breuer, P. R. Briddon, and S. ¨Oberg, “The twelve-line 1.682 ev luminescence center in diamond and the vacancy-silicon complex”, Phys. Rev. Lett. 77, 3041–3044 (1996). 6J. P. Goss...

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Observation of an envi- ronmentally insensitive solid-state spin defect in diamond

Srinivasan, L. Loudin, M. L. Markham, A. M. Edmonds, et al., “Observation of an envi- ronmentally insensitive solid-state spin defect in diamond”, Science 361, 60–63 (2018). 8E. Bourgeois, J. Soucek, J. Hruby, M. Gulka, and M. Nesladek, “Photoelectric detection of nitrogen-vacancy centers magnetic resonances in diamond: role of charge exchanges with other...

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