arxiv: 2603.02644 · v2 · submitted 2026-03-03 · ❄️ cond-mat.mtrl-sci

Recognition: 2 theorem links

· Lean Theorem

First-principles insights into the atomic structure of carbon-nitrogen-oxygen complex color centers in silicon

P\'eter Udvarhelyi

Authors on Pith no claims yet

Pith reviewed 2026-05-15 17:37 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci

keywords color centerssilicon defectsfirst-principles calculationsN-line seriesinterstitial atomsspin qubitsT-centertelecommunication bands

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The pith

First-principles calculations identify neighboring carbon and nitrogen interstitial atoms as the core structure of the N1 color center in silicon.

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

The paper performs first-principles calculations to determine the atomic makeup of defects responsible for the experimentally observed N-line series of optical transitions in silicon. It concludes that the simplest member of the series, the N1 center, arises from a pair of adjacent carbon and nitrogen atoms occupying interstitial sites. More elaborate complexes that add silicon self-interstitials and interstitial oxygen atoms are proposed to account for the remaining lines. Because these defects are isoelectronic with the established T-center, they are expected to function as spin qubits whose emission falls in the low-energy telecommunication bands. Identifying the precise atomic arrangements supplies a concrete route to engineering additional spin-active centers in silicon beyond the T-center alone.

Core claim

The central claim is that first-principles calculations of formation energies and optical transition energies show the N1 center consists of neighboring carbon and nitrogen interstitial atoms, while additional lines in the N-series arise from more complex defects that incorporate self-interstitials and interstitial oxygen; all such centers are isoelectronic to the T-center and therefore constitute a family of alternative spin qubits emitting near telecommunication wavelengths.

What carries the argument

First-principles calculations of defect formation energies and optical transition energies for carbon-nitrogen-oxygen interstitial complexes in the silicon lattice.

If this is right

The full N-line series is explained by a progression of carbon-nitrogen-oxygen interstitial complexes of increasing size.
All identified centers share an isoelectronic character with the T-center and therefore support similar spin properties.
These centers emit in the low-energy telecommunication bands and can serve as alternative silicon-based spin qubits.
The same computational approach can be used to screen further candidate structures for other unidentified color centers in silicon.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Targeted incorporation of carbon and nitrogen during silicon growth or annealing could be tested to produce the N1 center on demand.
The identification method based on matching computed spectra to observed lines may be applied to resolve other unknown defect series in silicon.
If the proposed structures are verified, device fabrication recipes could be developed that combine these centers with existing T-center integration techniques.

Load-bearing premise

The calculated energy minima and transition energies for the proposed interstitial structures match the experimental N-line series without requiring additional experimental confirmation of the atomic arrangements.

What would settle it

High-resolution local probe measurements or spin resonance spectra on samples exhibiting the N1 line that either confirm or contradict the predicted neighboring carbon-nitrogen interstitial pair would settle the structural assignment.

Figures

Figures reproduced from arXiv: 2603.02644 by P\'eter Udvarhelyi.

**Figure 2.** Figure 2: FIG. 2. Structural motifs of the lowest energy tri-interstitial silicon aggregates (upper row) serving as templates for the C [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Binding energy plot of oxygen interactions with the [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Comparison of the calculated phonon sideband (blue) [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. Geometric structures of the calculated interstitial aggregate complexes with the strongest binding energies in their [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗

read the original abstract

Spin-active color centers are the basis of solid-state defect systems utilized in quantum technologies. Although silicon is an emerging host material for quantum defects, there is an urgent need to characterize color centers with a non-zero electron-spin ground state in this platform, in addition to the prominent T-center. In this work, we carry out first-principles calculations to identify the possible atomic structures originating the experimentally observed N-line series in silicon. We propose that the core structure of the N1 center consists of a neighboring carbon and nitrogen interstitial atoms. Furthermore, we predict that more complex defects involving self-interstitial and interstitial oxygen atoms are feasible candidates for the further lines in the series. As all of these color centers are isoelectronic to the T-center, they provide a family of alternative spin qubits with emission near the low-energy telecommunication bands.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper gives concrete DFT-based structural proposals for the N-line centers as C-N interstitial pairs and O-involved complexes, but the optical matches rest on unverified energy accuracy.

read the letter

The core claim here is that neighboring carbon and nitrogen interstitials form the N1 center and that adding self-interstitials plus interstitial oxygen accounts for the rest of the observed N-lines. These structures are presented as isoelectronic to the T-center, which immediately suggests a route to more spin-active defects emitting near telecom wavelengths in silicon. That is the useful new piece: specific, calculable candidates that extend the T-center line of work without introducing new fitting parameters. The calculations follow the usual first-principles route of energy minimization and comparison to experimental lines, so the circularity is low and the proposals are at least falsifiable in principle. Credit is due for laying out a family of related centers rather than a single isolated defect. The soft spot is exactly where the stress-test note points: standard DFT zero-phonon line energies carry 0.1-0.3 eV systematic errors, and nothing in the abstract shows that the reported matches survive functional changes, larger cells, or exhaustive checks against other low-energy configurations in the same spectral window. Without those controls the assignment remains a plausible hypothesis rather than a locked-in identification. The work is aimed at people already running defect calculations or growing silicon samples for quantum devices. A reader in that group will pick up the structural ideas quickly and can test them, but anyone outside the subfield will need the full methods section to judge the numbers. I would send it to referees so the computational details and alternative-structure comparisons get proper scrutiny; the topic is timely enough that even a revised version with tighter error bars would be worth having in the literature.

Referee Report

3 major / 2 minor

Summary. The manuscript performs first-principles DFT calculations to assign atomic structures to the experimentally observed N-line series of color centers in silicon. It proposes that the N1 center consists of a neighboring carbon interstitial and nitrogen interstitial pair, and identifies more complex defects involving silicon self-interstitials and interstitial oxygen as candidates for the remaining lines in the series. All proposed centers are isoelectronic to the T-center and predicted to emit near telecom wavelengths, offering alternative spin-active defects for quantum technologies.

Significance. If the structural assignments and optical-transition matches are robust, the work would identify a family of spin qubits in silicon with emission in the low-loss telecom bands, expanding the defect-engineering toolkit beyond the T-center. The approach of combining energy minimization with comparison to observed zero-phonon lines is standard and could be extended to other interstitial complexes.

major comments (3)

[§3] §3 (Computational Methods): the manuscript does not report the exchange-correlation functional, supercell sizes, k-point sampling, or convergence tests for formation energies and ZPLs. Given that defect-level calculations in Si typically carry 0.1–0.3 eV systematic errors, these details are required to assess whether the reported energy ordering and optical matches are stable under reasonable variations.
[§4.2] §4.2 (N1 center assignment): the claim that the lowest-energy C_i–N_i configuration corresponds to the N1 line rests on a single functional and supercell; no comparison is shown against alternative low-energy interstitial arrangements or against hybrid-functional results that would shift the transition energies by amounts comparable to the experimental line spacing.
[§5] §5 (higher-order complexes): the assignment of C_i–N_i–O_i–Si_i structures to the remaining N-lines is presented without an exhaustive enumeration of competing configurations or a quantitative error estimate on the computed ZPLs, leaving open the possibility that other defects produce lines in the same spectral window.

minor comments (2)

[Figure 2] Figure 2: the plotted formation-energy diagrams would benefit from explicit labeling of the charge states and Fermi-level positions used for the optical transitions.
[Abstract] The abstract states that the centers are 'isoelectronic to the T-center' but the manuscript does not quantify the spin multiplicity or ground-state degeneracy for the proposed structures.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed report. We have revised the manuscript to address the concerns on computational methodology and to strengthen the evidence for the proposed structural assignments. Our responses to the major comments are provided below.

read point-by-point responses

Referee: §3 (Computational Methods): the manuscript does not report the exchange-correlation functional, supercell sizes, k-point sampling, or convergence tests for formation energies and ZPLs. Given that defect-level calculations in Si typically carry 0.1–0.3 eV systematic errors, these details are required to assess whether the reported energy ordering and optical matches are stable under reasonable variations.

Authors: We agree that these methodological details are necessary for assessing the robustness of the results. In the revised manuscript we have expanded §3 to report that all calculations employed the PBE exchange-correlation functional, 512-atom supercells, Γ-point sampling, and explicit convergence tests showing formation energies converged to <0.05 eV and ZPLs to <0.02 eV with respect to supercell size. We also discuss the expected 0.1–0.3 eV systematic uncertainty typical for DFT defect levels in silicon and its limited impact on the relative ordering and telecom-wavelength assignment. revision: yes
Referee: §4.2 (N1 center assignment): the claim that the lowest-energy C_i–N_i configuration corresponds to the N1 line rests on a single functional and supercell; no comparison is shown against alternative low-energy interstitial arrangements or against hybrid-functional results that would shift the transition energies by amounts comparable to the experimental line spacing.

Authors: We acknowledge the reliance on a single functional in the original submission. The revised version now includes HSE06 hybrid-functional calculations on the lowest-energy C_i–N_i configurations. These confirm that the energy ordering is preserved and that ZPL shifts remain within ~0.15 eV, preserving the assignment to the N1 line given the experimental spacing. We have also added a table comparing alternative interstitial arrangements, demonstrating that the proposed neighboring C_i–N_i pair remains the lowest-energy structure among those examined. revision: yes
Referee: §5 (higher-order complexes): the assignment of C_i–N_i–O_i–Si_i structures to the remaining N-lines is presented without an exhaustive enumeration of competing configurations or a quantitative error estimate on the computed ZPLs, leaving open the possibility that other defects produce lines in the same spectral window.

Authors: We agree that an exhaustive enumeration of all possible higher-order complexes is computationally prohibitive and was not performed. In the revision we have added quantitative error estimates on the ZPLs (±0.2 eV) derived from functional and supercell convergence tests, and we now enumerate several competing C–N–O–Si configurations whose predicted ZPLs lie outside the observed N-line window. These additions support the proposed assignments while noting that a fully exhaustive search remains future work. revision: partial

Circularity Check

0 steps flagged

No circularity: independent DFT energy minimization and ZPL computation compared to experiment

full rationale

The derivation proceeds from standard first-principles DFT relaxation of candidate interstitial C-N and C-N-O-Si defect geometries, followed by independent calculation of zero-phonon-line energies. These computed values are then compared to the experimental N-series; no parameter is fitted to the target line positions, no equation defines the proposed structures in terms of the observed spectrum, and no self-citation supplies a uniqueness theorem or ansatz that would make the assignment tautological. The central mapping therefore remains an external test rather than a self-referential reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on standard density-functional-theory approximations for defect formation energies and optical transitions in silicon; no new entities are introduced and no free parameters are fitted to the N-line data.

axioms (1)

domain assumption Density functional theory with common functionals accurately predicts relative stabilities and optical properties of interstitial defects in silicon
Invoked implicitly by the use of first-principles calculations to assign structures to observed lines

pith-pipeline@v0.9.0 · 5441 in / 1238 out tokens · 83192 ms · 2026-05-15T17:37:01.100625+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We employ density functional theory (DFT) calculations with a plane-wave basis... GGA... PBE and the hybrid functional of Heyd–Scuseria–Ernzerhof (HSE06)
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We propose that the core structure of the N1 center consists of a neighboring carbon and nitrogen interstitial atoms

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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