🔬 materials science

Identification of carbon-related color centers in hBN by high-resolution ab initio photoluminescence modeling

This paper demonstrates that extending force-constant embedding methodology to calculate high-resolution, vibrationally resolved photoluminescence lineshapes in hexagonal boron nitride successfully identifies the neutral carbon trimer ( $\mathrm{C_2 C_N}$ ) as the source of the 1.54 eV emission, overcoming the limitations of traditional supercell calculations in distinguishing between similar defect candidates.

Original authors: Vytautas Žalandauskas, Marek Maciaszek, Marianne Etzelmüller Bathen, Julius Janušonis, Tadas Paulauskas, Lukas Razinkovas

Published 2026-10-15

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CC BY 4.0

Original authors: Vytautas Žalandauskas, Marek Maciaszek, Marianne Etzelmüller Bathen, Julius Janušonis, Tadas Paulauskas, Lukas Razinkovas

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the microscopic world of quantum technology, scientists are hunting for tiny, reliable sources of single particles of light. These sources, known as single-photon emitters, are the building blocks for future quantum computers and ultra-secure communication networks. One of the most promising materials for hosting these light sources is hexagonal boron nitride, a substance that looks like a stack of atom-thin sheets. Within this material, tiny imperfections in the atomic grid—called defects—can trap electrons and cause them to glow with a specific color. The challenge lies in figuring out exactly what these imperfections are made of. Because different arrangements of atoms can produce light that looks almost identical, identifying the true structure of these glowing defects has been like trying to recognize a person by a blurry silhouette.

To solve this, researchers have turned to high-resolution modeling, a technique that simulates not just the color of the light, but the fine details of its sound. When a defect emits a photon, it also creates a tiny vibration in the surrounding crystal, similar to how a bell rings with a specific tone when struck. By calculating these vibrations with extreme precision, scientists can create a unique "fingerprint" for each type of defect. This new study demonstrates that this method works even in materials where atoms are strongly charged, a condition that makes the calculations notoriously difficult. The researchers successfully used this approach to identify the atomic makeup of several glowing defects, proving that the subtle ripples in the light spectrum can reveal the exact arrangement of atoms inside the crystal.

The team focused their efforts on a material called hexagonal boron nitride, which is prized for its ability to host bright, stable light sources that work at room temperature. However, for years, scientists have struggled to match the observed colors of these light sources to specific atomic structures. While some defects, like a pair of carbon atoms, had been identified, many others remained mysteries. The researchers suspected that carbon atoms, which often sneak into the crystal during its creation, were responsible for a large group of these emitters. Specifically, they wanted to test whether groups of three carbon atoms, known as trimers, were the source of the red and orange light seen in experiments. Previous theories had suggested that these three-atom groups might be responsible for light at a specific energy level, but the evidence was not definitive because the calculated light patterns looked too similar to those of other candidates.

To get a clearer picture, the researchers developed a sophisticated computer model capable of simulating the vibrations of a crystal containing thousands of atoms. Standard computer models are limited to small chunks of material, which often miss the long-range vibrations that create the fine details in the light spectrum. By using a technique that combines data from small, detailed simulations with the known behavior of the bulk material, the team could model a system large enough to capture these subtle features. They first tested their method on a known defect: a pair of carbon atoms responsible for ultraviolet light at 4.1 electron volts. Their simulation accurately reproduced the complex shape of the light spectrum, including a low-energy vibration peak that previous methods had missed. This success confirmed that their approach could handle the strong electrical forces present in this material, a hurdle that had prevented similar studies in the past.

With their method validated, the team turned to the mystery of the carbon trimers. They simulated two different arrangements of three carbon atoms: one where the atoms replaced two boron and one nitrogen atom, and another where they replaced two nitrogen and one boron atom. The simulations revealed distinct differences in how these two structures would vibrate and emit light. The results showed that the first arrangement, where the carbon atoms replace two nitrogens, produces a light spectrum that closely matches an experimental emitter known to glow at 1.54 electron volts. This finding suggests that this specific trimer is indeed the source of that particular red light.

However, the study also ruled out a long-held assumption. For some time, it was believed that carbon trimers were responsible for a different set of emitters that glow at around 2.1 electron volts, a color in the red-orange range. The researchers found that the calculated light patterns for their trimer models did not match the fine details of the spectra observed for these 2.1 electron volt emitters. The vibrations predicted for the trimers were simply too different from what was seen in the lab. This indicates that the trimers are unlikely to be the cause of the 2.1 electron violet light, forcing scientists to look for other atomic structures to explain those specific emitters.

The study concludes that high-resolution modeling of light spectra is a powerful tool for distinguishing between different atomic defects, even in complex materials. By analyzing the fine structure of the light, researchers can now tell the difference between a defect that is a pair of atoms and one that is a group of three, or between different ways those atoms can arrange themselves. This level of detail is crucial for the development of quantum technologies, as it allows scientists to identify and potentially engineer the exact defects needed for specific applications. The work confirms that carbon atoms play a significant role in creating light in hexagonal boron nitride, but it also clarifies that not all carbon-related defects are the same, and that the specific arrangement of atoms determines the precise color and character of the light they emit.

Technical Summary: Identification of carbon-related color centers in hBN by high-resolution ab initio photoluminescence modeling

Problem Statement
The structural identification of optically active defects (color centers) in hexagonal boron nitride (hBN) remains a significant challenge. While hBN is a promising platform for single-photon emitters (SPEs) due to its room-temperature stability and integration capabilities, the microscopic structures of many emitters, particularly in the near-infrared (NIR) and red-orange spectral ranges, are unconfirmed. A primary difficulty arises because different defect candidates can produce similar calculated photoluminescence (PL) lineshapes when using conventional modeling techniques. Standard first-principles calculations are limited by the size of computationally accessible supercells, which sample phonons too sparsely to resolve fine spectral details. Furthermore, the application of high-resolution vibrational modeling to strongly polar materials like hBN has been hindered by the complexity of long-range electrostatic interactions (LO–TO splitting) that are difficult to treat in defect supercells where translational symmetry is broken.

Methodology
The authors employ an advanced force-constant embedding methodology to calculate high-resolution, vibrationally resolved PL lineshapes. This approach extends previous work to the polar layered material hBN by:

Embedding Scheme: Combining the bulk Hessian of a pristine supercell (derived from a large $16 \times 16 \times 3$ repetition of the primitive cell, containing 3,072 atoms) with defect force constants obtained from explicit, smaller defect supercells ( $7 \times 7 \times 2$ , 392 atoms).
Handling Polar Interactions: To address the LO–TO splitting inherent in polar hBN, the authors calculate bulk force constants over a large real-space range to truncate dipole–dipole interactions far from the defect. They utilize a non-analytic term correction (Gonze and Lee formalism) for the pristine bulk but rely on a purely real-space treatment for the embedded defect, mitigating the issue by using a large cutoff radius.
Electronic Structure: Calculations utilize spin-polarized density functional theory (DFT). The $r2SCAN$ meta-GGA functional with $rVV10$ nonlocal van der Waals correction is used for phonon calculations and geometry optimization, while the HSE06 hybrid functional is used for zero-phonon line (ZPL) energy calculations. Excited states are modeled using the $\Delta$ -self-consistent-field ( $\Delta$ SCF) method.
Spectral Simulation: The electron–phonon coupling is described within the Huang–Rhys (HR) framework. The spectral function is calculated using the generating-function approach (Kubo and Lax) to obtain the optical lineshape at zero temperature, incorporating the full vibrational density of states from the embedded supercell (up to $40 \times 40 \times 4$ , 25,600 atoms).

Key Contributions and Results

Benchmarking on the 4.1 eV Carbon Dimer ( $C_{BCN}$ ):
The methodology was first validated against the well-identified carbon dimer defect ( $C_{BCN}$ ), responsible for the 4.1 eV UV emission. The embedding approach successfully reproduced the experimental low-temperature PL spectrum, including:
- A low-energy acoustic phonon peak at 10 meV, a feature inaccessible to direct supercell calculations due to sparse sampling of long-wavelength modes.
- Fine spectral features in the intermediate (40–145 meV) and high-energy (145–200 meV) regions, including a localized carbon-carbon stretching mode near 200 meV.
  This benchmark confirmed that the embedding methodology accurately captures the interplay between bulk-like phonons and localized defect vibrations in polar hBN.
Analysis of Carbon Trimers ( $C_2C_N$ and $C_2C_B$ ):
The authors applied the method to neutral carbon trimers, previously proposed as candidates for red-orange emission (ZPL $\approx$ 2.1 eV).
- Vibrational Fingerprints: The study revealed that while carbon trimers share general sideband features with the dimer (low-energy acoustic peaks and intermediate bulk-like features), their high-energy signatures differ. Unlike the dimer, which exhibits a spectrally isolated localized mode above the hBN band edge, the trimer vibrations hybridize with the host optical phonon continuum, appearing as quasi-localized resonances.
- Discrimination: The calculated PL lineshapes for $C_2C_N$ and $C_2C_B$ showed distinct differences in peak positions and Huang–Rhys factors ( $S_{tot} = 1.57$ for $C_2C_N$ vs. $1.83$ for $C_2C_B$ ).
- Re-assignment: The calculated PL lineshape and excitation energy of the neutral $C_2C_N$ trimer (ZPL $\approx$ 1.62 eV) were found to closely match the experimental low-temperature spectrum of an emitter with a ZPL at 1.54 eV (labeled PL1). Conversely, the results indicate that $C_2C_N$ is unlikely to be the source of emitters with ZPLs around 2.1 eV, challenging previous assignments based on lower-resolution spectral similarities.

Significance
The paper establishes high-resolution phonon-sideband modeling as a powerful tool for discriminating among candidate defect structures in polar materials. By successfully extending force-constant embedding to hBN, the authors demonstrate that:

Subtle spectral features, such as low-energy acoustic phonon peaks and fine structures in the phonon sideband, can be resolved and used as "fingerprints" to distinguish between defects that appear similar in coarse-grained models.
The specific vibrational signature of carbon-carbon bonds in hBN defects can be identified, distinguishing between localized modes (dimers) and hybridized resonances (trimers).
Careful treatment of long-range electrostatic interactions allows for accurate modeling in strongly polar layered materials, enabling the re-evaluation of defect assignments in hBN based on high-resolution spectral matching rather than just zero-phonon line energy or broad sideband shapes.

The study concludes that while the $C_2C_N$ trimer is a strong candidate for the 1.54 eV emitter, the identification of defects in the 2.1 eV range remains an open question, highlighting the necessity of high-resolution modeling to resolve the microscopic origins of hBN color centers.

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