# Ultrafast dynamics of carrier relaxation determining the quasi-1D and non-1D electronic behaviors in carbon nanostructures

Godai Noyama, Thomas Gauthier, Yusuke Arashida, Yui Iwasaki, Riyo Nagao, Yuri Saida, Nicolas Godin, Hiroo Suzuki, Yasuhiko Hayashi, Shota Ono, et al.

► To cite this version:

Godai Noyama, Thomas Gauthier, Yusuke Arashida, Yui Iwasaki, Riyo Nagao, et al. Ultrafast dynamics of carrier relaxation determining the quasi-1D and non-1D electronic behaviors in carbon nanostructures. Carbon Trends, 2025, 20, pp.100510. 10.1016/j.cartre.2025.100510. hal-05105335

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# Ultrafast dynamics of carrier relaxation determining the quasi-1D and non-1D electronic behaviors in carbon nanostructures

Godai Noyama<sup>a</sup>, Thomas Gauthier<sup>b,c</sup>, Yusuke Arashida<sup>d</sup>, Yui Iwasaki<sup>a</sup>, Riyo Nagao<sup>e</sup>, Yuri Saida<sup>a</sup>, Nicolas Godin<sup>b,c</sup>, Gaël Privault<sup>d,e</sup>, Hiroo Suzuki<sup>f</sup>, Yasuhiko Hayashi<sup>f,g</sup>, Shota Ono<sup>g,h</sup>, Roman Bertoni<sup>b,c,*</sup>, Masaki Hada<sup>d,h,*</sup>

## ARTICLE INFO

### Keywords:

- Carbon nanotubes

- van der Waals heterostructures

- Boron nitride nanotubes

- Carrier relaxation dynamics

- Transient absorption

- Dimensionality of carbon nanostructures

## ABSTRACT

We investigate the relaxation dynamics of photoexcited carriers in bundled few-walled carbon nanotubes (CNTs) and van der Waals (vdW) heterostructures of CNTs covered with boron nitride nanotubes (BNNT) using ultrafast transient absorption spectroscopy from the near-infrared to the ultraviolet spectral range. The relaxation constant of the photoexcited carriers in bundled CNTs decreases with the photon energy of the probe, conversely, that in vdW heterostructures is almost constant with respect to the photon energy. The energy dependence of the relaxation constants for the probing photon energy determines whether the bundled CNT materials show one-dimensional (1D) or non-1D electronic behavior. The bundled CNTs show a non-1D electronic character, and the vdW heterostructures show a quasi-1D electronic one. It suggests that the bundled structure and intercalation of the insulating BNNT layer strongly influence their electronic dimensionality. These insights, offering a precise understanding of material properties, are beneficial for designing future optoelectronic devices based on nanostructured materials.

## 1. Introduction

Electronic transport controlling the properties of nanostructured materials strongly relies on their dimensions. The dimensions of nano-structured materials are classified as zero-dimensional dots, one-dimensional (1D) wires, and two-dimensional (2D) sheets, exhibiting different properties from those in three-dimensional (3D) bulk materials. In general, the dimensions of nanostructured materials are determined by their shapes, i.e., nanostructured materials have at least one dimension between 0.1 and 100 nm [1–4]. However, a detailed understanding of the dimensionality based solely on the shape of these nanostructured materials is difficult. Here, we propose a method to investigate the electronic dimensional properties of carbon materials in terms of carrier relaxation using the dynamics of photoexcited carriers.

Within the Fermi liquid theory [5], the relaxation constant of carrier relaxation in 3D metals is determined to be proportional to the inverse square of the probe photon energy [6,7]. Apart from the Fermi liquid theory, literature experimentally shows that the decay constant of carrier relaxation in the 2D graphene or highly oriented pyrolytic graphite is proportional to the inverse of the probe photon energy [8–10], and that in 1D carbon nanotubes (CNTs) is constant with respect to the probe photon energy [11]. The electron density of states (DOS) plays an important role in the electron-electron scattering process. When an excited electron above the Fermi level collides with another electron, the decay time of the excited electron can be expressed by the combinations of the DOS and the distribution function within the random-k approximation [12]. This approximation implies that the photoexcited carriers relax faster with the number of states where the excited carriers

<footnote><sup>a</sup> Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8573, Japan</footnote>

<footnote><sup>b</sup> University of Rennes, CNRS, IPR (Institut de Physique de Rennes), UMR 6251, F-35000 Rennes, France</footnote>

<footnote><sup>c</sup> CNRS, University of Rennes, DYNACOM (Dynamical Control of Materials Laboratory), IRL 2015, The University of Tokyo, Tokyo, 113-0033, Japan</footnote>

<footnote><sup>d</sup> Institute of Pure and Applied Sciences, University of Tsukuba, Tsukuba 305-8573, Japan</footnote>

<footnote><sup>e</sup> College of Engineering Sciences, University of Tsukuba, Tsukuba 305-8573, Japan</footnote>

<footnote><sup>f</sup> Graduate School of Environmental, Life, Natural Science and Technology, Okayama University, Okayama 700-8530, Japan</footnote>

<footnote><sup>g</sup> Department of Sciences and Informatics, Muroran Institute of Technology, Muroran 050-8585, Japan</footnote>

<footnote><sup>h</sup> Tsukuba Research Center for Energy Materials Science (TREMS), University of Tsukuba, Tsukuba 305-8573, Japan</footnote>

<footnote>* Corresponding authors.</footnote>

<footnote>E-mail addresses: shotaono@muroran-it.ac.jp (S. Ono), roman.bertoni@univ-rennes.fr (R. Bertoni), hada.masaki.fm@u.tsukuba.ac.jp (M. Hada).</footnote>
can decay. Thus, the relaxation constant of photoexcited carriers strongly depends on the DOS of the materials, which is directly connected to the dimension of the materials in terms of carrier property. In the following, we address the question of free carrier dynamics in bundled few-walled CNTs. The photoexcited electrons are free to move along the CNT axis and in the radial direction (interlayer electron motions within a CNT and inter-CNT electron transports) of the bundled few-walled CNTs [13–15]. Thus, the bundled few-walled CNTs consist of 1D materials in shape; however, they may not exhibit 1D character as a whole system, especially when considering electronic properties. Comparing the dimension of bundled CNTs with that of van der Waals (vdW) heterostructures of CNTs covered with boron nitride nanotubes (BNNTs) should be interesting because the insulating BNNT layers may prevent the carrier transport in the radial direction, which as a consequence may influence on the dimensionality of the material.

CNTs exhibit excellent transport and mechanical properties at the nanoscale. Among CNTs, single-walled CNTs have higher thermal and electrical conductivity with higher mechanical strength than multi-walled CNTs [16–23]. In contrast, multi-walled CNTs have excellent heat resistance and chemical stability [24,25]. In general, multi-walled CNTs are fabricated in a low-cost fashion [26]. Few-walled CNTs, namely double-walled CNTs and triple-walled CNTs, exhibit characteristics similar to single-walled CNTs [27–30]. Few-walled CNTs are easily bundled to fabricate yarns or sheets via the dry-spinning method [26, 31–34], making them convenient for electronic devices. By stacking low-dimensional materials, so-called vdW heterostructures, unique characteristics related to their structural and electronic properties emerge [35–39]. Recently, studies have investigated electronic and phononic transports between the layers in vdW heterostructures of CNTs covered with BNNTs [40]. Our study aims to monitor the decay constant of the photoexcited carriers in bundled few-walled CNTs and vdW heterostructures of few-walled CNTs covered with multi-walled BNNTs using femtosecond transient absorption spectroscopy. The energy dependence of the decay constants for the probing photon energy should determine the dimensionality of the electronic transport in the bundled few-walled CNTs and the vdW heterostructures of CNTs covered with BNNTs.

## 2. Experimental

We chose few-walled carbon nanotubes (CNTs) and van der Waals (vdW) heterostructures of few-walled CNTs covered with multi-walled boron nitride nanotubes (BNNTs) for the materials under scrutiny. The synthesis process is provided in the Supplementary Materials [26]. Few-walled CNTs contain all types of CNTs with semiconducting and metallic characters [34]. The few-walled CNT sheet, as a whole, exhibits a semiconducting character with a small bandgap [15]. Raman spectra from the samples and their analyses are summarized in Fig. S1. Figs. 1(a) and 1(b) show optical micrographs and model illustrations of the bundled few-walled CNT sheet and the vdW heterostructures of few-walled CNTs covered with multi-walled BNNTs. The materials synthesis procedure is also given in Supplementary Materials. The bundled few-walled CNTs and the vdW heterostructures of few-walled CNTs covered with multi-walled BNNTs are labeled as samples I and II, respectively. The absorption spectrum of sample I is shown in Fig. 1(c). Since the CNT sheet contains CNTs with various diameters and chirality, a broad absorption is observed over a wide energy region [32]. The absorption spectrum of sample I has a maximum of around 4.5 eV, corresponding to the π-plasmonic peak. The absorption decreased below 4.5 eV because the DOS decreases in this region. We can observe dips at approximately 3.0 eV (UV region), 1.8 eV (visible region), and 0.73 eV (near-IR region), as marked with the red arrows, which may correspond to levels with a locally small DOS induced by van Hove singularity. These dip structures result in a band gap-like structure in the electronic structure of the samples. The absorption spectrum from sample II shows similar dip structures with a strong absorption peak of BNNTs at around ~6 eV [Fig. 1(d)] related to its electronic bandgap. In the following experiments, we photoexcited carriers using pump photons with energy (3.1 eV, 400 nm) slightly above the highest dip-like structure.

## 3. Results and discussion

First, the dynamics of photo-excited carriers in bundled few-walled CNTs (sample I) are discussed. Fig. 2(a) shows the transient absorption spectrum map from sample I probed in the 0.62–3.05 eV range

<figure><img src="image_2.png" /><figcaption>(b) Sample II</figcaption></figure>

<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /><figcaption>**Fig. 1.** Micrographs and model structures of (a) the bundled few-walled CNTs (sample I) and (b) the vdW heterostructures of CNTs covered with BNNTs (sample II). White scale bars in the micrographs correspond to 100 µm. Absorption spectra of (c) sample I and (d) sample II as a function of photon energy. The red and blue arrows show the dip-like structures and excited photon energy, respectively. The purple arrow shows the absorption peak of BNNT.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Fig. 2. Ultrafast transient spectrum from sample I. (a) Two-dimensional map of the transient spectrum as functions of photon energy (wavelength) and time delay. The single wavelength dynamics at (b) 1.3 eV and (c) 0.62 eV photon energies. The orange-shaded areas indicate the IRF. The red curves are fitting curves using Eq. (2). (d) Relaxation time constant of the carrier in bundled few-walled CNTs as a function of probe photon energy. The blue arrow indicates the kink position. The shaded areas show the relaxation constant below the IRF.</figcaption></figure>

following near-UV excitation (3.1 eV, 6 mJ/cm²). The details of the experiment are shown in Supplementary Materials. Upon photoexcitation, the absorption decreased on a time scale of tens to hundreds of femtoseconds because the photoexcited carriers in the CNTs from the valence band to the conduction band induced the Pauli blocking effect. Fig. 2(b) and (c) show single wavelength dynamics at probe photon energies of 1.3 eV and 0.62 eV, respectively. The relaxation of the photoexcited carriers gets slower at lower probe photon energies. The time constant of carrier relaxation ($\tau_1$) is estimated by using the following equation:

$$ \Delta A(t) = A_1 \cdot \left[ \frac{\exp\left(\frac{t - \frac{\sigma}{\tau_1}}{\sqrt{2}}\right) + 1}{2} \right] \cdot \exp\left[\frac{\left(\frac{\sigma}{\tau_1}\right)^2}{2} - \frac{t}{\tau_1}\right] + A_2 \cdot \left[ \frac{\exp\left(\frac{t - \frac{\sigma}{\tau_2}}{\sqrt{2}}\right) + 1}{2} \right] \cdot \exp\left[\frac{\left(\frac{\sigma}{\tau_2}\right)^2}{2} - \frac{t}{\tau_2}\right], \quad (2) $$

where $\Delta A$, $A_1$, $t$, and $\sigma$ are normalized transient absorption, amplitude change in the transient absorption for the carrier relaxation component, delay time, and the instrumental response function (IRF) (~0.07 or ~0.1 ps), respectively. $A_2$ and $\tau_2$ are amplitude changes in the transient absorption and time constant of long-life (lattice thermal) components. Eq. (2) is the convolution of the Gaussian IRF with the Heaviside mimicking the instantaneous electronic excitation and exponential decay for relaxation. The convolution of a Heaviside step function with a Gaussian function yields an error function (erf). Because the signal originating from the thermalization of the lattice is more significant in the near-IR region (<1.5 eV), as shown in Supplementary Materials (Fig. S2), the

normalized transient absorption was fitted with one component ($A_2 = 0$) in the UV to visible region and two components in the near-IR region. Time constants of the carrier relaxation at probe photon energies of 1.3 eV and 0.62 eV are estimated to be 0.15 ± 0.01 ps and 0.26 ± 0.01 ps, respectively. Since the decay constants related to the defects or trapping sites are slow on the pico-, nano-, or microsecond timescales, the observed fast decay constants at 100–300 fs should occur via electron-phonon coupling. The thermalization of the lattice occurs in a few picoseconds ($\tau_2 \sim 2$ ps) as shown in Fig. S3. Fig. 2(d) shows the probe photon energy dependence of the electronic relaxation time constant extracted by fitting. According to Fig. 2(d), the relaxation constants show a clear kink at around probe photon energy of 1.7 eV corresponding to the energy where the dip-structure is observed in the visible region [Fig. 1(a)]. The relaxation constants get rapidly slowed down by the dip-structure. Due to the lattice thermal effect, the carrier relaxation in the near-IR region, especially in the region of <0.9 eV, has a large deviation, and a clear change was not observed around the dip-structure in the near-IR region. We also found that the time constant gradually increases toward the lower energy side in the energy range where the dip-structures are not observed (0.75–1.3 eV). The gradual changes in the relaxation constant may be induced by the DOS decreases toward the lower energy side, as shown in the absorption spectrum. It is difficult to interpret the spectral region where the observed relaxation constant is almost constant above 1.9 eV. This observation might be due to the limitation of our time resolution in this given spectral region.

We study the dip structure near 1.5 eV and demonstrate that this likely originates from the presence of van-Hove singularity in the 1D electron DOS. To support this statement, we have performed theoretical calculations based on the hot electron relaxations in a model CNT band. We calculate the absorption spectra of photoexcited solids having the electron DOS $N(\epsilon)$ at an energy $\epsilon$. To investigate the impact of $N(\epsilon)$, we assume no energy-dependence of the matrix element of dipole transition, which is an excellent approximation to qualitatively reproduce the band-to-band absorption peaks of single-walled CNTs [41]. The
absorption spectra are then equivalent to the joint DOS (the density-of-states for the electron-hole systems) that is given by

$$A_{\text{model}}(\Omega) = \int_{-\infty}^{\infty} f(\epsilon)[1 - f(\epsilon + \hbar\Omega)]N(\epsilon)N(\epsilon + \hbar\Omega)d\epsilon, \quad (3)$$

where $f(\epsilon)$ is the electron distribution function, and $\hbar\Omega$ is the photon energy. In the present study, we assume that the electron-electron scattering occurs frequently so that $f(\epsilon)$ can be approximated to the Fermi-Dirac function with the electron temperature $T_e$ at any time, and $T_e$ decreases with time due to the energy transfer into phonons, as in the two-temperature model [42]. This assumption is supported by experimental results that evidence a timescale of electronic thermalization below 50 fs in low-dimensional material [43]. In this approximation, $A_{\text{model}}$ may be expressed as $A_{\text{model}}(\Omega, T_e)$. Whereas the quasi-equilibrium approximation (i.e., $T_e$ can be defined at any moment) will not hold strictly for the initial stage of the electron relaxation in ultrafast photoexcited systems [44,45]; such an approximation allows us to derive the decay time $\tau$ in an analytical way. In the present work, we considered two models: $N(\epsilon)$ is independent of $\epsilon$ (model 1) and exhibits two van Hove peaks $\epsilon = \pm E_0/2$ around the Fermi level (model 2). The details of these models and derivation of the decay time are provided in Supplementary Materials. The model 1 predicts that $A_{\text{model}}(\Omega, T_e)$ increases with $T_e$, which is inconsistent with experimental observations, where the absorption decreases in the initial response for the photon incident [Fig. 2(b) and (c)]. On the other hand, the model 2 predicts that the $A_{\text{model}}(\Omega, T_e)$ at a higher $T_e$ is smaller than at a lower $T_e$ [Fig. 3(a)], which is consistent with negative $\Delta\Lambda$. In addition, $A_{\text{model}}(\Omega, T_e)$ exhibits a significant increase at a specific energy $\hbar\Omega = E_0$ that corresponds to the optical transition between two van Hove peaks, where $E_0$ is set to be 1.5 eV. Furthermore, $\tau$ of $A_{\text{model}}(\Omega, T_e)$ increases with decreasing $\hbar\Omega$ and exhibits a kink at $\hbar\Omega = E_0$ [Fig. 3(b)]. This behavior is consistent with experimental observations in Fig. 2(d).

The dip structures yield significant points at the decay constant of the carrier relaxation in the materials; therefore, the dimension estimation of the nanostructured materials should be discussed using the probe energy range without dip structures. Fig. 4(a) shows that the time constant of carrier decay in sample I gradually increases toward the lower energy side in the energy range where the dip-structures are not observed (0.75–1.3 eV). The gradual changes in the relaxation constant may be induced by the DOS decreases toward the lower energy side, as shown in the absorption spectrum. As shown in Fig. 2(d), the relaxation time constants for probe energies between 1.6 and 3.1 eV are shorter than the IRF of our setup, which is limited to approximately 70 fs for the probe energy range of 0.75 to 3.1 eV. The relaxation time constants within the probe energy range of 1.3 to 1.7 eV are influenced by the dip structure at approximately 1.7 eV. Therefore, we cannot address the relaxation time constants in the probe photon energy range of 1.3 to 3.1 eV.

For the subsequent discussion, we refer to the relaxation constants in the probe photon energy range of 0.75 to 1.3 eV. As discussed in the introduction, the electronic relaxation constants of 3D materials are proportional to the inverse square of the probe photon energy, following the Fermi-liquid model [6,7]. The electronic relaxation constants of 2D and 1D materials are proportional to the inverse of the probe photon energy and are constant, respectively [8–11]. According to the estimation of dimensionnality in terms of carrier properties in carbon nanostructures, the observed dynamic in sample I shows a rather 2D-like predisposition in the intermediate tendency ($\tau \propto E^{-0.84 \pm 0.06}$) between 1D and 2D systems. Noting that the sample is not a single-layer sheet. The electronic transfer in the axis-direction of CNTs would be most effective, but the lateral- and depth-direction electron transfer also partially contributes to the electronic conduction in the bundled few-walled CNTs. Thus, we can conclude that the bundled few-walled CNTs exhibit a non-1D electronic character. In a second step, we investigate with the same methodology the 1D vdW heterostructure. The material is excited with 3.1 eV photon energy while probed over a broad spectrum ranging from 0.62 to 3.05 eV. The absorption spectrum of sample II [Fig. 1(b)] shows the energy range without dip structures at 0.75–1.3 eV. The relaxation dynamics of photo-excited carriers display time constant in the hundreds of femtosecond range. As shown in Fig. 4(a), the decay constant of carrier relaxation of sample II is almost flat with respect to the probe photon energy ($\tau \propto E^{-0.11 \pm 0.07}$). As previously mentioned, the bundled few-walled CNTs show non-1D electronic properties; however, the insulating BNNT layers block the carrier transport in the radial direction of the vdW heterostructures, resulting in quasi-1D electronic properties for the vdW heterostructures of CNTs covered with BNNTs [Fig. 4(b)]. The carrier relaxation constants of the vdW heterostructures of CNTs covered with BNNTs in the energy range of 0.8–2.3 eV, where the dip structure is observed, are provided in the Supplementary Materials (Fig. S3). Figure S3 shows a kink behavior similar to the few-walled CNTs around the dip structure. The lattice decay component is shown in Fig. S4. Figure S5 shows the fluence dependence of the electric decay constants in the near-infrared region (0.8 and 0.9 eV) for the bundled few-walled CNT sheet and the vdW heterostructures of few-walled CNTs covered with multi-walled BNNTs. The electric decay constants for both samples are almost constant in this excitation density range. Excitonic dynamics also play an important role in the electronic relaxation processes of different low-dimensional systems [46]. However, it suggests the linear character of the photo-response while excluding multi-photon absorption or exciton-exciton annihilation effects from contributing to the observed phenomenon.

## 4. Conclusions

In summary, we have performed ultrafast transient absorption

<figure><img src="image_7.png" /><figcaption>Fig. 3. (a) Theoretically calculated absorption and (b) normalized decay time ($\tau/\tau_{\text{temp}}$) as a function of photon energy. The red arrow shows the dip structure in the absorption spectrum, and the blue arrow shows the kink position. $\tau_{\text{temp}}$ is the relaxation time for the electron temperature due to the electron-phonon scattering.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>**Fig. 4.** (a) Relaxation time constants of the carrier in the bundled few-walled CNTs and the vdW heterostructures of CNTs covered with BNNTs as a function of probe photon energy (0.75–1.3 eV). (b) Schematic illustrations of dimensions of the materials in terms of carrier properties, where the few-walled CNTs show non-1D character and the vdW heterostructures of CNTs covered with BNNTs show quasi-1D character.</figcaption></figure>

spectroscopy on bundled few-walled CNTs and the vdW heterostructures of CNTs covered with BNNTs to investigate the relaxation dynamics of photoexcited carriers in quasi-1D systems. The experimental results suggest that the relaxation time constant of photoexcited carriers increases with decreasing photon energy in the bundled few-walled CNTs and is almost constant with respect to the photon energy in the vdW heterostructures of CNTs covered with BNNTs. This suggests that the bundled few-walled CNTs display a non-1D character and the vdW heterostructures of CNTs covered with BNNTs a rather 1D-like character. The electrons can freely move along the CNT axis and the radial direction in the bundled few-walled CNTs; however, the insulating BNNT layers block the electronic transport in the radial direction of the vdW heterostructures. Those electronic motions are adequate for determining the dimensionality of nanostructured materials. Furthermore, we found that the relaxation time constant of photoexcited carriers increases rapidly in near gap-like structures formed by van Hove singularity that derive from the 1D character of the material. In addition, theoretical models and calculations support these findings. The insights obtained from the combination of the experimental and theoretical works, determining the dimension of the materials, would be beneficial for designing future optoelectronic devices based on low-dimensional nanostructured carbon materials.

### CRediT authorship contribution statement

**Godai Noyama:** Writing – original draft, Investigation, Formal analysis, Data curation. **Thomas Gauthier:** Writing – review & editing,

Methodology, Investigation, Data curation. **Yusuke Arashida:** Writing – review & editing, Validation, Formal analysis, Conceptualization. **Yui Iwasaki:** Investigation, Data curation. **Riyo Nagao:** Investigation, Data curation. **Yuri Saida:** Investigation, Formal analysis, Data curation. **Nicolas Godin:** Writing – review & editing, Methodology, Investigation, Data curation. **Gaël Privault:** Writing – review & editing, Investigation, Formal analysis, Data curation. **Hiroo Suzuki:** Writing – review & editing, Resources. **Yasuhiko Hayashi:** Supervision, Resources. **Shota Ono:** Writing – review & editing, Writing – original draft, Software, Conceptualization. **Roman Bertoni:** Writing – review & editing, Writing – original draft, Validation, Supervision, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. **Masaki Hada:** Writing – review & editing, Writing – original draft, Validation, Supervision, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgments

This work was supported by JSPS KAKENHI Grants-in-Aid [Nos. JP22KK0225, JP23K17369, JP23H01101, and JP24KF0102] and the Japan Science Technology Agent (JST) FOREST Program [No.
JPMJFR211V]. R.B. acknowledges Agence Nationale de la Recherche (ANR) for funding under grant, ANR-21-CE30-0011-01 CRITICLAS. This work was also supported by Dynacom [International Research Laboratory between the CNRS, the University of Tokyo and the University of Rennes]. Some of the numerical calculations were done using the facility of the Supercomputer Center, the Institute for Solid State Physics, the University of Tokyo.

## Supplementary materials

Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.cartre.2025.100510.

## Data availability

Data will be available on request.

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