Optical transitions in semiconducting zigzag carbon nanotubes with small diameters: A first-principles broad-range study
Bibliographic record
Abstract
We study all possible band-to-band transitions between 12 valence and 16 conduction bands of (8,0), (10,0), and (7,0) nanotubes and calculate the corresponding dipole moments using first-principles methods in a wide ultraviolet-visible-infrared range of photon energies. The goal is to investigate the optical transitions and the selection rules for nanotubes with small diameters in a broad range of energies, taking into account the curvature and rehybridization effects on the dipole moment. Our calculations show the conservation of a modified quantum number, $\stackrel{\fontencoding{LECO}\selectfont\char177{}}{m}$, for all the transitions and reversal of the horizontal parity. Besides the $\ensuremath{\pi}\text{\ensuremath{-}}{\ensuremath{\pi}}^{\ensuremath{\ast}}$ transitions, we observe the possibility of $\ensuremath{\pi}\text{\ensuremath{-}}{\ensuremath{\sigma}}^{\ensuremath{\ast}}$, $\ensuremath{\sigma}\text{\ensuremath{-}}{\ensuremath{\pi}}^{\ensuremath{\ast}}$, and $\ensuremath{\sigma}\text{\ensuremath{-}}{\ensuremath{\sigma}}^{\ensuremath{\ast}}$ transitions. In fact, the maximum dipole moment for the three nanotubes corresponds to the transition between valence and conduction bands that are both of $\ensuremath{\sigma}$ nature. The maximum transition rate for an (8,0) nanotube happens at approximately 1.42 eV, corresponding to the transition between the first valence and fourth conduction bands and mapping to the infrared region. The maximum of transition rate for (10,0) and (7,0) nanotubes happens at 0.79 eV and 3.03 eV, respectively. There exist high absorption probabilities in the infrared and visible region in all three nanotubes. Also, high absorption probability in the low ultraviolet region is demonstrated, mostly as a result of $\ensuremath{\sigma}\text{\ensuremath{-}}{\ensuremath{\sigma}}^{\ensuremath{\ast}}$ transitions.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".