# Exciton Kataura Plot Page

## The Kataura plot by Saito Lab

We are frequently asked to share our numerical database of the Kataura plot.
This page is then created for nanotube researchers who wish to assign the (n,m) value from:

1. Optical transition energies Eii
Especially the environmental effects on Eii are taken into account for several surrounding materials.
2. Raman intensity of radial breathing modes (RBM)
Based on exciton programs within the extended tight binding (ETB) method.

Most of the descriptions of the data are already given in the papers mentioned in the section "how to cite".
However, we also give some brief descriptions below.

1. Calculated Eii with constant κ = 2.22
2. Without considering environmental effects, the following Kataura plot is already good enough to assign a bundled SWNT sample with medium diameter of about ~1.4 nm.
- Available data (ver. 1.03):

3. Calculated Eii with κ function (considering environmental effects):
• Eii for any environment with respect to the supergrowth (SG) sample EiiSG is calculated using the following formula:
Eii = EiiSG - Čκ [A + B(p/dt) + C(p/dt)2] ...(1)
where A, B, and C are the fitting parameters depending on our sample;
p is the nanotube cutting line index for each Eii transition, i.e.
p = 1, 2, 4, 5, 7, 8, ... for E11S, E22S, E33S, E44S, E55S, E66S, ... (S-SWNTs)
p = 3, 6, 9, 12, ... for E11L, E11H, E22L, E22H, ... (M-SWNTs)
Čκ = Cκ/CκSG is unique for each surrounding material system.
• The Cκ values are obtained from fitting dielectric constant:
κ - 1 = Cκ [p0.8 (1/dt)1.6 (1/lk)0.4 - 1.39] ...(2)
Once we know the Cκ value for a specific SWNT sample, we can extrapolate all Eii for that sample using Eq. (1).
• In the case of SG, AACVD (alcohol-assisted CVD), and HiPco we can use
A = 42.8 meV, B = 46.34 meV nm, C = 7.47 meV nm2.
(If the values of A, B, and C here are not good for your sample, please send us your data and we will recalculate these parameters.
In our experience we could minimize the discrepancy between theory-experiment down to 50 meV).

- Available data (ver. 1.03):
• Eii for the standard supergrowth (SG) sample (Cκ = 0.84): download (*.xls, 140kb)
• Cκ values for some environment:  Measurement Raman spectroscopy (RRS) Photoluminiscence (PL) Synthesis method(Environment) SG(as-grown) AACVD(as-grown) HiPCO(SDS)b) HiPCO(SDS)b,c) AACVD(hexane)c) AACVD(Chloroform)c) air-suspended SWNTd) air-suspended SWNT + BSTd,e) Cκ 0.84 +/- 0.03 1.19 +/- 0.02 1.28 +/- 0.05 1.29 +/- 0.05 1.49 +/- 0.04 1.73 +/- 0.06 1.28 +/- 0.03 0.84 +/- 0.05 Čκa) 1.00 1.42 1.52 1.54 1.77 2.06 1.52 1.00
• a)Here we define: Čκ = Cκ/CκSG.
b)The Čκ values from two different measurements (PL and RRS) are within their error bars.
c)The experimental Eii values used in the κ calculations are obtained from Y. Ohno et al., phys. stat. sol. (b) 244, 4002 (2007).
d)The experimental Eii values used in the κ calculations are obtained from P. Finnie et al., Phys. Rev. Lett. 94, 247401 (2005).
e)BST = Bandgap Shift Transition, which makes the air evaporated by temperature.

5. RBM Raman intensity
6. The resonance Raman intensity is calculated for several chiralities with dt = 0.6-1.6 nm
- Available data (ver 1.02):
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## How to cite

If you use the data in this webpage for any presentation, please cite the following papers:
1. For the optical transition energies with the environmental effect correction:

• A. R. T. Nugraha, R. Saito, K. Sato, P. T. Araujo, A. Jorio, and M. S. Dresselhaus, Dielectric constant model for environmental effects on the exciton energies of single wall carbon nanotubes, Appl. Phys. Lett. 97, 091905 (2010), doi:10.1063/1.3485293

• K. Sato, R. Saito, J. Jiang, G. Dresselhaus, and M. S. Dresselhaus, Discontinuity in the family pattern of single-wall carbon nanotubes, Phys. Rev. B 76, 195446 (2007), doi:10.1103/PhysRevB.76.195446

2. For the Raman intensity:

• K. Sato, R. Saito, A. R. T. Nugraha, S. Maruyama, Excitonic effects on radial breathing mode intensity of single wall carbon nanotubes, Chem. Phys. Lett. 497, 94 (2010).doi:10.1016/j.cplett.2010.07.099
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If you have experimental data for a specific surrounding material not mentioned in this page, please send us the data.
We may help in analyzing them and send you back.

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## Restriction for usage

You have to agree with the following restriction if you use the data from this page.
1. The usage of this data is purely for science.
2. There is no responsibility from us for any loss or damage when you use the data.
3. The data might be updated when the programs are improved.
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## References on Raman spectroscopy and excitons in carbon nanotubes

### Review articles/thesis:

1. Raman spectroscopy of graphene and carbon nanotubes, R. Saito, M. Hofmann, G. Dresselhaus, A. Jorio, M. S. Dresselhaus, Advances in Physics 60, 413-550, (2011).
2. Exciton Photophysics of Carbon Nanotubes, M. S. Dresselhaus, G. Dresselhaus, R. Saito, A. Jorio, Annu. Rev. Phys. Chem. 58, 719-747, (2007).
3. Raman Spectroscopy of Carbon Nanotubes, M. S. Dresselhaus, G. Dresselhaus, R. Saito, and A. Jorio, Physics Reports 409, 47-99 (2005).
4. Exciton environmental effects of single wall carbon nanotubes, Ahmad R. T. Nugraha, Master Thesis, Tohoku University (2010).

### Original papers:

1. Excitonic Effects on Raman Intensity of Single Wall Carbon Nanotubes, Kentaro Sato, Ahmad R. T. Nugraha and Riichiro Saito, e-Journal of Surface Science and Nanotechnology 8, 358-361 (2010).
2. Exciton energy calculations for single wall carbon nanotubes, R. Saito, K. Sato, P. T. Araujo, A. Jorio, G. Dresselhaus, M. S. Dresselhaus, Phys. Stat. Sol. B 246, 2581-2585, (2009).
3. Diameter Dependence of the Dielectric Constant for the Excitonic Transition Energy of Single-Wall Carbon Nanotubes, P. T. Araujo, A. Jorio, M. S. Dresselhaus, K. Sato, R. Saito, Phys. Rev. Lett. 103, 146802-1-4, (2009).
4. Dependence of exciton transition energy of single-walled carbon nanotubes on surrounding dielectric materials, Y. Miyauchi, R. Saito, K. Sato, Y. Ohno, S. Iwasaki, T. Mizutani, J. Jiang, S. Maruyama, Chem. Phys. Lett. 442, 394-399, (2007).
5. Chirality dependence of exciton effects in single-wall carbon nanotubes:Tight-binding model, J. Jiang, R. Saito, Ge. G. Samsonidze, A. Jorio, S. G. Chou, G. Dresselhaus, and M. S. Dresselhaus, Phys. Rev. B 75, 035407, (2007).
6. Exciton-photon, exciton-phonon matrix elements, and resonant Raman intensity of single-wall carbon nanotubes, J. Jiang, R. Saito, K. Sato, J. S. Park, Ge. G. Samsonidze, A. Jorio, G. Dresselhaus, and M. S. Dresselhaus, Phys. Rev. B 75, 035405, (2007).
7. Photoluminescence and population analysis of single walled carbon nanotubes produced by CVD and pulsed-laser vaporization methods,T. Okazaki, T. Saito, K. Matsuura, S. Ohshima, M. Yumura, Y. Oyama, R. Saito, S. Iijima, Chem. Phys. Lett. 420, 286-290 (2006).
8. Carbon nanotube population analysis from Raman and photoluminescence intensities, A. Jorio, C. Fantini, M. A. Pimenta, D. A. Heller, M. S. Strano, M. S. Dresselhaus, Y. Oyama, J. Jiang, and R. Saito, Appl. Phys. Lett. 88, 023109 (2006).
9. Phonon-assisted excitonic recombination channels observed in DNA-wrapped carbon nanotubes using Photoluminescence spectroscopy, S. G. Chou, F. Plentz Filho, J. Jiang, R. Saito, D. Nezich, H. B. Ribeiro, A. Jorio, M. A. Pimenta, Ge. G. Samsonidze, A. P. Santos, M. Zheng, G. B. Onoa, E. D. Semke, G. Dresselhaus, and M. S. Dresselhaus, Phys. Rev. Lett. 94, 127402, (2005).
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## Contact

Any questions? Feel free to ask us:

 A. R. T. Nugraha (nugraha) K. Sato (kentaro) R. Saito (rsaito)
(e-mail addresses are combined with @flex.phys.tohoku.ac.jp)