A.Jorio, M. A. Pimenta and P. T. Araujo. S. K. Doorn. S. Maruyama

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NT06: eventh International Conference on the cience and

Optical Transitions in Carbon Nanotubes and Population

Araujo Physics Department, UFMG, Belo Horizonte, Brazil.

1 NT06: eventh International Conference on the cience and Application of Nanotubes June 18-23, 2006 Nature of Optical Transitions in Carbon Nanotubes and Population Analysis A.Jorio, M. A. Pimenta and P. T. Araujo Physics Department, UFMG, Belo Horizonte, Brazil.. K. Doorn Chemistry Division, Los Alamos National Laboratory, UA. Maruyama Dept. of Mechanical Engineering, University of Tokyo, Tokyo, JAPAN M.. Dresselhaus (MIT) Y. Oyama, J. Jiang, R. aito (Tohoku)

2 Outline Introduction Resonance Raman cattering maps The exciton and the band-to-band pictures in carbon nanotubes? E 11 E 22 E 22 E 11 Band model exciton model PLE Bachilo et al. RR Fantini et al. Rayleigh feir et al.

3 The Resonance Raman cattering (RR) Maps Radia Breathing Mode RBM Fantini et al. PRL (2004) (E ii, ω RBM ) (n,m)

4 The Resonance Raman cattering (RR) Maps As grown Alcohol WNTs HiPco WNTs + D CoMoCAT WNTs + D (6,5) (6,5) E 11 M E 11 M Characterizing sample growth and...

5 ...sample processing CoMoCAT (Resasco) D vs. DNA wrapping... by Fantini et al.

6 The Kataura plot The optical transition energies E ii as a function of carbon nanotube diameter d t Proposed by H. Kataura in 1999, considering first neighbour π-only TB model E 22 E 11

7 The deviations from a simple graphene zone folding picture TB with curvature effect and σ-π hybridization + many-body effects imple tight binding σ-π hybridization Lattice distortion e-e and e-h interaction γ 1 γ 3 γ 2 ε? As shown by the ratio problem...

8 The ratio problem for E 22 and E 11 E 22 / E 11 smaller than 2! From EPL Bachilo et all. cience 298, 2361(2002) For a linear dispersion E 22 / E 11 = 2 2/d t 2/d t Why do we have the ratio problem?

9 Why do we have the ration problem? Optics without many-body effects Optics with many-body effects E 11 E 22 E 11 E 22 e-e attraction plus e-h repulsion gives rise to a net blueshift How is the big picture?

10 The big picture: E ii s obey a scaling law 2/d t 2/d t E 11 and E 22 follow a single scaling law when plotted as a function of p/d t E 11 (d t ) = E 22 (d t /2) E 22 E 11 E 22 PRL 2004 E 11 p = p/d t

11 All the physics is for 0.7 < d t <1.3nm and 0.6 < E ii < 2.7eV PL Bachilo et al. cience 298, 2361 (2002) RR Fantini et al. PRL (2004) E 33 What about d t > 1.3 nm? What about higher E ii?

12 The RR of alcohol WNTs E 44 E 33 Alcohol-WNTs Maruyama E 11 M E 22

13 RR on alcohol CVD WNTs Measurements over a broad energy (1.26 to 2.71eV) and diameter (0.7 to 2.3nm) range Now we have to analise the E ii and ω RBM!

14 Good agreement with published E 22, E 33 and E 44 Rayleigh by feir et al. RR by Fantini et al. RR ο PLE Bachilo et all. cience 298, 2361(2002)

15 The anomalous scaling law for the higher optical transitions E 33 E 44 E 22 E 11 Kane and Mele p =

16 E b (ev) The difference between the scaling laws The two photons experiment... E b Wang et al. cience 308, 838 (2005) Maultzsch et al. PRB72, 24402(R) (2005) Ma et al. JPCB109,15671 (2005)

17 Band-to-band vs excitons? Kane and Mele E b (ev) E b (ev) Exciton binding energy: E b = /d t (ev) E 11 and E 22 Excitons E 33 and E 44 free e-h pairs?

18 Measuring the E b energy Exciton binding energy: E b11 = /d t (ev) E b22 = /d t (ev)

19 Chirality dependence of E ii imilar to prediction by the extended tight binding (ETB) within experimental accuracy (~ ±30meV)

20 ummary 1 Optics is a well established tool to characterize single wall carbon nanotube samples. 2 E 11 and E 22 excitons 3 E 33 and E 44 band-to-band? 4 Exciton binding energy: E b = /d t

21 Acknowledgement M.A.Pimenta, C.Fantini, P.T.Araujo, I.O.Maciel, L. G. Cancado (UFMG) R H.B.Ribeiro and F.Plentz (UFMG) (PLE) L.O.Ladeira, R. G. Lacerda, A. Ferlauto (UFMG) (amples) A. P. antos and C. A. Furtado (CDTN) (Chemistry). K. Doorn (LANL) (RR) M.. Dresselhaus, G. Dresselhaus,. G. Chou, Ge. G. amsonidze (MIT) (exp and theory) R. aito, J. Jiang, A. Grueneis, N. Kobayashi, Y.Oyama (Tohoku) (theory) H. Chacham (UFMG), R. B. Capaz (UFRJ),. G. Louie (Berkeley) (Theory). Maruyama (TU), M. trano (UI), D. Resasco (UO). A.M.Rao (samples)

Chirality and energy dependence of first and second order resonance Raman intensity

NT06: 7 th International Conference on the Science and Application of Nanotubes, June 18-23, 2006 Nagano, JAPAN Chirality and energy dependence of first and second order resonance Raman intensity R. Saito