1. January 24, 2005SZFKI-MFA Carbon Nanotube Learning Seminar1 Optical properties of carbon nanotubes I. (Absorption) Kamarás Katalin MTA SzFKI

2. January 24, 2005SZFKI-MFA Carbon Nanotube Learning Seminar2 Outline 1.Basics of optical properties 2.Selection rules 3.Polarization effects 4.Kataura plot 5.Isolated nanotubes

3. January 24, 2005SZFKI-MFA Carbon Nanotube Learning Seminar3 10 – 400 nm 15 – 1000 20 keV – 12 MeV 1 – 2.5 3 – 120 eV >0.3 mm 1 – 4 meV 0.5 – 1.5 eV -sugárzás 400 - 4000 12000 - 24000 <10 12 Hz TartományFrekvenciaHullámszám (cm -1 )EnergiaHullámhossz Rádióhullámok, mikrohullámok Szubmilliméter 10 11 – 10 12 Hz 10 -300.3 – 1 mm Távoli infravörös (FIR) 0.1 – 10 THz 10 - 7001 – 90 meV Infravörös (MIR) 12 – 120 THz 0.05 – 0.5 eV2.5 – 25 Közeli infravörös (NIR) 120 – 400 THz 4000 - 12000 Látható (VIS) 1.5 – 3 eV400 – 800 nm Ultraibolya (UV) Röntgen 50 eV – 120 keV0.01 – 10 nm 0.1 – 10 pm The electromagnetic spectrum

4. January 24, 2005SZFKI-MFA Carbon Nanotube Learning Seminar4 I 0 I T I R Reflexiós Abszorpciós spektroszkópia (transzmissziós) spektroszkópia Bolometrikus (direkt abszorpciós) spektroszkópia I A Typical optical measurement arrangements

5. January 24, 2005SZFKI-MFA Carbon Nanotube Learning Seminar5 Basics of optical properties We want to determine the complex dielectric function: SI ! (RTM not in SI) through the complex index of refraction: RTM: or the absorption coefficient: dispersionabsorption Measured: , n”, calculated:   f n’ is slowly varying with ,  ~  ” BEWARE!

6. January 24, 2005SZFKI-MFA Carbon Nanotube Learning Seminar6  ’,  ” n’, n” Frequency dependence of optical functions R Drude-Lorentz dielectric function:   from independent oscillators additive, but n not!  because of square root)  where absorption is strong, n’ also varies strongly! (because of dispersion relations)  where absorption is strong, reflectance is also high!

7. January 24, 2005SZFKI-MFA Carbon Nanotube Learning Seminar7 Fresnel’s equations for normal incidence: R large, if n’>>1 or n”>>n’ Reflectance spectroscopy Extraction of optical constants from reflectance: use of dispersion relations Kramers-Kronig (KK) transformation: n’, n”  ’,  ”,... Because of the integral, broad spectral range or reasonable extensions are needed!

8. January 24, 2005SZFKI-MFA Carbon Nanotube Learning Seminar8 if R<<1, Beer’s law (Lambert-Beer) specific (molar) absorption coefficient Absorption spectroscopy (from transmittance) not a definition! (measured  sometimes called “extinction coefficient”) Transmission can also be subject to KK analysis, if the spectral range is broad enough:

9. January 24, 2005SZFKI-MFA Carbon Nanotube Learning Seminar9 Optical functions of a transparent nanotube  ~ -log T and  ” ~  is a good approximation above 3000 cm -1 only! -log T is a reasonable approximation for the optical conductivity  ’=  ” rather than  ”

10. January 24, 2005SZFKI-MFA Carbon Nanotube Learning Seminar10 Optical functions for extended bands k-dependence: E c (k) – conduction band, E v (k) – valence band, M cv (k) – dipole matrix element  k=0, but k is not restricted If we neglect the k-dependence of the matrix elements, we obtain an expression containing the joint density of states n j (E): Parallel bands contribute most to the absorption

11. January 24, 2005SZFKI-MFA Carbon Nanotube Learning Seminar11 Band structure of nanotubes n,n (armchair) metallic n,m semiconducting n-m=mod 3 small-gap N. Hamada, S. Sawada, A.Oshiyama: PRL 68, 1579 (1992)

12. January 24, 2005SZFKI-MFA Carbon Nanotube Learning Seminar12 Density of states of nanotubes J.W. Mintmire, C.T. White: PRL 81, 2506 (1998) First approximation:(see talk of M. Veres)

13. January 24, 2005SZFKI-MFA Carbon Nanotube Learning Seminar13 Selection rules Selection rules: for E z :  m=0, parity change for E xy :  m= 1, no parity change z: 13 13,14 14,15 15 xy: 12 13, but not 13 14 z-polarized light: 0 A 0 - xy-polarized light: 0 E +1 + u

14. January 24, 2005SZFKI-MFA Carbon Nanotube Learning Seminar14 Depolarization (antenna effect)

15. January 24, 2005SZFKI-MFA Carbon Nanotube Learning Seminar15 Polarized absorption in nanotubes Due to depolarization, only tubes with their axis parallel to the field show a structured response Calculation: S. Tasaki, K. Maekawa, T. Yamabe: Phys. Rev. B 57, 9301 (1998) Experiment: N. Wang, Z.K. Tang, G.D. Li, J.S. Chen: Nature 408, 50 (2000)

16. January 24, 2005SZFKI-MFA Carbon Nanotube Learning Seminar16 Optical spectra of carbon nanotubes Selection rules: only symmetric transitons are allowed

17. January 24, 2005SZFKI-MFA Carbon Nanotube Learning Seminar17 Optical spectra of macroscopic nanotube samples Háttér:  -plazmon P. Petit, C. Mathis, C. Journet, P. Bernier: Chem. Phys. Lett. 305, 370 (1999) 1 eV = 8000 cm -1 FIR MIR NIR VIS UV Baseline subtraction of high-frequency absorption: “plasmons” (  perpendicular polarization tube-tube interaction in bundles

18. January 24, 2005SZFKI-MFA Carbon Nanotube Learning Seminar18 Kataura plot - calculated H. Kataura, Y. Kumazawa, Y. Maniwa, I. Umezu,S. Suzuki, Y. Ohtsuka, Y. Achiba: Synthetic Metals 103, 2555 (1999)

19. January 24, 2005SZFKI-MFA Carbon Nanotube Learning Seminar19 Kataura plot – improved (RTM) Tubes with the same diameter but different chiralities have different transition energies! Optical measurements (NIR,VIS) experimental Kataura plot

20. January 24, 2005SZFKI-MFA Carbon Nanotube Learning Seminar20 Transmission of nanotube film Z. Wu, Z. Chen, X. Du, J.M. Logan, J. Sippel, M. Nikolou, K. Kamaras, J.R. Reynolds, D.B. Tanner, A. F. Hebard A.G. Rinzler: Science 305, 1273 (2004)

21. January 24, 2005SZFKI-MFA Carbon Nanotube Learning Seminar21 Isolated nanotubes: absorption M.J. O’Connell, S.M. Bachilo, C.B. Huffmann, V.C. Moore, M.S. Strano, E.H. Haroz, K.L. Rialon, P.J. Boul, W.H. Noon, C. Kittrell, J. Ma, R.H. Hauge, R.B. Weisman, R.E. Smalley: Science 297, 593 (2002)