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Optical properties of carbon nanotubes I. (Absorption)

Optical properties of carbon nanotubes I. (Absorption). MTA SzFKI. Kamar ás Katalin. Outline. Basics of optical properties Selection rules Polarization effects Kataura plot Isolated nanotubes. The electromagnetic spectrum. Tartomány. Frekvencia. Hullámszám (cm -1 ). Energia.

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Optical properties of carbon nanotubes I. (Absorption)

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  1. Optical properties of carbon nanotubes I.(Absorption) MTA SzFKI Kamarás Katalin SZFKI-MFA Carbon Nanotube Learning Seminar

  2. Outline • Basics of optical properties • Selection rules • Polarization effects • Kataura plot • Isolated nanotubes SZFKI-MFA Carbon Nanotube Learning Seminar

  3. The electromagnetic spectrum Tartomány Frekvencia Hullámszám (cm-1) Energia Hullámhossz Rádióhullámok, mikrohullámok <1012 Hz >0.3 mm Szubmilliméter 1011 – 1012 Hz 10 -30 1 – 4 meV 0.3 – 1 mm Távoli infravörös (FIR) 0.1 – 10 THz 10 - 700 1 – 90 meV 15 – 1000 Infravörös (MIR) 12 – 120 THz 400 - 4000 0.05 – 0.5 eV 2.5 – 25 Közeli infravörös (NIR) 120 – 400 THz 4000 - 12000 0.5 – 1.5 eV 1 – 2.5 Látható (VIS) 12000 - 24000 1.5 – 3 eV 400 – 800 nm Ultraibolya (UV) 3 – 120 eV 10 – 400 nm Röntgen 50 eV – 120 keV 0.01 – 10 nm -sugárzás 20 keV – 12 MeV 0.1 – 10 pm SZFKI-MFA Carbon Nanotube Learning Seminar

  4. Typical optical measurement arrangements I0 IT IR Reflexiós Abszorpciós spektroszkópia (transzmissziós) spektroszkópia Bolometrikus (direkt abszorpciós) spektroszkópia IA SZFKI-MFA Carbon Nanotube Learning Seminar

  5. Basics of optical properties We want to determine the complex dielectric function: SI ! (RTM not in SI) through the complex index of refraction: RTM: dispersion absorption or the absorption coefficient: Measured: a, n”, calculated: e If n’ is slowly varying with w, a ~ e” BEWARE! SZFKI-MFA Carbon Nanotube Learning Seminar

  6. Frequency dependence of optical functions e’, e” Drude-Lorentz dielectric function: • e 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! n’, n” R SZFKI-MFA Carbon Nanotube Learning Seminar

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

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

  9. Optical functions of a transparent nanotube • ~ -log T and e” ~ a is a good approximation • above 3000 cm-1 only! • -log T is a reasonable approximation for the optical conductivity s’=we” rather than e” SZFKI-MFA Carbon Nanotube Learning Seminar

  10. Optical functions for extended bands k-dependence: Ec(k) – conduction band, Ev(k) – valence band, Mcv(k) – dipole matrix element Dk=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 nj(E): Parallel bands contribute most to the absorption SZFKI-MFA Carbon Nanotube Learning Seminar

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

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

  13. Selection rules Selection rules: for Ez: Dm=0, parity change for Exy: Dm= 1, no parity change u z: 13 13,14 14,15 15 xy: 12 13, but not 13 14 z-polarized light: 0A0- xy-polarized light: 0E+1+ SZFKI-MFA Carbon Nanotube Learning Seminar

  14. Depolarization (antenna effect) SZFKI-MFA Carbon Nanotube Learning Seminar

  15. Polarized absorption in nanotubes Calculation: S. Tasaki, K. Maekawa, T. Yamabe: Phys. Rev. B57, 9301 (1998) Due to depolarization, only tubes with their axis parallel to the field show a structured response Experiment: N. Wang, Z.K. Tang, G.D. Li, J.S. Chen: Nature 408, 50 (2000) SZFKI-MFA Carbon Nanotube Learning Seminar

  16. Optical spectra of carbon nanotubes Selection rules: only symmetric transitons are allowed SZFKI-MFA Carbon Nanotube Learning Seminar

  17. Optical spectra of macroscopic nanotube samples Háttér: p-plazmon 1 eV = 8000 cm-1 UV VIS NIR MIR FIR P. Petit, C. Mathis, C. Journet, P. Bernier: Chem. Phys. Lett. 305, 370 (1999) • Baseline subtraction of high-frequency • absorption: • “plasmons” (p, s+p) • perpendicular polarization • tube-tube interaction in bundles SZFKI-MFA Carbon Nanotube Learning Seminar

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

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

  20. 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) SZFKI-MFA Carbon Nanotube Learning Seminar

  21. 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) SZFKI-MFA Carbon Nanotube Learning Seminar

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