“Probing Electronic Transitions in Individual Carbon Nanotubes by Rayleigh Scattering” Matthew Y. Sfeir, 1 Feng Wang, 2 Limin Huang, 3 Chia-Chin Chuang, 4 J. Hone, 4 Stephen P. O’Brien, 3 Tony F. Heinz, 2 Louis E. Brus 1 1 Department of Chemistry, 2 Departments of Physics and Electrical Engineering, 3 Department of Applied Physics and Applied Mathematics, 4 Department of Mechanical Engineering, Columbia University Nano-Optics Journal Club Andy Walsh January 12, 2006 Science, Vol 306, 1540, 26 November 2004

Outline Motivation - Why I Selected This Paper Brief Overview of Carbon Nanotube Electronic Structure The Experiment Supercontinuum Generation Results Summary

Why I Selected This Paper As stated by the authors, Raleigh scattering is usually discounted as a method for probing nano-scale objects since it is assumed that the signals will be prohibitively small. This is shown not to be the case (at least for carbon nanotubes). The experiment uses a high power broadband supercontinuum generated by femtosecond laser pulses and a photonic crystal fiber. 1 2 I intend to focus on the experimental technique which I believe will be of more interest to most of the group than the actual nanotube-specific results. Having said that, here’s a quick overview of carbon nanotube electronic structure… An elegant technique with a broad range of possible applications = If I start using nanotube terminology that I have failed to define, please stop me!

Carbon Nanotube Electronic Structure I Real Space k z along tube axis is continuous k  is quantized since  must be single valued  (x=0) =  (x=L) e ikx = e ik(x+L) k  =2m  /L m=-N/2 to N/2 kzkz kk k - Space kzkz kk Different wrappings lead to different optical and electronic properties…

Carbon Nanotube Electronic Structure II TB Graphene Electronic Band Structure + Quantized K ┴ = Bands J. Menendez, et al, ASU This is obviously a first approximation and there are many corrections that should be included, such as curvature effects, excitonic effects, etc. but, for our purposes, this picture is sufficient for now…

Full Empty Carbon Nanotube Electronic Structure III Ref 2 Fluorescence For single tube spectroscopy, this technique is time consuming and yields the energies of only two transitions E 22 (or higher) and E 11

The Experiment I (My interpretation….) Femtosecond Ti:Sapphire Photonic Crystal Fiber Focusing Objective Sample Collection To spectrometer and CCD Collecting elastically scattered photons Normalize by the excitation spectrum ( from Ref 3 )

The Experiment II SEM Nanotube Optical Image Slit Edges Raleigh Scattering

Supercontinuum Generation I Ref 3 “Supercontinuum generation is the formation of broad continuous spectra by propagation of high power pulses through nonlinear media … The term supercontinuum does not cover a specific phenomenon but rather a plethora of nonlinear effects, which, in combination, lead to extreme pulse broadening.”

Supercontinuum Generation II Ref 3

Supercontinuum Generation III Ref 4

Supercontinuum Generation IV Ref 5 “These simulations and measurements clearly showed that, while the input pulse can propagate large distances in these fibers without distortion, the continuum cannot. Thus- the optimal approach to supercontinuum generation is to use a short, ~1 cm, fiber. Indeed, using such a fiber, we have recently succeeded in generating a supercontinuum pulse only 25 fs long-considerably shorter than the 40-fs pulse that created it-and also much smoother and much more stable. This short-fiber continuum is not only a nearly ideal pulse for most broadband applications, but it is also potentially compressible to a few fs.” “In particular, for SC generated with femtosecond pulse pumping, the dominant contribution to the long wavelength extension of the SC has been shown to be associated with soliton break up combined with the Raman self-frequency shift whilst an important contribution to the short- wavelength portion of the SC is due to the associated transfer of energy into the normal dispersion regime via the generation of non-solitonic dispersive wave radiation.” According to Ref 4:

Supercontinuum Generation V Ref 3

Energy Intensity DOS “E 33 ”“E 44 ” Multiple Tubes “E 33 ” in (a) Excitonic Model Free-carrier Model “E 22 M ”DOS Results I ( Inconclusive ) σ(ω) ~ r 4 ω 3 | Є(ω)-1 | 2 Cross-section follows the dielectric function which “reflects the wavefunctions and electronic transitions”

Results II

Results III ω RBM = a + b / d t where d t is the nanotube diameter and a and b are fit parameters Raman spectra taken in reflection mode with a single laser line using a sharp notch filter to reject the laser light Raman provides complementary information (especially the RBM energy) to help make (n,m) identification “Radial Breathing Mode”“G Band”

Summary The authors demonstrate that “Rayleigh scattering spectra … can be obtained with high signal to noise ratio” from nano-scale sized objects. Those spectra can be obtained quickly (<1 min) over broad spectral ranges by use of a “white light source of laser brightness” directly probing the electronic levels of the sample. Though the results were inconclusive as to the nature of the electronic transitions (excitonic or free-carrier) in carbon nanotubes, the method allows for (1) quick discrimination between individual nanotube and bundles and (2) better (n.m) determination when coupled with Raman spectroscopy.

Additional References 2. S. Bachilo, et al, Science, Vol 298, 2361 (2002) 3. Hansen & Kristiansen, “Application Note: Supercontinuum Generation in Photonic Crystal Fibers” 4. A. Yariv, et al, Optics Letters, 24, 711 (1999) 6. E. Yablonovitch, PRL, 58, 2059 (1987) 7. S. John, PRL, 58, 2486 (1987) 5. Dudley, et al, Optics Express, 10, 1215 (2002) 8. J. C. Knight, et al, Optics Letters, 21, 1547 (1996)

Questions?