“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. Brus1

1Department of Chemistry, 2Departments of Physicsand Electrical Engineering, 3Department of AppliedPhysics and Applied Mathematics, 4Department 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 applications1 2+ =

If I start using nanotubeterminology that I have failed to define, please stop me!

Carbon Nanotube Electronic Structure I

Real Space• kz along tube axis is continuous• k is quantized since must be

single valued

(x=0) = (x=L)

eikx = eik(x+L)

k=2m/L m=-N/2 to N/2

kz

k

k - Space

kz

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 E22 (or higher) and E11

The Experiment I

(My interpretation….)

FemtosecondTi:SapphirePhotonic

CrystalFiber

FocusingObjective

Sample

Collection

To spectrometer and CCD

Collecting elastically scattered photons

Normalize by the excitation spectrum

( from Ref 3 )

The Experiment II

SEM

Nanotube

Optical ImageSlit 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

Inte

nsity

DOS“E33” “E44”

Multiple Tubes “E33” in (a)

Excitonic Model

Free-carrier Model

“E22M ” DOS

Results I

( Inconclusive )

σ(ω) ~ r4 ω3 | Є(ω)-1 |2

Cross-section follows the dielectric function which

“reflects the wavefunctions and electronic transitions”

Results II

Results III

ωRBM = a + b / dt

where dt is the nanotube diameterand 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, www.blazephotonics.com, “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?