NT06: 7th International Conference on the Science and Application of Nanotubes,

June 18-23, 2006 Nagano, JAPAN

Chirality and energy dependence of firstand second order resonance Raman intensity

R. Saito（Tohoku Univ. CREST JST）J. Jiang, K. Sato, Y. Oyama, J.S. Park, G. S. Chou, G. Samsonidze,

A. Jorio，M. A. Pimenta, A. G. Souza-Filho, G. Dresselhaus, M.S. Dresselhaus

Dept. Physics, Tohoku Universityand CREST JSThttp://flex.phys.tohoku.ac.jp/~rsaito/

e-mail: rsaito@flex.phys.tohoku.ac.jp

東北大学TOHOKU UNIVERSITY

Intensity calculation of PL and Raman spectra-- Not all SWNTs are bright. --

Emission wavelength (nm)

Excitation wavelength (nm)

PhotoluminescenceWeisman et al.2002

ELaser(eV)

E22S

E11M

E33S

ωRBM (cm-1)

Resonance RamanFantini et al.2003

Phonon associated PLS. G. Chou et al.2005

Relative Raman intensity(n,m) dependenceRBM,G, D, G’-band

Photoluminescence Intensity(n,m) population analysisphonon associated relaxation processExciton based phenomena

Type dependent PLMaruyama et al.2004

Excitation wavelength(eV)

Emission wavelength (eV)

Pressure dependent RamanA. Souza-Filho et al.2006

2n+m family in SWNTR. Saito et al., Phys. Rev. B, 72, 153413 (2005)

2n+m = const familytype I ‒ type II separation

(example)

(8,0), (7,2), (6,4)

→ 2n+m = 16 type I family

Brillouin zone (BZ)

0 : metal1 : type I SC2 : type II SC

Family

mod (2n+m, 3) =

type I type II

K

K’

SWNT BZ2D graphite BZ

2n+m and n-m family in SWNT

K

type I

K

type II

1 2

1

2

222n+m=19

16

27

24

21

30

17

20

23

2 1=−=+

)3,(mod)3,2(mod

mnmn

E1110741258

n - m=

n - m = 2R. Saito et al., Appl. Phys. Lett.60, 2204 (1992)

ωRBM (cm-1)

ELaser (eV)

•Raman measurement 76 different laser lines(ArKr, HeNe, 3 different dyes, Ti:Sapphire).•Dilor XY triplemonochromator•Calibration: CCl4Raman spectra- Sample from M.Strano

Spectroscopic measurements on Spectroscopic measurements on HiPco Nanotubes in Solution HiPco Nanotubes in Solution (SDS wrapped)(SDS wrapped)

PhotoluminescenceWeisman et al.2002

E22S

Valley of metals E11

ME33

S

Fantini et al. Unpublished

LightLightemissionemission

Electron phonon Electron phonon interactioninteraction

LightLightabsorptionabsorption

Resonance Raman Intensity

AFM Images

• 1st order Raman

• 2nd order Raman

k1

k3

k2

δα

β

γ

k0

k1

k2

α

β

γ

k0

2nd order Raman1st order Raman

RBM: Family pattern of el-phonon matrix elementJ. Jiang et al, Phys. Rev. B 72 235408 (2005)

Type I Type IIdt dependence q dependence

Type I Type II

node node

n - m = 2• n-m family pattern, node

• 1/dt dependence

•Type I > type II

Family pattern for G-band matrix elementJ. Jiang et al, Phys. Rev. B 72 235408 (2005)

G+ (LO) Type I Type IIG-(TO)

Type I

Type IIG+: not sensitive on diameter and q

G-: sensitive both on diameter and q

(G- near armchair)

Z. Yu, L. E. Brus, J. Phys. Chem. B 105, 6831 (2001)

ExpZ

A

Photo-Luminescence (PL)

Emission wavelength (nm)Excitation wavelength (nm)

Optical Process of PL

PL Intensity chirality dep.type I ‒ type II dep.

PL from diffrent (n,m)

DOS

energy

h+

e-

M. J. O’Connel et al., Science 297, 593 (2002)S. M. Bachilo et al., Science 298, 2361 (2002)Y. Miyauchi et al., Chem. Phys. Lett. 387, 198 (2004)

E11

E22

(1) photo absorption

(2) relaxation by phonon

(3) photo emission

Chirality dependence of Photo-LuminescenceA. Gruneis et al, Chem. Phys. Lett. 387, 301 (2004)

S. Maruyama et al, nano-carbon (2004)

PL is strong around Armchair.type I > type II (for E22 absorption)

0.75 1 1.250

10

20

30

Tube diameter (nm)

Chi

ral a

ngle

(deg

.)

9,19,1

8,38,3

6,56,57,57,5

7,67,68,68,6

8,78,7

8,48,49,49,4

9,59,5

7,37,310,510,5

9,29,2 10,210,2

10,310,311,311,3

11,111,1

10,010,0 11,011,0

12,112,1

13,013,0

12,212,2

6,46,49,79,7

10,610,6

13,213,2

12,412,4

9,89,810,810,8

11,611,6

12,512,5 13,513,5

13,313,3

15,115,1

11,411,4

8,18,1

14,014,0

14,114,1

16,016,0

15,2

14,314,3

11,711,7

9,19,1

8,38,3

6,56,57,57,5

7,67,68,68,6

8,78,7

8,48,49,49,4

9,59,5

7,37,310,510,5

9,29,2 10,210,2

10,310,311,311,3

11,111,1

10,010,0 11,011,0

12,112,1

13,013,0

12,212,2

6,46,49,79,7

10,610,6

13,213,2

12,412,4

9,89,810,810,8

11,611,6

12,512,5 13,513,5

13,313,3

15,115,1

11,411,4

8,18,1

14,014,0

14,114,1

16,016,0

15,2

14,314,3

11,711,7

Theory A. Gruneis et al.

Exp. S. Maruyama et al.

S. M. Bachilo et al., JACS, 125 (2003) 11186.

type I type II

A

Z

AZ

Induced absorption Spontaneous emissionphonon emission at E22

PL intensity at E11

quantum efficiency = 3% Evaluation of (n,m) abundance

Fluorescence spectroscopy

HiPCO sample

Y. Miyauchi et al. Chem. Phys. Lett. 387 198 (2004)Y. Oyama et al, Carbon, 44, 873 (2006)

small diameter, near armchairPL intensity large

polarization // tube axis

0.75 1 1.250

10

20

30

Tube diameter (nm)C

hira

l ang

le (d

eg.)

9,19,1

8,38,3

6,56,57,57,5

7,67,68,68,6

8,78,7

8,48,49,49,4

9,59,5

7,37,310,510,5

9,29,2 10,210,2

10,310,311,311,3

11,111,1

10,010,0 11,011,0

12,112,1

13,013,0

12,212,2

6,46,49,79,7

10,610,6

13,213,2

12,412,4

9,89,810,810,8

11,611,6

12,512,5 13,513,5

13,313,3

15,115,1

11,411,4

8,18,1

14,014,0

14,114,1

16,016,0

15,2

14,314,3

11,711,7

9,19,1

8,38,3

6,56,57,57,5

7,67,68,68,6

8,78,7

8,48,49,49,4

9,59,5

7,37,310,510,5

9,29,2 10,210,2

10,310,311,311,3

11,111,1

10,010,0 11,011,0

12,112,1

13,013,0

12,212,2

6,46,49,79,7

10,610,6

13,213,2

12,412,4

9,89,810,810,8

11,611,6

12,512,5 13,513,5

13,313,3

15,115,1

11,411,4

8,18,1

14,014,0

14,114,1

16,016,0

15,2

14,314,3

11,711,7

Theory (Oyama) Exp (Miyauchi)

Population of (n,m) by PL Iexp/Ical Y. Oyama et al, Carbon, 44, 873 (2006)

Population analysis:

1. PL Iexp/IcalY. Oyama et al, Carbon, 44, 873 (2006).

2. I(PL)/I(Raman)A. Jorio et al., APL, 88, 023109, (2006).

3. Iexp/Ical and TEMT. Okazaki, CPL, 420286 (2006)

population analysis

A. Jorio, et al., Appl. Phys. Lett. 88, 023109 (2006).

type I type II

Expe

rimen

tTh

eory

TEM PLfitting withGaussians

pulsed-laser vaporization

CVD

T. Okazaki, et al., Chem. Phys. Lett. 420, 286 (2006).

Summary of PL and Raman intensity

RBM intensity zigzag G+ intensity no chirality dep. G- intensity armchair PL intensity armchair

Type I > Type II (optical absorption)(E22-E11) vs phonon energyresonance width (relaxation time)

Population analysis for Raman and PL is available.

Method: Our computational library for SWNTs-- What do we need for intensity calculation? --

Electron and phonon energy dispersionextended tight binding (ETB, up 20 n.n. sites)Porezag’s interatomic potential

Optical absorption and emissiondipole approximation

Electro-phonon interactionrelaxation, ETB

Raman intensity calculationPL intensity calculationExciton calculation

Exciton calculationWhy?

Large binding energy (0.5eV)even room temperature, exciton exists.

Exciton specific phenomenadark exciton, two photon, environment

What can we know or imagine? Cancellation by self energy

ETB + many body effects reproduce EiiLocalized exciton wave function

enhancement of optical processrelatively short k dependence.

A11 (1s)1- A11 (2p)2+

Wang et al. Science 308, 838 (2005)

ETB extension for Exciton

Bethe-Salpeter Equation

quasi-particle (QP) energy Coulomb interaction (C)

exchange C direct C

Self-energy (Coulomb repulsion)

RPA approximation:

C. D. Spataru et al. PRL 92, 077402 (2004)T. Ando J. Phys. Soc. Japan, 66, 1066 (1997),

)()(*)()(*''

'',,

)''(

)(sCsCsCsC

q usus

ususkv kvvqkvqkkv

sRuRusiqeq

V++

−∑ ∑=Εε

:a static dielectric constant toconsider polarization of environment

Ohno’spotential

G028

Symmetry consideration

:Good quantum number

Centre of mass motion

Relative motion

e h

K

K

K’Γ

A±

C2

e hK Γ

e h

K

K

K’Γ

A symmetry exciton

J. Jiang et al. unpublished

Bright and dark exciton

A- : bright excitonA+, E and E*: dark excitons

Exciton energy dispersion

e

h

K

K

K’

e

h

KK

K’

K’

K

E * exciton

Bright and dark exciton

A- : bright excitonA+, E, E*: dark excitons

J. Jiang et al. unpublished

E exciton

Dispersion for (6,5) NT

Dark state is the lowest

11 11 11 11

A- : bright excitonA+, E and E*: dark excitons

Exciton wavefunction for (8,0) NTs

A111- (1s) A11

2- (2p) A113- (3s)

J. Jiang et al. unpublished

Distribute only one cutting line

for any diameter.

Cutting line spacing

Bright exciton Kataura plotJ. Jiang et al. unpublished

The origin of the large family spread in Kataura plot - single particle part

ESP

Σ

Ebd

Σ−Ebd

Justification of ETB+MB

κ=2 is used for E22(S) and E11(M)

Environment effectJ. Jiang et al. unpublished

Solution Bundle

Experiment data

Circle: Square: :=3.5

=1.75

C. Fanitini et al PRL 93, 147406 (2004)

Ratio problem

With MB Without MB

E33, E44 has similar

Ebd to E11 and E22.

Exciton-photon matrix elementJ. Jiang et al. unpublished.

No type dep, No family pattern but dt dep.

Exciton-phonon matrix elementJ. Jiang et al. unpublished.

Matrix element, No difference!

Intensity enhanced drastically

(M(opt) appears 4 times)RBM

x102

Summary

Solution of BS equationwavefunction on one cutting lineExciton Kataura plot (family pattern)similar Eb E22, E33, E44

exciton-phonon (no change)exciton-phonon (enhanced)Raman and PL intensity with exciton wavefunction (in progress)

Electron-photon and electron-phonon matrix elements-- Dipole approximation and Deformation potential --

A. Gruneis et al, Chem. Phys. Lett. 387, 301 (2004)J. Jiang et al, Chem. Phys. Lett. 392, 383 (2004)

electron-photon (P vector ・ dipole vector)

electron-phonon (A-vib ・ V-deform))(Ψ)(Ψ VC k'kP ∇⋅

c c

Tight binding expansion: anisotropic around K

・

Dipole vector DPolarization vector

Optical aOptical absorption bsorption in graphitein graphiteA. A. GrueneisGrueneis et al. , PRB 67 165402 (2003)et al. , PRB 67 165402 (2003)

R. Saito et al., R. Saito et al., ApplAppl. Phys. A (2004). Phys. A (2004)ΓΓ

K ′

K ′

K ′

K

K

K

Node

SWNT (J. Jiang, 2003)

⎥⎦

⎤⎟⎠⎞

⎜⎝⎛ −+

⎭⎬⎫

⎩⎨⎧

−×⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −= ′′

2sin

23sin

6cos3

23cos

2coscos

6sin

)(2)( , akakakak

akw

MD yxxy

yz θπθπδδ µµ

kk kk,

kx

kyK

zcvcv DMM ∝=⋅∝ →→ ),1,0,0(, //PDP

vcti

cvife

cI

meiM Ψ∇Ψ⋅= −−

→ P)( ωωω

εωh

)(kzD

anisotropic )1,,0(

||

Tk

TN

k

ππµ

µ

<<−−=

+=

L

22

1 KK

Kk

The (n,m) assignment is based on the family patterns observed in the (ωRBM , Eii) plot

Good agreement with experimental results obtained by PL for semiconducting SWNTs

Extended tight binding method, including curvature effect and many body interactions fit better the experimental results

Only the lower E11M

branch is observed

The Kataura plot for HiPco SWNTs - ResultTight bindingγ0=2.9eVac-c=1.42Å

Experimental results- From the Stokes and anti-Stokes Raman resonance windows

Extended tight binding modelGe.G.Samsonidzeet al. Appl. Phys. Lett. 85, 5703(2004) .

2219

16

27

24

21

30

17

20

23

Exp. Theory

Accuracy: Eii ~ 10meV, ωRBM ~ 0.5cm-1

Atomic Deformation potential vector

6.7eV/A the largest0

3.4eV/A the secondlargest (off site)

0

(on site)

three center integralGraphiteDeformation vector is

parallel to the planeNo Raman for out-of-plane phonon modes

6.7eV/A: the largest m

SWNTDeformation vector has

perpendicular components

Strong Raman for RBM and out-of-plane phonon modes

Curvature effect in electron-phonon interaction

J. Jiang et al, Phys. Rev. B 72 235408 (2005)

terms

(1)-(5): along bond direction(6)-(9): perpendicular to bond direction

Slater-Kosterparameters for electron-phonon matrix element

0 0.5 1 1.5 2 θ/π

0

2

4

6

LOTO

[eV

/A]

0

D (k

, k)

ν

K θ

q=0, D(k,k)→ 1st order Raman

chirality dependence of G-band

Z. Yu, L. E. Brus, J. Phys. Chem. B 105, 6831 (2001)

R. Saito et al, Phys. Rev. B63, 085312 (2001)

Electron-phonon interaction for G-bandJ. Jiang et al. Chem. Phys. Lett. 392, 383 (2004)

Analysis of RBM Raman intensitiesA. Jorio et al, , Phys. Rev. B (2005)

Experiment Calculations

Diameter, chirality and type I vs. type II dependence is observedin good agreement with calculations of Raman intensity

SISII M

Quantum interference effect of RBM Raman intensity

J. Jiang et al, Phys. Rev. 71, 205420 (2005)

M

M

SI SII

Fluorescence from SDSFluorescence from SDS--wrapped nanotubeswrapped nanotubesStructure-Assigned Optical Spectra of Single-Walled Carbon Nanotubes

S. M. Bachilo et al., Science 298, 2361 (2002)

Each peak on the figure represents the observed E22 & E11transitions for one SWNT.

Absorption and Emission

Sample:SDS-wrapped nanotubes

22ex EE = ωh211ex −= EE ωh−= exPL EE CE =ex

11PL EE = 11PL EE =

Electronic transition 2-phonon jump Raman line

Raman lin

e

hot electron emission

hot electron emission

Electronic transition

11PL EE =

resonance condition

Phonon States of Nanotubes Observed in PL

0

400

800

1200

1600LO

oTO

LA

LO

iTA

oTA

oTAoTA

iTAiTA LALA

oTOoTO

LOiTO iTO

Γ Μ Κ Γ

A:LA,TWB:RBMC:oTA(near K)D:oTO(near K)E:oTOF:iTA(near K)G:iLA(near K)H:TO(near K)I: LO

Summary

PL and Resonance Raman intensityMatrix element 1/dt

type I > type II, chirality dependenceRBM near zigzagG+: not dt chirality dependentG-: near armchair

Population analisys of SWNT is established.