Chirality and energy dependence of first and second order resonance Raman intensity

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NT06: 7 th International Conference on the

Sato, Y. Oyama, J.S. Park, G. S. Chou, G.

Souza-Filho, G. Dresselhaus, M.S. Dresselhaus Dept.

1 NT06: 7 th International Conference on the Science and Application of Nanotubes, June 18-23, 2006 Nagano, JAPAN Chirality and energy dependence of first and 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 JST rsaito@flex.phys.tohoku.ac.jp TOHOKU UNIVERSITY

Photoluminescence Weisman et al.2002 phonon associated relaxation process Exciton based phenomena Pressure dependent Raman A.

2 Intensity calculation of PL and Raman spectra -- Not all SWNTs are bright. -- Relative Raman intensity (n,m) dependence RBM,G, D, G -band Photoluminescence Intensity (n,m) population analysis Photoluminescence Weisman et al.2002 phonon associated relaxation process Exciton based phenomena Pressure dependent Raman A. Souza-Filho et al.2006 Type dependent PL Maruyama et al.2004 Resonance Raman Fantini et al.2003 E 33 S E 11 M (e V) aser ω RBM (cm -1 ) Phonon associated PL S. G. Chou et al.2005 EL E 22 S

3 R. Saito et al., Phys. Rev. B, 72, (2005)

m,3) = 1 2 mod ( n m,3) = 2 1 30 27 24 23 21

4 n - m = 2 R. Saito et al., Appl. Phys. Lett. 60, 2204 (1992) type I K type II K mod (2n + m,3) = 1 2 mod ( n m,3) = n+m= n - m= E

5 Photoluminescence Weisman et al.2002 Valley of metals Spectroscopic measurements on HiPco Nanotubes in Solution (SDS wrapped) E 33 S E 11 M E 22 S Raman measurement 76 different laser lines (ArKr, HeNe, 3 different dyes, Ti:Sapphire). Dilor XY triplemonochromator Calibration: CCl 4 Raman spectra - Sample from M.Strano ω RBM (cm -1 ) ELaser (ev) Fantini et al. Unpublished

6 k 1 β k 2 α γ Resonance Raman Intensity k 1 β k 2 k 3 γ α δ k 0 k 0 1st order Raman 1st order Raman 2nd order Raman Light AFM Images emission 2nd order Raman Electron phonon interaction Light absorption

7 RBM: Family pattern of el-phonon matrix element J. Jiang et al, Phys. Rev. B (2005) d t dependence q dependence Type I Type II Type I Type II node node n-m family pattern, node 1/d t dependence Type I > type II n - m = 2

8 Family pattern for G-band matrix element J. Jiang et al, Phys. Rev. B (2005) G+ (LO) G-(TO) Type I Type II Type I Type II G+: not sensitive on diameter and q Exp Z G-: sensitive both on diameter and q (G- near armchair) A Z. Yu, L. E. Brus, J. Phys. Chem. B 105, 6831 (2001)

9 (1) photo absorption (2) relaxation by phonon (3) photo emission

Gruneis et al, Chem. Phys. Lett. 387, 301 (2004) S.

10 PL is strong around Armchair. type I > type II (for E22 absorption) Chirality dependence of Photo-Luminescence A. Gruneis et al, Chem. Phys. Lett. 387, 301 (2004) S. Maruyama et al, nano-carbon (2004) Z A A Z Theory A. Gruneis et al. Chiral angle (deg.) Exp. S. Maruyama et al. 6,5 7,6 8,7 9,8 8,6 9,7 10,8 7,5 6,4 11,7 10,6 9,5 11,6 8,4 10,5 7,3 9,4 8,3 11,4 12,5 13,5 12,4 10,3 11,3 9,2 13,3 10,2 14,3 12,2 13,2 8,1 15,2 9,1 11,1 12,1 14,1 15,1 10,0 11,0 13,0 14,0 16, Tube diameter (nm) S. M. Bachilo et al., JACS, 125 (2003)

11 PL intensity at E11 quantum efficiency = 3% Evaluation of (n,m) abundance Induced absorption phonon emission at E22 Spontaneous emission

Fluorescence spectroscopy Y. Miyauchi et al. Chem. Phys. Lett. 387 198 (2004) Y.

12 Fluorescence spectroscopy Y. Miyauchi et al. Chem. Phys. Lett (2004) Y. Oyama et al, Carbon, 44, 873 (2006) Theory (Oyama) small diameter, near armchair PL intensity large Exp (Miyauchi) Chiral angle (deg.) ,5 7,6 8,7 9,8 8,6 9,7 10,8 7,5 6,4 11,7 10,6 9,5 11,6 8,4 10,5 7,3 9,4 8,3 11,4 12,5 13,5 12,4 10,3 11,3 9,2 13,3 10,2 14,3 12,2 13,2 8,1 15,2 9,1 11,1 12,1 14,1 15,1 10,0 11,0 13,0 14,0 16, Tube diameter (nm) polarization // tube axis HiPCO sample

13 Population of (n,m) by PL I exp /I cal Y. Oyama et al, Carbon, 44, 873 (2006) Population analysis: 1. PL I exp /I cal Y. Oyama et al, Carbon, 44, 873 (2006). 2. I(PL)/I(Raman) A. Jorio et al., APL, 88, , (2006). 3. I exp /I cal and TEM T. Okazaki, CPL, (2006)

14 population analysis Experiment Theory fitting with Gaussians CVD pulsed-laser vaporization A. Jorio, et al., Appl. Phys. Lett. 88, (2006). T. Okazaki, et al., Chem. Phys. Lett. 420, 286 (2006).

15 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 energy resonance width (relaxation time) Population analysis for Raman and PL is available.

16 Method: Our computational library for SWNTs -- What do we need for intensity calculation? -- Electron and phonon energy dispersion extended tight binding (ETB, up 20 n.n. sites) Porezag s interatomic potential Optical absorption and emission dipole approximation Electro-phonon interaction relaxation, ETB Raman intensity calculation PL intensity calculation Exciton calculation

Cancellation by self energy ETB + many body effects reproduce Eii Localized exciton wave function

17 Why? Exciton calculation Large binding energy (0.5eV) even room temperature, exciton exists. Exciton specific phenomena dark exciton, two photon, environment What can we know or imagine? Cancellation by self energy ETB + many body effects reproduce Eii Localized exciton wave function enhancement of optical process relatively short k dependence. Wang et al. Science 308, 838 (2005) 2+ A 1-11 (2p) A 11 (1s)

18 G028 Bethe-Salpeter Equation ETB extension for Exciton T. Ando J. Phys. Soc. Japan, 66, 1066 (1997), C. D. Spataru et al. PRL 92, (2004) quasi-particle (QP) energy Coulomb interaction (C) exchange C Self-energy (Coulomb repulsion) direct C Ohno s potential :a static dielectric constant to consider polarization of environment RPA approximation: Ε kv = q sus' u' V ε ( q) sus' u' iq e ( Rus Ru ' s ') C * kv ( s) C k+ q, v ( s) C * k+ q, v ( s) C kv ( s)

19 Symmetry consideration J. Jiang et al. unpublished Centre of mass motion :Good quantum number Relative motion A symmetry exciton Bright and dark exciton A - : bright exciton A +, E and E *: dark excitons K K Γ K e h K A ± e h C Γ 2 K Γ e hk K

20 Exciton energy dispersion E exciton J. Jiang et al. unpublished h K E * exciton K K e K K e K K Bright and dark exciton K h A - : bright exciton A +, E, E *: dark excitons Dispersion for (6,5) NT

21 Dark state is the lowest A - : bright exciton A +, E and E *: dark excitons

unpublished Cutting line spacing A 11 1-

22 Exciton wavefunction for (8,0) NTs J. Jiang et al. unpublished Cutting line spacing A (1s) A (2p) A (3s) Distribute only one cutting line for any diameter.

23 Bright exciton Kataura plot J. Jiang et al. unpublished E SP Σ E bd Σ E bd κ=2 is used for E22(S) and E11(M) Justification of ETB+MB The origin of the large family spread in Kataura plot - single particle part

24 Environment effect J. Jiang et al. unpublished Circle: =1.75 Square: :=3.5 Solution Bundle Experiment data C. Fanitini et al PRL 93, (2004)

25 Ratio problem With MB Without MB E33, E44 has similar E bd to E11 and E22.

26 J. Jiang et al. unpublished. No type dep, No family pattern but d t dep.

27 J. Jiang et al. unpublished. Matrix element, No difference! Intensity enhanced drastically (M(opt) appears 4 times) x10 2 RBM

E 33, E 44 exciton-phonon (no change) exciton-phonon

28 Summary Solution of BS equation wavefunction on one cutting line Exciton Kataura plot (family pattern) similar E b E 22, E 33, E 44 exciton-phonon (no change) exciton-phonon (enhanced) Raman and PL intensity with exciton wavefunction (in progress)

29 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) P Ψ C ( k) Ψ V ( k' ) electron-phonon (A-vib V-deform) c c Tight binding expansion: anisotropic around K

εc π sin θ cosk 6 A. Grueneis et al., PRB 67 165402 (2003) R. Saito et al.

A (2004) e i ( ω ω ω ) t f Polarization vector M i P v c P D, P// = (0,0,1 ),

30 K K K Γ K M Node v c K SWNT (J. Jiang, 2003) M Dz ( k) = 2w( k) = K i eh mω Optical absorption a in graphite I εc π sin θ cosk 6 A. Grueneis et al., PRB (2003) R. Saito et al., Appl.. Phys. A (2004) e i ( ω ω ω ) t f Polarization vector M i P v c P D, P// = (0,0,1 ), kya a cos cos 2 a + Dipole vector D δ k,k δµ, µ 3k 3k a kya x x y sin Ψ c 2 Ψ v M v c D π 3cos θ sin 6 z 2 2 k y k x K D z (k) k k = µ K1 + K K 2 2 anisotropic π π ( = 0, L, 1 < < ) µ N T k T

31 The Kataura plot for HiPco SWNTs - Result Exp. Theory Tight Extended binding tight γbinding 0 =2.9eV amodel c-c =1.42Å Ge.G.Samsonidze et al. Appl. Phys. Lett. 85, 5703 (2004). Experimental results - From the Stokes and anti- Stokes Raman resonance windows The (n,m) assignment is based on the family patterns observed in the (ω RBM, E ii ) 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 E 11 M branch is observed Accuracy: E ii ~ 10meV, ω RBM ~ 0.5cm -1

vector has perpendicular components Strong Raman for RBM and out-of-plane phonon modes

32 Atomic Deformation potential vector Graphite Deformation vector is parallel to the plane No Raman for out-of-plane phonon modes three center integral SWNT Deformation vector has perpendicular components Strong Raman for RBM and out-of-plane phonon modes 0 6.7eV/A the largest (on site) 0 3.4eV/A the second largest (off site) 6.7eV/A: the largest m

33 Curvature effect in electron-phonon interaction J. Jiang et al, Phys. Rev. B (2005) terms Slater-Koster parameters for electron-phonon matrix element (1)-(5): along bond direction (6)-(9): perpendicular to bond direction

34 Electron-phonon interaction for G-band J. Jiang et al. Chem. Phys. Lett. 392, 383 (2004) q=0, D(k,k) 1 st order Raman chirality dependence of G-band 6 K θ Z. Yu, L. E. Brus, J. Phys. Chem. B 105, 6831 (2001) 0 [ev/a] 4 LO TO ν D (k, k) θ/π R. Saito et al, Phys. Rev. B63, (2001)

35 Analysis of RBM Raman intensities A. Jorio et al,, Phys. Rev. B (2005) Experiment Calculations SI SII M Diameter, chirality and type I vs. type II dependence is observed in good agreement with calculations of Raman intensity

36 Quantum interference effect of RBM Raman intensity J. Jiang et al, Phys. Rev. 71, (2005) M M SI SII

, Science 298, 2361 (2002) Absorption and Emission Sample: SDS-wrapped

37 Fluorescence from SDS-wrapped nanotubes Structure-Assigned Optical Spectra of Single-Walled Carbon Nanotubes S. M. Bachilo et al., Science 298, 2361 (2002) Absorption and Emission Sample: SDS-wrapped nanotubes Each peak on the figure represents the observed E 22 & E 11 transitions for one SWNT.

38 Electronic transition hot electron emission resonance condition Raman line E PL = E 11 Electronic transition 2-phonon jump Raman line hot electron emission E ex = E 22 Eex = E11 2hω E PL = E 11 E PL = E11 E PL = E ex hω E = ex C

39 Phonon States of Nanotubes Observed in PL LO LO ito oto LO oto LA ito oto ita LA ita ita ota LA ota ota Γ Μ Κ Γ A:LA,TW B:RBM C:oTA(near K) D:oTO(near K) E:oTO F:iTA(near K) G:iLA(near K) H:TO(near K) I: LO

40 Summary PL and Resonance Raman intensity Matrix element 1/d t type I > type II, chirality dependence RBM near zigzag G+: not d t chirality dependent G-: near armchair Population analisys of SWNT is established.

Exciton Photophysics of Carbon Nanotubes

Exciton Photophysics of Carbon Nanotubes Annu. Rev. Phys. Chem. 27.58:719-747. Downloaded from arjournals.annualreviews.org Annu. Rev. Phys. Chem. 27. 58:719 47 First published online as a Review in Advance on January 2, 27 The Annual Review