KETTŐS REZONANCIA GRAFIT

ésSZÉN NANOCSÖVEK

RAMAN SPEKTRUMÁBAN

MTA SZFKI , 2005. április 4.

Kürti Jenő

ELTE Biológiai Fizika Tanszék

e-mail: kurti@virag.elte.hu www: virag.elte.hu/~kurti

VÁZLAT• Bevezetés

– rendezetlenség („disorder”) által indukált sáv (D-sáv) sp2 szén vegyületek Raman spektrumában

• Kettős rezonancia (elmélet)– grafit– egyfalú szén nanocsövek (SWCNTs)

• Összefoglalás

• graphite single crystal

• stress-annealed pyrolite graphite

• commercial graphite

• activated charcoal

λ = 488 nm

F.Tuinstra and J.L.Koenig, J. of Chem. Phys. 53, 1126 (1970)

G: 1575 cm-

1

D: 1355 cm-1

D band in graphiteG

D

A grafit D-sávjának diszperziója Elaser függvényében

I. Pócsik, M. Hundhausen, M. Koós and L. Ley, J. of Non-Crystalline Solids 227-230B, 1083 (1998)

ωD /Elaser 50 cm-1/eV

D band

Measured D band of SWCNTs

Bundles

with

Gaussian diameter distribution:

p(d) exp(-(d-d0)2/22)

with d0 = 1.32 nm and = 0.14 nm

various laser excitation (eV)

J.Kürti, V.Zólyomi, A.Grüneis and H.Kuzmany, PRB 65, 165433, 2002

ωD(cm-1) = 1219 + 52 Elaser (eV)

ωD*(cm-1) = 2419 + 106 Elaser (eV) (G’)Measured anomalous dispersion of the D band of

SWCNTs

Tight binding

R.A.Jishi et al. CPL 209 77 (1983)

DFT

D.Sanchez-Portal et al. PRB 59 12678 (1999)

Valence force field MO/8

C.Mapelli et al.

PRB 60 12710 (1999)

DFT (VASP)

G.Kresse et al. Europhys. Lett. 32 729 (1995)

Raman basics

Stokes, 0 = 2 – 1, :

i

b

a

1

1

2

Raman basics

Stokes, = 1 – 2, :

1

1

2

ba

Disorder induced resonant Raman scattering

defect scattering

phonon scattering

Raman amplitudes for the Feynman diagrams

Stokes

anti Stokes

Double resonance: two of the denominators are zero at the same time

(C.Thomsen and S.Reich, PRL 85, 5214, 2000 : for graphite)

Eael = conduction(k) - valence(k) Eb

el = conduction(k’) - valence(k)

( = 0.01-0.1 eV)

Disorder induced resonant Raman scattering

defect scattering

phonon scattering

Graphene electron energy dispersion from book: R.Saito, G.Dresselhaus, M.S.Dresselhaus, Physical Proprties of Carbon Nanotubes, Imperial College Press, 1998

conduction band

valence band

E 18 eV

EM 6 eV

EK 0 eV

Relevant 4th order Feynman diagrams for Stokes and antiStokes processes

defect scattering

phonon scattering

Eael = conduction(k) - valence(k), Eb

el = conduction(k’) - valence(k), etc

( = 0.01-0.1 eV)

Raman amplitudes for the Feynman diagrams

Stokes

anti Stokes

Double resonance: two of the denominators are zero at the same time

(C.Thomsen and S.Reich, PRL 85, 5214, 2000 : for graphite)

Relevant 4th order Feynman diagrams for Stokes processes

Graphene electron energy dispersion from book: R.Saito, G.Dresselhaus, M.S.Dresselhaus, Physical Proprties of Carbon Nanotubes, Imperial College Press, 1998

conduction band

valence band

conduction band

valence band

III, IV

I, II

E 18 eV

EM 6 eV

EK 0 eV

equi excitation energy curves of electrons

equi phonon frequency curves

electron dispersion phonon dispersion

q0 = K’K K’

q0

q0

Calculated D band of graphene

Elaser = 2.0 eV —

Elaser = 2.5 eV ---

Simple qualitative interpretation of the maxima 1, 2 and 3

q0 = |K’K|

q1 > q0

q2 < q0

q3a = q3b q0

Points in k-space of a general (chiral) SWCNT for double resonance condition

2/d

qphonon

Calculated D band for a (11,9) SWCNT

Triple (quadruple) resonance = double resonance + VH enhancement

Eii

Van Hove singularity

1D - DOS

Van Hove singularity

Calculated van Hove enhancement for the (11,9) tube

EE2222 = 1.197 eV = 1.197 eV

E33 = 2.382 eV

EE4444 = 2.860 eV = 2.860 eV

in out

S.L.Zhang et al., PRB 66, 35413, 2002

Abnormal anti-Stokes Raman scattering for the D mode of SWCNTs

Elaser = 2.41eV

V.Zólyomi and J. Kürti, PRB 66, 073418, 2002

a-S

S

Calculated dispersion of the Stokes and anti-Stokes D band for a bundle of SWCNTs

ω ωD /Elaser• hωphonon

0.16 eV

0.16 eV

SUMMARY

The D band (around 1300 cm-1) of sp2 carbon materials (graphite as well as SWCNTs) is induced by disorder. Defects allow higher order Raman process involving non-zone-center phonons

The D* (G’) band (around 2600 cm-1) is te result of a two-phonon process, and needs no disorder

The position of the D band shifts with increasing laser excitation energy ( 50 cm-1/eV). Similar dispersion holds for the D* (G’) band ( 100 cm-1/eV)

Additional (selective) enhancement due to Van Hove singularities in the case of SWCNTs

Characterization of “Defects”A. C. Dillon et al.,

CPL 401 (2005) 522

R. Czerw et al. Nanoletters 1, 457 (2001)M. Terrones et al. Appl. Phys. A, 74, 355 (2002)

Microscopy and ab initio…

from Ado Jorio

A. C. Dillon et al.CPL 401, 522 (2005)

Mass-transport-limited oxidation inducing defects

The D band intensity depends on reaction time

D band increases with increasing B doping

M. Terrones et al. Materials Today Magazine (2004)

from Ado Jorio

Defect-free SWNT bundles

Forbidden Raman modes are observed in

defective materials

Defective sample

Defect-free sample

PMMA+SWNT fiberM.Souza et al. PRB (2004)

Disorder G-band proposed by Maultzsch et al. PRB (2003)

from Ado Jorio

Micro-Raman spectra from graphite edges

AFM

STM

Raman Spectra

D band is strong for armchair edgeand weak for zigzag edge

zigzag edge

armchair edge

Cancado et al. PRL (2004)

HOPG substrate

Raman can tell us if the edge has an

armchair or zigzag structure

Double resonance one “1D defect” explains the resultCancado et al. PRL (2004)

Micro-Raman spectra from graphite edges

Such an effect has been predicted for SWNTs but not yet

observed[Maultzsch et al.,

PRB(2001)]