1. Carbon nanotubes Stephanie Reich
Fachbereich Physik, Freie Universität Berlin

2. Pure sp2 & sp3 carbon
iron age
1991
2004
4 cen BC
1985

3. Single-walled carbon nanotubes
diameter: 1 – 5 nm, length: up to cm
Nanotubes are not one, but many materials
Nanotubes consist only of surface atoms
U. Bristol

4. Single-walled carbon nanotubes
Growth of carbon nanotubes
Zone folding & fundamentals
Electronic properties
Optical properties
Nanotube vibrations
(Functionalization)

5. Nanotube growth grow out of a carbon plasma metal catalysts
laser ablation
arc discharge
chemical vapor deposition
metal catalysts
nickel, cobalt, iron …
carbon tubes
diameter ~ 1 nm
length 500 nm – 4 cm
industrial scale production
started 2005
since 2009 large scale

6. Chemical vapor deposition
long tubes & high yield
high quality
high degree of control during growth
Hata, Science (2004); Zhang, Nat Mat (2004); Milne

7. Nanotube growth grow out of a carbon plasma metal catalysts
laser ablation
arc discharge
chemical vapor deposition
metal catalysts
nickel, cobalt, iron …
carbon tubes
diameter ~ 1 nm
length 500 nm – 4 cm
industrial scale production
started 2005
since 2009 large scale

8. Nanotube structure
nanotube diameter d & chiral angle Θ determine microscopic structure
Carbon nanotubes (Wiley, 2004) , Freitag group

9. Nanotube structure
nanotube diameter d & chiral angle Θ determine microscopic structure
Carbon nanotubes (Wiley, 2004)

10. Chiral vector - (n,m) nanotube
c = n a1 + m a2 = 8 a1 + 8 a2 a2 a1
nanotube diameter d & chiral angle Θ determine microscopic structure
specified by the chiral vector c around the circumference
Carbon nanotubes (Wiley, 2004)

11. Chiral vector - (10,0) nanotube
c = n a1 + m a2 = 10 a1 a2 a1
nanotube diameter d & chiral angle Θ determine microscopic structure
specified by the chiral vector c around the circumference
Carbon nanotubes (Wiley, 2004)

12. Nanotube structure (8,8) (6,6) (10,0) (8,3)
(8,8) (6,6) (10,0) (8,3)
typical samples contain 40 – 100 different chiralities
controlling chirality during growth is impossible
Carbon nanotubes (Wiley, 2004)

13. Quantum confinement circumference – periodic boundary conditions
 = p diameter/p (p integer)
Carbon nanotubes (Wiley, 2004)

14. Confined phase space K  M
Carbon nanotubes (Wiley, 2004)

15. One-dimensional Brillouin zone
Carbon nanotubes (Wiley, 2004)

16. Band structure (10,0) tube
Carbon nanotubes (Wiley, 2004)

17. Metal or semiconductor? – (n-m)/3
quantization in (n,0)
n+1 allowed lines between G and M
G K = 2/3 KM = 1/3
metals (3,0), (6,0), (9,0), (12,0) …
semiconductors (2,0), (4,0), (5,0), (7,0) …
general condition metallic if (n-m)/3 = integer
(10,0) semiconductor (9,0) metal
Carbon nanotubes (Wiley, 2004)

18. Metal & semiconductor in experimentk

19. Concept of zone folding
quantization along the circumference
reduced phase space
find nanotube properties by reference to graphene
works for
electrons, phonons, and other quasi-particles
interactions, e.g., electron-phonon coupling
central concept of nanotube research

20. Graphene – a semimetal
valence and conduction band touch in a single point
Reich, Carbon nanotubes (Wiley, 2004)

21. HOMO & LUMO HOMO & LUMO are degenerate
Nanotube chiral vector compatible with HOMO/LUMO wave function?
Reich, Carbon nanotubes (Wiley, 2004)

22. Metal or not?
three nanotube families metal semiconductor small gap semiconductor large gap

23. Electronic properties of nanotubes
quantum confinement
band gap depends on structure
most properties depend on band gap E k
metal semiconductors

24. Optical properties of nanotubes
Every nanotube – colorful
Bulk nanotube samples – black

25. Transitions between subbands
valence
conduction

26. Chirality from luminescence
every (n,m) nanotube has specific pairs of transition energy
use this for assignment
Bachilo, Science (2002)

27. Chirality from luminescence
(6,6)
(8,4)
(10,0) ?
luminescence detects semiconducting tubes, metallic not
some tubes were not observed
Bachilo, Science (2002)

28. Nanotubes, optics & excitons
chirality, electron-electron, and electron-hole interaction
sensitive to environment
E. Malic, M. Hirtschulz

29. Phonons in carbon nanotubes
100 – 1000 vibrations
strong coupling to electronic system
radial-breathing mode (RBM)
high-energy mode (HEM)
D mode
twiston and low-energy phonons
RBM
HEM
D mode
Raman scattering on carbon nanotubes (Springer, 2006)

30. Phonons in carbon nanotubes
100 – 1000 vibrations
strong coupling to electronic system
radial-breathing mode (RBM)
high-energy mode (HEM)
D mode
twiston and low-energy phonons
characterizie nanotubes
presence
metallic/semiconductor
chirality
RBM
RBM
HEM
HEM
D mode
D mode

31. Electron-phonon coupling
doping hardens phonon frequencies
metallic into semiconducting spectrum?
bundling effect?
semiconducting
metallic
H. Farhat

32. Phonon softening vibration periodically opens and closes a band gap
softening of the phonon frequencies
phonon dispersion is singular
q = k1 – k2
Kohn (1959)

33. Phonons limit nanotube transport
ballistic transport
resistance approaches quantum limit 13kΩ/channel
no scattering by defects
ballistic transport breaks down by hot phonons
phonon emission faster than decay
Yang PRL (2000); Javey Science (2003)

34. Functionalization change nanotube properties tune pristine properties
solubility
composite materials
sensitivity & reactivity
tune pristine properties
electron interaction
defects
vibrations

35. Quintessential nanotubes
Many different nanotube structures
Porperties differ vastly
Essential ingredients:
Quantum confinement – pick properties
Large surface area – manipulate properties
sp2 carbon bond – ultra-strong material
We cannot control the type of tube

36. Summary
Nanotube properties depend on their structure; there is no „typical nanotube“
Growth of carbon nanotubes produces many different tubes = different materials
Nanotube absorb light & show infrared luminescence
Particularly strong electron-phonon coupling
Functionalize nanotubes for further tailoring

37. Thanks to…
Cinzia Casiraghi (AvH) Antonio Setaro (FUB) Vitalyi Datsyuk (BmBF)
Rohit Narula (FUB) Sebastian Heeg (ERC) Oliver Schimek (DFG) Asaf Avnon (SfB) Thomas Straßburg (BmBF) Stefan Arndt (BmBF)
Ermin Malić (SfB) Megan Brewster (MIT, NSF)
TU Berlin Christian Thomsen Janina Maultzsch
MIT Michael Strano Francesco Stellacchi Jing Kong
KIT Frank Hennrich
University of Cambridge Stefan Hofmann John Robertson

38. The end
Thank you!