1. Carbon Nanotube Intramolecular Junctions

2. Nanotubes A graphene sheet with a hexagonal lattice…

3. Nanotubes …wrapped up into a cylinder

4. Structure The structure of a nanotube is characterized by: Diameter (1-2 nm) Chirality

5. Structure Diameter and chirality are characterized by the vector c h =na 1 +ma 2 = (n,m) a 1 and a 2 are the graphene lattice vectors n and m are integers

6. Structure Armchair (n,n) Zig-zag (n,0) Chiral (n,m)

7. Structure Armchair (n,n) Zig-zag (n,0) Chiral (n,m)

8. Structure Armchair (n,n) Zig-zag (n,0) Chiral (n,m)

9. Structure Singlewall (SWNT) Multiwall (MWNT)

10. Structure Singlewall (SWNT) Multiwall (MWNT)

11. Electronic properties Nanotubes can be: Metallic (n-m a multiple of 3) Semiconducting depending on their diameter and chirality

12. Nanotube heterojunctions Nanotubes can be used to realize functional devices on individual molecules, for example to create intra-molecular junctions Metal-Metal Metal-Semiconductor Semiconductor-Semiconductor

13. What is an heterostructure? It is a structure that contains an heterojunction in order to build quantum structures like tunnel barrier and quantum wells. In an heterostructure : The interface IS the device

14. Nanotube heterojunctions It consists in: a change in the chirality within a single nanotube It can be obtained by: Local mechanical deformation A pentagon-heptagon (5-7) topological defect pair

15. Nanotube heterojunctions The insertion of a (5-7) topological defect pair creates a kink. In order to generate a kink of a large angle this pair must be placed on opposite sides of the kink.

16. Nanotube heterojunctions They obtained nanotubes that contain: A single kink of 36° (M-S heterojunction) A single kink of 41° (M-M heterojunction)

17. (M-S) Nanotube heterojunction The nanotube is lying on 3 electrodes. The upper straight segment has a resistance of 110 kΏ with no gate- voltage dependence (it is metallic)

18. (M-S) Nanotube heterojunction The lower straight segment is a semiconductor.

19. (M-S) Nanotube heterojunction This is the I-V characteristic across the kink: nonlinear and asymmetric resembling that of a diode

20. (M-S) Nanotube heterojunction The strong gate modulation demonstrates that the lower nanotube segment is semiconducting.

21. (M-M) Nanotube heterojunction The nanotube is lying on 4 electrodes. At room temperature R upper = 56kΏ R lower =101kΏ R junction =608kΏ

22. (M-M) Nanotube heterojunction Conductances depend on temperature There is no gate-voltage dependence, demonstrating that both are metallic The conductance across the junction is much more temperature dependent then that of the 2 straight segments

23. (M-M) Nanotube heterojunction The data are plotted on a double- logarithmic scale. The data can be fitted with a power- law function (if eV<<k B T)

24. (M-M) Nanotube heterojunction Power-law behaviour of G versus T was interpreted as a signature for electron-electron correlation. The nanotube behaves as a Luttinger liquid

25. Luttinger liquid An LL is a one-dimensional correlated electron state characterized by a parameter g that measures the strength of the interaction between electrons. g<<1 for strong repulsive interactions g=1 for non-interacting electron gas In SWNTs g theory ≈ 0.28. The tunnelling amplitude vanishes as a power-law function of energy:

26. Luttinger liquid Tunnelling into the end of an LL is more strongly suppressed than into the bulk α end > α bulk α end = (g -1 -1)/4 α bulk = (g -1 +g-2)/8 When a tunnel junction is placed between 2 LLs the tunnelling conductance is : α end-end = 2 α end

27. (M-M) Nanotube heterojunction At large bias (eV>>k B T)

28. (M-M) Nanotube heterojunction If we scale dI/dV by T α and V by T the curves obtained at different temperatures collapse onto one universal curve

29. Conclusions SWNTs are promising candidates for obtaining individual molecules as functional devices using their particular electronic properties.

30. Future development A better process of fabrication of SWNTs and their junctions is necessary. These junctions could be the building blocks of nanoscale electronic devices made entirerly of carbon.