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Graphene conductivity

Graphene conductivity. A lot of effort has been devoted to the question of transport in pure graphene due to the remarkable fact that the dc conductivity is finite without any dissipation process present. M. Lewkowicz and B. Rosenstein, PRL 102, 106802 (2009)

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Graphene conductivity

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  1. Graphene conductivity A lot of effort has been devoted to the question of transport in pure graphene due to the remarkable fact that the dc conductivity is finite without any dissipation process present.

  2. M. Lewkowicz and B. Rosenstein, PRL 102, 106802 (2009) Dynamics of Particle-Hole Pair Creation in Graphene find: They support this value of the dc conductivity of pure graphene Other authors find

  3. Measurement of conductivity

  4. 4

  5. semiinfinite semiinfinite

  6. 6

  7. Fullerenes Sir Harold W. Kroto, University od Sussex,Nobel Prize for Chemistry in 1996 Discovery September 4,1985 Was known initially as soccerene Fullerenes consist of 20 hexagonal and 12 pentagonal rings as the basis of an icosohedral symmetry closed cage structure.

  8. In theory, an infinite number of fullerenes can exist, their structure based on pentagonal and hexagonal rings, constructed according to rules for making icosahedra. Il fullerene non è molto reattivo data la stabilità dei legami simili a quelli della grafite ed è inoltre ragionevolmenteinsolubile nella maggioranza dei solventi. I ricercatori hanno potuto aumentare la reattività fissando dei gruppi attivi alla superficie del fullerene.

  9. per produrre i fullereni: arco elettrico, a circa 5300°K, con una corrente elevata e bassa tensione, utilizzando elettrodi in grafite in atmosfera inerte (argon) a bassa pressione.

  10. Endohedral compounds They are fullerene cages with La or other metal atoms inside. Some have been crystallized and found to superconduct

  11. The art of hitting the goal with every shot We have observed de Broglie wave interference of the buckminsterfullerene C60 with a wavelength of about 3 pm through diffraction at a SiNx absorption grating with 100 nm period. This molecule is the by far most complex object revealing wave behaviour so  far. The buckyball is the most stable fullerene with a mass of 720 atomic units, composed of 60 tightly bound carbon atoms. http://www.univie.ac.at/qfp/research/matterwave/c60/index.html

  12. Carbon Nanotubes • Fascinating electronic and mechanical • Properties: • Depending on their chiralities, nanotubes can be metallic, semimetallic or semiconducting • 2. Remarkably high Young’s moduli • and tensile strength “Imagine the possibilities: materials with ten times the strength of steel and only a small fraction of the weight!” ------Former resident Bill Clinton

  13. Multi-Walled NanoTube (MWNT) S. Iijima. "Helical microtubules of graphitic carbon." Nature 354 56 (1991)

  14. Carbon Nanotubes S. Iijima, Nature 354, 56 (1991)

  15. Carbon Nanotubes: Lattice Structure From Wikipedia

  16. Carbon Nanotubes: Lattice Structure S. Iijima, Nature 354, 56 (1991) L≈1m d≈nm Graphene sheet Nanotube 19

  17. This is a possible choice of the basis which is often used: Then, (n,0) nanotubes are called zigzag nanotubes, and (n,n) nanotubes are called armchair nanotubes. Otherwise, they are called chiral.

  18. (n,0) alias Zigzag CNT axis of CNT path towards the tip path around the belt: 2n atoms

  19. armchair CNT CNT axis = y axis path along the y axis All armchair nanotubes are metallic, as suggested by paths along axis

  20. “Armchair” geometry (n,m) with m=n, always metallic “Zig-zag” geometry (n,m) with m=0 e.g. (5,0),(6,4),(9,1) are semiconducting • “Chiral” geometry • all the rest 23

  21. The alternative basis which we used for the band structure of Graphene is also in use for CNT Since both conventions are used we must be ready to handle both of them. Zigzag CNT path around the belt: 2n atoms

  22. Zigzag CNT using alternative basis CNT axis = x axis

  23. pz Electronic bands of (n,-n) zigzag CNT-tight-binding approximation

  24. Carbon Nanotubes as quasi 1D systems: one component of k quantized • Band Structure of graphene • NT: Compact transverse dimension Discretization of k Subbands correspond to different values of k k|| is a continuous variable 27 k||

  25. Note: the (4,-4) zigzag CNT has 8 atoms around the belt. Generally, (n,-n) zigzag  2n atoms in belt  2n bands

  26. From Mahan’s nutshell book : band structure of a (5,0) zigzag nanotube. Labels indicate angular momentum a values

  27. From Mahan’s nutshell book : band structure of a (6,0) zigzag nanotube. Labels indicate angular momentum a values. If m-n is a multiple of 3 the nanotube is metallic.

  28. armchair CNT CNT axis = y axis path along the axis All armchair nanotubes are metallic, as suggested by paths along axis

  29. Recall Primitive vectors

  30. Armchairs are (n,n) using basis CNT axis = y axis

  31. From Mahan’s nutshell book : band structure of a (5,5) armchair nanotube. Labels indicate angular momentum a values. All armchair nanotubes are metallic.

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