Presentation on theme: "Graphene conductivity"— Presentation transcript:
1Graphene 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.
2M. 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 grapheneOther authors find
8Fullerenes Discovery September 4,1985 Was known initially as soccerene Sir Harold W. Kroto, University od Sussex,Nobel Prize for Chemistry in 1996Discovery September 4,1985Was known initially as soccereneFullerenes consist of 20 hexagonal and 12 pentagonal rings as the basis of an icosohedral symmetry closed cage structure.8
9In 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
10per 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
11Endohedral compoundsThey are fullerene cages with La or other metal atoms inside. Some have been crystallized and found to superconduct11
12The 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.12
13Carbon Nanotubes Fascinating electronic and mechanical Properties: Depending on their chiralities, nanotubes can be metallic, semimetallic or semiconducting2. Remarkably high Young’s moduliand 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
20This 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.
21(n,0) alias Zigzag CNTaxis of CNTpath towards the tippath around the belt: 2n atoms
22armchair CNT path along the y axis CNT axis= y axispath along the y axisAll armchair nanotubes are metallic, as suggested by paths along axis
23“Chiral” geometry “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” geometryall the rest23
24The 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 CNTpath around the belt: 2n atoms
25Zigzag CNT using alternative basis CNT axis= x axis25
26pz Electronic bands of (n,-n) zigzag CNT-tight-binding approximation
27Carbon Nanotubes as quasi 1D systems: one component of k quantized Band Structure of grapheneNT: Compact transverse dimension Discretization of kSubbandscorrespondto differentvalues of kk|| is acontinuousvariable27k||27
31From Mahan’s nutshell book : band structure of a (5,0) zigzag nanotube From Mahan’s nutshell book : band structure of a (5,0) zigzag nanotube. Labels indicate angular momentum a values
32From Mahan’s nutshell book : band structure of a (6,0) zigzag nanotube 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.
33armchair CNT path along the axis CNT axis= y axispath along the axisAll armchair nanotubes are metallic, as suggested by paths along axis