Lecture 2 Nanocarbon

Lecture 2. Nanocarbon C60, CNT’s

Synthesis and e-beam lithography

Graphene (synthesis, relativistic

QM nature, transport)

Aligned Carbon Nanotubes

AAO template CNT array in AAO

CVD @ CAER, Dr. Rodney Andrews Group

TEM of smallest MWNT

AA4 CNT- MWNT with a 2 nm inner diameter

We have fabricated CNT

arrays in AAO template

with varying pore diameter.

Our observations indicate

that, CNT inner core

diameter decreases with

decreasing AAO pore

diameter, while the wall

thickness remains almost

the same.

Graphene

Obtaining Graphene

• Micromechanical cleavage from bulk graphite (on oxidized Si)

• Thermal decomposition of 4-H SiC (Si terminated surface) in UHV

• Vapor deposition from hydrocarbons (e.g. CVD from xylene as is done for CNT’s)

• Pulsed Laser Deposition

• Exfoliation by Ultasonification of Graphite and Spin-on Coating

• Plasma-enhanced Chemical Vapor Deposition

A carbon nanotube is a honeycomb lattice rolled

up into a cylinder. Although carbon nantoube seems to

have a 3D structure, it can be considered as 1D because of

their small size, which is in size of nano-order. The

specifying of carbon naonotube is very simple.

To define the structure, 2 numbers known as the

chiral index is used. In Fig. 1, 2 unit vectors, a1 and a2, are

defined on the hexagonal lattice. These 2 vectors define

the chiral vector Ch, and equation is shown below.

Ch= n a1+m a2≡ (n, m), (n, m are integers, 0≤|m|≤n)

(n, m) is called the chiral index, or it is just called

chirality. The example of (3, 3) is shown in Fig. 2.

This chirality is important because it tells the

characteristic of a carbon nanotube. For example, if the

difference of n and m is the multiple of 3, then that carbon

nanotube is metal. If not, it is semiconductor.

The first two of these, known as “armchair” (top left) and “zig-zag” (middle left) have a high degree of

symmetry. The terms "armchair" and "zig-zag" refer to the arrangement of hexagons around the

circumference. The third class of tube, which in practice is the most common, is known as chiral,

meaning that it can exist in two mirror-related forms. An example of a chiral nanotube is shown at the

bottom left. The structure of a nanotube can be specified by a

vector, (n,m), which defines how the graphene sheet is rolled up. This can be understood with reference to figure on the right. To produce a nanotube with the indices (6,3), say, the sheet is rolled up so that the

atom labelled (0,0) is superimposed on the one labelled (6,3). It can be seen from the figure that m =

0 for all zig-zag tubes, while n = m for all armchair tubes.

To calculate the band structure of CNT’s, it is useful to discuss

graphene first. We’ll then do a simple

modification to this calculation for CNT’s.

Band Structure of Graphene

Figure 1 Two unit vectors

a1

a2

a1

a2

Left: Diagram of the Brillouin zone of graphite. Center: Dirac fermions in momentum space near corner H of the Brillouin zone are characterized by

a sharply linear Λ-shaped dispersion relation, similar to that found in graphene. Right: As a result of interlayer interactions, other regions of

momentum space (near corner K) display a parabola-shaped dispersion, signifying the existence of quasiparticles with finite mass whose energy is

quadratically dependent on momentum.

• Magnetoconductance

Schibli group University of Colorado/JILA

Band Structure of CNT’S

Other Materials with (Possible) Dirac Fermions

Left: Diagram of the Brillouin zone of graphite. Center: Dirac fermions in momentum space near corner H of the Brillouin zone are characterized by

a sharply linear Λ-shaped dispersion relation, similar to that found in graphene. Right: As a result of interlayer interactions, other regions of

momentum space (near corner K) display a parabola-shaped dispersion, signifying the existence of quasiparticles with finite mass whose energy is

quadratically dependent on momentum.

Copyright ©2005 by the National Academy of Sciences

Novoselov, K. S. et al. (2005) Proc. Natl. Acad. Sci. USA 102, 10451-10453

Fig. 3. Electric field effect in single-atomic-sheet crystals

We’ll see in Lecture 6 that MoS2

is useful as a gate in graphene FET’s

Devices

Can Graphene be a Superconductor?

• Plasmon-mediated SC possible (Uchoa et al) PRL 98 146801 (2007)

• Proximity effect supercurrents observed (Heersche et al) Solid State Comm.143, 72 (2007)

• SC consistent with LAMH resistive transition theory in Single-walled CNT (Zhao) PRB 71 113404 (2005)