Graphene Wooten

Report
Graphene
Rachel Wooten
Department of Physics
Solid State Physics II
March 6, 2008
Taught by Professor Dagotto
[email protected]
Outline
• What is graphene?
• How it is made
• Properties
– Electronic & physical properties
– Relativistic charge carriers
– Anomalous quantum Hall effect
• Future Applications
What is graphene?
• 2-dimensional
hexagonal lattice of
carbon
• sp2 hybridized carbon
atoms
• Basis for C-60 (bucky
balls), nanotubes, and
graphite
• Among strongest
bonds in nature
A. K. Geim & K. S. Novoselov. The rise of graphene. Nature Materials Vol 6 183-191 (March 2007)
A Two dimensional crystal
• In the 1930s, Landau and Peierls (and Mermin, later)showed
thermodynamics prevented 2-d crystals in free state.
• Melting temperature of thin films decreases rapidly with
temperature -> monolayers generally unstable.
• In 2004, experimental discovery of graphene- high quality 2-d
crystals
• Possibly, 3-d rippling stabilizes crystal
Representation of
rippling in
graphene. Red
arrows are
~800nm long.
http://www.nature.com/nmat/journal/v6/n11/fig_tab/nmat2011_F1.html#figure-title
How to make graphene
• Strangely cheap and easy.
• Either draw with a piece of graphite, or
repeatedly peel with Scotch tape
• Place samples on specific thickness of Silicon
wafer. The wrong thickness of silicon leaves
graphene invisible.
• Graphene visible through feeble interference
effect. Different thicknesses are different
colors.
Samples of graphene
a) Graphite films
visualized through
atomic force
microscopy.
b) Transmission
electron
microscopy image
c) Scanning
electron
microscope image
of graphene.
A. K. Geim & K. S. Novoselov. The rise of graphene. Nature Materials Vol 6 183-191 (March 2007)
Electrons in graphene
• Electrons in porbitals above and
below plane
• p-orbitals become
conjugated across
the plane
• Electrons free to
move across plane in
delocalized orbitals
• Extremely high
tensile strength
http://en.wikipedia.org/wiki/Aromaticity
-Graphene and graphite are great
conductors along the planes.
Properties: charge carriers
• Samples are excellent- graphene is ambipolar:
charge carrier concentration continuously tunable
from electrons to holes in high concentrations
A. K. Geim & K. S. Novoselov. The rise of graphene. Nature Materials Vol 6 183-191 (March 2007)
Relativistic charge carriers
• Linear dispersion relation- charge
carriers behave like massless Dirac
fermions with an effective speed of light
c*~106. (But cyclotron mass is nonzero.)
• Relativistic behavior comes from
interaction with lattice potential of
graphene, not from carriers moving near
speed of light.
• Behavior ONLY present in monolayer
graphene; disappears with 2 or more
layers.
K . S. N o vo sel ov , A . K . G eim, S . V . M or ozov , D . Jian g, M. I. K at sne lson , I. V . G ri gor ieva , S . V .
D u bo nos , & A . A . F ir so v. T w o- dime n siona l gas of m assles s D irac fer mi o ns in gra phe ne.
N at ur e, 43 8 1 97- 20 0 (2 00 5)
Anomalous quantum Hall effect
• Classical quantum Hall effect.
– Apply B field and current. Charges build up on opposite sides
of sample parallel to current.
– Measure voltage: + and - carriers create opposite Hall voltages.
• Quantum Hall effect
– Classical Hall effect with voltage differences = integer times
e2/h
http://www.eeel.nist.gov/812/effe.htm
Anomalous quantum Hall effect
• Fractional Quantum Hall effect
– Quantum Hall effect times rational fractions.
Not completely understood.
• Graphene shows integer QHE shifted by 1/2
integer
• Non-zero conductivity as charge carrier
dentsity -> zero.
• Hall
conductivity
xy (red) and
resistivity xy
vs. carrier
concentration.
• Inset: xy in 2layer graphite.
• Half-integer
QHE unique to
monolayer.
*Note non-zero conductivity as carrier concentrations approach zero.
K . S. N o vo sel ov , A . K . G eim, S . V . M or ozov , D . Jian g, M. I. K at sne lson , I. V . G ri gor ieva , S . V .
D u bo nos , & A . A . F ir so v. T w o- dime n siona l gas of m assles s D irac fer mi o ns in gra phe ne.
N at ur e, 43 8 1 97- 20 0 (2 00 5)
Possible Applications
• High carrier mobility even at highest electric-fieldinduced concentrations, largely unaffected by
doping= ballistic electron transport over < m
distances at 300K
– May lead to ballistic room-temperature transistors.
– GaTech group made proof of concept transistor- leaks
electrons, but it’s a start.
• Energy gap controlled by width of graphene strip.
– Must be only 10s of nm wide for reasonable gap.
– Etching still difficult consistently and random edge
configuration causes scattering.
Even more applications?
• Very high tensile strength
• Replacement of nanotubes for cheapness in
some applications: composite materials and
batteries for improved conductivity
• Hydrogen storage
• Graphene based quantum computation?
Low spin-orbit coupling-> graphene may be
ideal as a q-bit.
In Conclusion
• Graphene is a novel material with very
unusual properties
• Easy to make in lab; may prove easy and
economical to manufacture (unknown).
• Broad range of applications for future
research.
• Variety of possible practical applications.
Resources
• 1.
A. K. Geim & K. S. Novoselov. The rise of graphene. Nature Materials Vol 6 183-191 (March
2007)
• 2.
N. D. Mermin. Crystalline Order in Two Dimensions. Phys. Rev. 176, 1 250-253
• 3.
H. W. Kroto, J. R. Heath, S. C. O’Brien, R. F. Curl & R. E. Smalley. C60: Buckminsterfullerene.
Nature 318, 162-163 (1985).
• 4.
Sumio Iijima. Helical microtubules of graphitic carbon. Nature 354, 56-58 (1991).
• 5.
P. R. Wallace. The band theory of graphite. Phys. Rev. 71, 622-634 (1947).
• 6.
J. C. Slonczewski & P. R. Weiss. Band structure of graphite. Phys. Rev. 109, 272-279 (1958).
• 7.
A. Fasolino, J. H. Los & M. I. Katsnelson. Intrinsic ripples in graphene. Nature Materials 6,
858-861 (2007)
• 8.
K. S. Novoselov, et al. Electric field effect in atomically thin carbon films. Science 306, 666-669
(2004).
• 9.
K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V.
Dubonos, & A. A. Firsov. Two-dimensional gas of massless Dirac fermions in graphene. Nature, 438
197-200 (2005)
• 10.
Adriaan M. J. Schakel. Relativistic quantum Hall effect. Phys. Rev. D 43, 4 1428-1431 (1991)
• 11.
J. Hass, R. Feng, T. Li, X. Li, Z. Zong, W. A. de Heer, P. N. First & E. H. Conrad. Highly
ordered graphene for two dimensional electroncs. Applied Physics Letters 89, (2006)
• 12.
Prachi Patel-Predd. “Ultrastrong paper from graphene”. July 25, 2007.
http://www.technologyreview.com/Nanotech/19097/
End
•
http://en.wikipedia.org/wiki/Graphite

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