Graphene_Wooten.ppt

7/29/2019 Graphene_Wooten.ppt

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Graphene

Rachel WootenDepartment of Physics

Solid State Physics II

March 6, 2008

Taught by Professor Dagotto

[email protected]


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Outline

What is graphene?

How it is made

Properties

Electronic & physical properties

Relativistic charge carriers

Anomalous quantum Hall effect

Future Applications


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2-dimensionalhexagonal lattice of

carbon

sp2 hybridized carbon

atoms Basis for C-60 (bucky

balls), nanotubes, and

graphite

Among strongestbonds in nature

What is graphene?

A. K. Geim & K. S. Novoselov. The rise of graphene. Nature Materials Vol 6183-191 (March 2007)


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A Two dimensional crystal

In the 1930s, Landau and Peierls (and Mermin, later)showedthermodynamics prevented 2-d crystals in free state.

Melting temperature of thin films decreases rapidly withtemperature -> monolayers generally unstable.

In 2004, experimental discovery of graphene- high quality 2-dcrystals

Possibly, 3-d rippling stabilizes crystal

http://www.nature.com/nmat/journal/v6/n11/fig_tab/nmat2011_F1.html#figure-title

Representation of

rippling in

graphene. Red

arrows are

~800nm long.


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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 differentcolors.


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Samples of graphenea) Graphite films

visualized through

atomic forcemicroscopy.

b) Transmissionelectron

microscopy image

c) Scanning

electron

microscope imageof graphene.



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Electrons in graphene

Electrons in p-orbitals above andbelow plane

p-orbitals becomeconjugated acrossthe plane

Electrons free to

move across plane indelocalized orbitals

Extremely high

tensile strength

http://en.wikipedia.org/wiki/Aromaticity

-Graphene and graphite are great

conductors along the planes.


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Properties: charge carriers

Samples are excellent- graphene is ambipolar:charge carrier concentration continuously tunable

from electrons to holes in high concentrations



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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. 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.

ature, 438 197-200 (2005)


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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


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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 carrierdentsity -> zero.


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Hall

conductivity

xy (red) andresistivity xyvs. carrier

concentration.

Inset: xy in 2-layer graphite.

Half-integer

QHE unique to

monolayer.

*Note non-zero conductivity as carrier concentrations approach zero.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.

ature, 438 197-200 (2005)


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Possible Applications

High carrier mobility even at highest electric-field-induced concentrations, largely unaffected bydoping= ballistic electron transport over < mdistances at 300K

May lead to ballistic room-temperature transistors.

GaTech group made proof of concept transistor- leakselectrons, but its 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 edgeconfiguration causes scattering.


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Even more applications?

Very high tensile strength

Replacement of nanotubes for cheapness in

some applications: composite materials andbatteries for improved conductivity

Hydrogen storage

Graphene based quantum computation?Low spin-orbit coupling-> graphene may beideal as a q-bit.


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In Conclusion

Graphene is a novel material with veryunusual properties

Easy to make in lab; may prove easy andeconomical to manufacture (unknown).

Broad range of applications for future

research. Variety of possible practical applications.


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Resources 1. A. K. Geim & K. S. Novoselov. The rise of graphene. Nature Materials Vol 6183-191 (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. OBrien, 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.Science306, 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. Highlyordered 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/


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End

http://en.wikipedia.org/wiki/Graphite

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