1. Graphene
- Electric Properties
Shpyrko Research Group. UCSD
Oct 15th 2010
Jong Woo Kim

2. Motivation
• 2010 Nobel Prize for Physics
Physicists Konstantin Novoselov (left) and Andre Geim of University of Manchester

3. History
Massless Dirac equation
of Graphene
Massless Dirac Fermion Proved
A. K. Geim, K. S. Novoseolv
Y. Zhang, P. Kim
G. W. Semenoff
1947
1984
Theory of Graphene
P. R. Wallace
2004
2005
Isolated atomic layer from graphite
A. K. Geim, K. S. Novoseolv
[Fabrication techniques]
CVD
Epitaxial growth on SiC
Chemical method by reducing agent

4. Graphene?
Fullerene
(Bucky ball*)
0D
Nanotube
* Nobel Prize in Chemistry 1996
1D
Graphene
2D

5. Graphene?
• Thin, mechanically strong, transparent and flexible conductor
• Can be used in touch screen, light panel, solar cells (ITO) and
flexible display

6. Electrical Properties
• Verified Exotic Electrical Behaviors
– Dirac Fermions with zero effective mass
– Half-Integer Quantum Hall effect
• Novoselov, et al. Nature (2005), Zhang et al, Nature (2005)
– Klein Tunneling
• A. F. Young and P. Kim, Nature (2009)
• Revisited topics
– Quantum dot, p-n junction, nanoribbons, quantum point
contacts, magnetotransport near neutrality point

7. Electrical Properties
• Exceptional Band Structure
Dirac Cone
Dirac Point
Brillouin Zone

8. Electrical Properties
• Unique Band Structure
Energy
Band Gap
Electrons in usual solids
(Schrodinger equation)
Momentum
Energy
Electrons in graphene
(Dirac equation)
Momentum

9. Electrical Properties
• Hall Effect
– Electric field developed across two faces of conductor in the direction j × H
when a current j flows across a magnetic field H
• Quantum Hall Effect
– Discovered in 1980
– σxy =νˑe2/h (ν is an integer)
– At low temperature and strong magnetic field
• Half-integer quantum Hall effect
– σxy =4ˑ(N+ ½)e2/h (N is an integer)
– At room temperature (300K)
Novoselov et al, 2005

10. Electrical Properties
• Klein tunneling
– In 1929, Oscar Klein
– A tunnel barrier can become fully transparent for normal incidence of
massless particles
– Test in graphene was suggested by Katsnelson, Geim and Noveselov in
2006 and verified by Young and Kim in 2009

11. Reference
•
•
•
•
Novoselov et al. Nature. 438, 197-200 (2005)
Zhang et al. Phys. Lett. 86, 073104 (2005)
A. F. Young et al. Nature Phys. 5, 222 (2009)
A. K. Geim. Science Vol. 324. no. 5934, pp. 1530 – 1534(2009)