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

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

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
Electrons in usual solids
(Schrodinger equation)
Energy
Band Gap
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, (2005)
A. F. Young et al. Nature Phys. 5, 222 (2009)
A. K. Geim. Science Vol no. 5934, pp – 1534(2009)