seoul

Report
Graphene: electrons in the
flatland
Antonio H. Castro Neto
Seoul, September 2008
Disclaimer
Andre Geim
Kostya
Novoselov
IQHE measured
Graphene is
discovered
AHCN, P. Guinea, N. Peres, K. Novoselov,
A. Geim, Rev. Mod. Phys. (2008)
Philip Kim
A brief history of graphene
5 mm
Plus some nanotechnology…
2m m
optical image
SEM image
design
contacts and mesa
Au contacts
SiO2
Si
graphite
Some electronic properties of graphene
t’ ~ 0.1 eV
A
t ~ 2.7 eV
A
B
Next Nearest
Nearest
neighbors
neighbors
In momentum space
Dirac Cone
E ( p)  vF
px  p y  vF p
2
2
4
2
E ( p, m )   m vF  vF p
2
vF 
3 ta
2
 c / 300
2
Semi-Metal
with
m 0
“Ultra relativistic” Solid
State at low speed of light
Novoselov et al, Science 306, 666 (2004)
Outline
•Coulomb impurity in graphene
Vitor M. Pereira, Johan Nilsson, AHCN
Phys.Rev.Lett. 99, 166802 (2007);
Vitor M. Pereira, Valeri Kotov, AHCN
Phys. Rev. B 78, 085101 (2008).
Vitor Pereira
•Anderson impurity in graphene
Bruno Uchoa, Valeri Kotov, Nuno Peres, AHCN
Phys. Rev. Lett. 101, 026805 (2008);
Bruno Uchoa, Chiung-Yuan Lin, Nuno Peres, AHCN
Phys.Rev.B 77, 035420 (2008).
Nuno Peres
Johan Nilsson
Valeri Kotov
Bruno Uchoa
Pereira et al., Phys.Rev.Lett. 99, 166802 (2007);
Coupling
3D Schroedinger
l  
Undercritical
Supercritical
Andrei’s group
HIC
Neutron stars
L  107 a
  0 . 06 t
 C  50 a
r  21 a
C 

mv 1Fnm
 L
E
m
0
T>TK
0 U
N(E)
Anderson’s Impurity Model
0  0
0  0
Non-interacting: U=0
V=0
Broadening
Energy
0
R
Energy
Mean-Field
0  0
0  0
U = 1 eV
n_up
n_down
V=1eV, e0=0.2 eV
The impurity moment can be switched on and off!
U = 40 meV
U = 0.1 eV
Conclusions
• Impurities in graphene behave in an unusual
way when compared to normal metals and
semiconductors.
• One can test theories of nuclear matter under
extreme conditions.
• Control of the magnetic moment formation of
transition metals using electric fields.

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