a few topics in graphene physics antonio h. castro neto san sebastian, may 2008
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A few topics in Graphene physics
Antonio H. Castro Neto
San Sebastian, May 2008
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• Coulomb impurity in graphene Vitor M. Pereira, Johan Nilsson, Valeri Kotov
Phys.Rev.Lett. 99, 166802 (2007); arXiv:0803.4195
• Anderson impurity in graphene Bruno Uchoa, Chiung-Yuan Lin, Valeri Kotov, Nuno Peres
Phys.Rev.B 77, 035420 (2008); arXiv:0802.1711
Outline
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-40 -20 0 4020Vg (V)
(1
/k
)
0
1
2
Nim (1012 cm-2)
(1
03 c
m2/V
s)
0
2
4
6
0 1 2
NO 2
Controlling scattering
Geim’s group
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Tail Mobility (m2/V sec)
min
(e2 /
h) 12
8
4
01.41.21.00.80.60.40.20
16
10
8
6
4
2
0-50 0 50
Vg (V)
con
duct
ivit
y (m
S)
X 2
10
8
6
4
2
0-50 0 50
Vg (V)
con
duct
ivit
y (m
S) 10
8
6
4
2
0-50 0 50
Vg (V)
con
duct
ivit
y (m
S)
10
8
6
4
2
0-50 0 50
Vg (V)
con
duct
ivit
y (m
S)
4e2/h
4e2/h
Kim’s group
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Pereira et al., Phys.Rev.Lett. 99, 166802 (2007);
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3D Schroedinger l
Coupling
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UndercriticalSupercritical
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Andrei’s group
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HIC Neutron stars
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LmvF
C
ar
a
t
aL
C
21
50
06.0
107
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E
N(E)
0
U0
Anderson’s Impurity Model
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00 00
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Non-interacting: U=0
Broadening
EnergyEnergy
0
V=0
R
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00
Mean-Field
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00
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The impurity moment can be switched on and off!
U = 1 eV
n_down
V=1eV, e0=0.2 eV
n_up
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U = 40 meV
U = 0.1 eV
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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.