is graphene a strongly correlated electron system ? antonio h. castro neto buzios, august 2008
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Is graphene a strongly correlated electron system ?
Antonio H. Castro Neto
Buzios, August 2008
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1564 – Invention of the pencil2004 – Graphene isisolated by A. Geimand collaborators
Andre Geim
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Plus some nanotechnology…
2m
SiO2
Si
Au contacts
graphite
optical image
SEM imagedesign contacts and mesa
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t ~ 2.7 eV
Some electronic properties of graphene
B
t’ ~ 0.1 eV
A
A
Unit cell Nearest neighborsNext Nearest neighbors
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In momentum space
300/2
3
0 with ),(
)(
2242
22
cta
v
mpvvmmpE
pvppvpE
F
FF
FyxF
Dirac Cone
Semi-Metal
“Ultra relativistic” Solid State at low speed of light
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Electron-electron interactions
300 137
1
0
2
Gc
e
1 , 2 00
2
F
G v
e
Controlling parameter:
In QED:
Gonzalez et al. PRL 77, 3589 (96)
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4
2
d
d
δμ/δ
Vb
g
density [Vbg]Martin et al., Nat. Phys. 4, 144 (2008)
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• 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).
• Anderson impurity in graphene Bruno Uchoa, Valeri Kotov, Nuno Peres, AHCN Phys. Rev. Lett. 101, 026805 (2008)
What about impurity atoms ?
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UndercriticalSupercritical
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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.