A few topics in Graphene physics Antonio H. Castro Neto

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Is graphene a strongly correlated electron system
?Antonio H. Castro Neto
Buzios, August 2008
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A brief history of graphene
2004 Graphene is isolated by A. Geim and
collaborators
1564 Invention of the pencil
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Plus some nanotechnology
2?m

• optical image

• SEM image

• design

• contacts and mesa

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Some electronic properties of graphene
t 0.1 eV
A
t 2.7 eV
A
B
Nearest neighbors
Next Nearest neighbors
Unit cell
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In momentum space
Dirac Cone
Semi-Metal
Ultra relativistic Solid State at low speed of
light
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Electron-electron interactions
Controlling parameter
In QED
Gonzalez et al. PRL 77, 3589 (96)
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Perturbative Renormalization group
Marginally Irrelevant
dµ/dVbg
density Vbg
Martin et al., Nat. Phys. 4, 144 (2008)
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What about impurity atoms ?

• 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)

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Undercritical
Supercritical
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E
N(E)
Andersons Impurity Model
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Non-interacting U0
V0
Broadening
Energy
Energy
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Mean-Field
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U 1 eV
n_up
n_down
V1eV, e00.2 eV
The impurity moment can be switched on and off!
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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.