Title: A%20few%20topics%20in%20Graphene%20physics%20Antonio%20H.%20Castro%20Neto
1Graphene electrons in the flatlandAntonio H.
Castro Neto
Seoul, September 2008
2Disclaimer
IQHE measured
Graphene is discovered
AHCN, P. Guinea, N. Peres, K. Novoselov, A. Geim,
Rev. Mod. Phys. (2008)
3A brief history of graphene
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6Plus some nanotechnology
2?m
7Some electronic properties of graphene
t 0.1 eV
A
t 2.7 eV
A
B
Nearest neighbors
Next Nearest neighbors
Unit cell
8In momentum space
Dirac Cone
Semi-Metal
Ultra relativistic Solid State at low speed of
light
9Novoselov et al, Science 306, 666 (2004)
10Outline
- 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)
- Bruno Uchoa, Chiung-Yuan Lin, Nuno Peres, AHCN
- Phys.Rev.B 77, 035420 (2008)?.
11Pereira et al., Phys.Rev.Lett. 99, 166802 (2007)
12Coupling
3D Schroedinger
13Undercritical
Supercritical
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15Andreis group
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17HIC
Neutron stars
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191 nm
20E
TgtT
K
N(E)
Andersons Impurity Model
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22Non-interacting U0
V0
Broadening
Energy
Energy
23Mean-Field
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25 U 1 eV
n_up
n_down
V1eV, e00.2 eV
The impurity moment can be switched on and off!
26U 40 meV U 0.1 eV
27Conclusions
- 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.