Transcript A few topics in Graphene physics Antonio H. Castro Neto

Adatoms in Graphene
Antonio H. Castro Neto
Trieste, August 2008
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).
•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).
 (1/k)
NO 2
2
1
0
-40 -20
0
20
40
Vg (V)
6
 (103 cm2/Vs)
Controlling scattering
4
2
Geim’s group
0
0
1
Nim
(1012
2
cm-2)
12
conductivity (mS)
min (e2/h)
16
8
4
4e2/h
4e2/ph
0
0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
10
8
6
4
2
0
-50
Tail Mobility (m2/V sec)
0
50
8
6
4
X2
2
0
-50
0
Vg (V)
50
10
conductivity (mS)
10
conductivity (mS)
conductivity (mS)
Vg (V)
8
6
4
2
0
-50
0
50
Vg (V)
Kim’s group
10
8
6
4
2
0
-50
0
Vg (V)
50
Artificial structures:
Chemistry, engineering, material science
How do adatoms modify graphene’s properties ?
Hashimoto et al. Nature 430, 870 (04)
Pereira et al., Phys.Rev.Lett. 99, 166802 (2007);
Coupling
3D Schroedinger
l
Undercritical
Supercritical
Andrei’s group
HIC
Neutron stars
L  107a
  0.06t
C  50a
r  21a

C 
L
m vF
E

0
T>TK
0 U
N(E)
Anderson’s Impurity Model
0  0
0  0
Non-interacting: U=0
V=0
0
Broadening
Energy
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.