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

A few topics in Graphene
physics
Antonio H. Castro Neto
San Sebastian, May 2008
Outline
• 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
 (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
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
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.