Post on 20-Jan-2016
A few topics in Graphene physics
Antonio H. Castro Neto
San Sebastian, May 2008
• 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
Outline
-40 -20 0 4020Vg (V)
(1
/k
)
0
1
2
Nim (1012 cm-2)
(1
03 c
m2/V
s)
0
2
4
6
0 1 2
NO 2
Controlling scattering
Geim’s group
Tail Mobility (m2/V sec)
min
(e2 /
h) 12
8
4
01.41.21.00.80.60.40.20
16
10
8
6
4
2
0-50 0 50
Vg (V)
con
duct
ivit
y (m
S)
X 2
10
8
6
4
2
0-50 0 50
Vg (V)
con
duct
ivit
y (m
S) 10
8
6
4
2
0-50 0 50
Vg (V)
con
duct
ivit
y (m
S)
10
8
6
4
2
0-50 0 50
Vg (V)
con
duct
ivit
y (m
S)
4e2/h
4e2/h
Kim’s group
Pereira et al., Phys.Rev.Lett. 99, 166802 (2007);
3D Schroedinger l
Coupling
UndercriticalSupercritical
Andrei’s group
HIC Neutron stars
LmvF
C
ar
a
t
aL
C
21
50
06.0
107
E
N(E)
0
U0
Anderson’s Impurity Model
00 00
Non-interacting: U=0
Broadening
EnergyEnergy
0
V=0
R
00
Mean-Field
00
The impurity moment can be switched on and off!
U = 1 eV
n_down
V=1eV, e0=0.2 eV
n_up
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.