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

Is graphene a strongly
correlated electron system ?
Antonio H. Castro Neto
Buzios, August 2008
A
brief history of
gr
2004
is
1564 – Graphene
Invention of
isolated
A. Geim
the by
pencil
and collaborators
Andre Geim
Plus some nanotechnology…
2 m
optical image
SEM image
design
contacts and mesa
Au contacts
SiO2
Si
graphite
Some electronic properties of graphene
t’ ~ 0.1 eV
A
t ~ 2.7 eV
A
B
Next Nearest
Nearest
neighbors
neighbors
In momentum space
Dirac Cone
E ( p)  vF p x2  p y2  vF p
Semi-Metal
E ( p, m)   m 2vF  vF p 2 with m  0
4
3ta
vF 
 c / 300
2
2
“Ultra relativistic” Solid
State at low speed of light
Electron-electron interactions
Controlling parameter:
In QED:
e2
G 
 2 , 0  1
 0vF
e2
1


 0c 137
 G  300
Gonzalez et al. PRL 77, 3589 (96)
Perturbative Renormal
d


d
4
2
δμ/δVbg
Marginally Ir
density [Vbg]
Martin et al., Nat. Phys. 4, 144 (2008)
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)
Undercritical
Supercritical
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.