Is graphene a strongly correlated electron system ? Antonio H. Castro Neto Buzios, August 2008.

Is graphene a strongly correlated electron system ?

Antonio H. Castro Neto

Buzios, August 2008

1564 – Invention of the pencil2004 – Graphene isisolated by A. Geimand collaborators

Andre Geim

Plus some nanotechnology…

2m

SiO2

Si

Au contacts

graphite

optical image

SEM imagedesign contacts and mesa

t ~ 2.7 eV

Some electronic properties of graphene

B

t’ ~ 0.1 eV

A

A

Unit cell Nearest neighborsNext Nearest neighbors

In momentum space

300/2

3

0 with ),(

)(

2242

22

cta

v

mpvvmmpE

pvppvpE

F

FF

FyxF

Dirac Cone

Semi-Metal

“Ultra relativistic” Solid State at low speed of light

Electron-electron interactions

300 137

1

0

2

Gc

e

1 , 2 00

2

F

G v

e

Controlling parameter:

In QED:

Gonzalez et al. PRL 77, 3589 (96)

4

2

d

d

δμ/δ

Vb

g

density [Vbg]Martin et al., Nat. Phys. 4, 144 (2008)

• 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)

What about impurity atoms ?

UndercriticalSupercritical

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.