Graphene: electrons in the flatland

Antonio H. Castro Neto

Seoul, September 2008

Disclaimer

Graphene is discovered

IQHE measuredAndre Geim

Kostya Novoselov

Philip Kim

AHCN, P. Guinea, N. Peres, K. Novoselov,A. Geim, Rev. Mod. Phys. (2008)

A brief history of graphene

5 m

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

Novoselov et al, Science 306, 666 (2004)

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).

Johan Nilsson

Bruno Uchoa

Vitor Pereira

Valeri Kotov

Nuno Peres

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

1 nm

E

N(E)

0

U0

Anderson’s Impurity Model

T>TK

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.