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.