Graphene deconstructed

Antonio H. Castro Neto

Evora, November 2008

Disclaimer

AHCN, P. Guinea, N. Peres, K. Novoselov,

A. Geim, Rev. Mod. Phys. (2008)

Disclaimer

Graphene is

discovered

Andre Geim

Kostya

Novoselov

AHCN, P. Guinea, N. Peres, K. Novoselov,

A. Geim, Rev. Mod. Phys. (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 µm

5 µm

Plus some nanotechnology…

2µm

!optical image

Plus some nanotechnology…

2µm

!optical image

!SEM image

Plus some nanotechnology…

2µm

!optical image

!SEM image

!design

Plus some nanotechnology…

2µm

!optical image

!SEM image

!design

!contacts and mesa

Plus some nanotechnology…

2µm

!!!"#$%

"#

&'!()*+,(+-

./,01#+2

!optical image

!SEM image

!design

!contacts and mesa

Some electronic properties of graphene

Some electronic properties of graphene

B

A

Unit cell

t ~ 2.7 eV

Some electronic properties of graphene

B

A

Unit cell Nearest neighbors

Some electronic properties of graphene

B

t’ ~ 0.1 eV

A

A

Next Nearest neighbors

In momentum space

In momentum space

In momentum space

Dirac Cone

In momentum space

Dirac Cone

“Ultra relativistic” Solid

State at low speed of light

In momentum space

“Ultra relativistic” Solid

State at low speed of light

In momentum space

Semi-Metal

“Ultra relativistic” Solid

State at low speed of light

Novoselov et al, Science 306, 666 (2004)

Novoselov et al, Science 306, 666 (2004)

Novoselov et al, Science 306, 666 (2004)

10

Graphene-Based Chemical Sensorsresponse to various gases

in concentration 1ppm

10

Graphene-Based Chemical Sensorsresponse to various gases

in concentration 1ppmcontinuous doping

by donors and acceptors

10

Graphene-Based Chemical Sensors

! straightforward 1 ppb resolution

response to various gases in concentration 1ppm

continuous doping by donors and acceptors

! graphene can be doped in concentrations >1012

cm-2

11

Single-Molecule Detection

step-like changes in Hall conductivitynear zero concentration

0 200 400 600

time (s)

0

10

20

30

!R

xy ("

)

adsorption

desorption

1e

1e

x1 x50

11

Single-Molecule Detection

step-like changes in Hall conductivitynear zero concentration

0 200 400 600

time (s)

0

10

20

30

!R

xy ("

)

adsorption

desorption

1e

1e

-4 -2 0 2 40

200

400

600

0

200

400

600

num

ber

of ste

ps

!Rxy (")

annealed

desorption adsorption

-1e+1e

x1 x50

11

Single-Molecule Detection

step-like changes in Hall conductivitynear zero concentration

0 200 400 600

time (s)

0

10

20

30

!R

xy ("

)

adsorption

desorption

1e

1e

extremely electronically quiet: few unstable defects highly conductive even in the limit of no carriers

4-probe measurements on single-crystal with low-R contactsall the volume exposed to environment

-4 -2 0 2 40

200

400

600

0

200

400

600

num

ber

of ste

ps

!Rxy (")

annealed

desorption adsorption

-1e+1e

x1 x50

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

E

N(E)

Anderson’s Impurity Model

T>TK

Non-interacting: U=0

Non-interacting: U=0

Energy

V=0

Non-interacting: U=0

Energy

Non-interacting: U=0

Energy

Non-interacting: U=0

Broadening

EnergyEnergy

Mean-Field

Mean-Field

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.

• Control of the magnetic moment formation

using electric fields.

• Atoms that are not magnetic in ordinary

metal hosts (like hydrogen) can become

magnetic in graphene.