Graphene: Experimental Overvieeandrei/research/graphene/andrei-nobel... · Graphene: Experimental...

Nobel symposium Stockholm 2010

102 papers

103 papers

Graphene: Experimental Overview

Nobel Symposium – Stockholm May 2010

Eva Y. Andrei

Rutgers University


Graphene: An Experimental overview

Making graphene

Gee Wizz experiments

Graphene decoupled from substrate

Graphene on graphite

Suspended graphene


Making Graphene

Novoselev et al Science (2004)

< 100 mm

Exfoliation

Scotch tape with graphite flakes Press Si/SiO2 onto flakes on the tape

SiO2 300 nm

Si


Making Graphene

2009 IEEE

Epitaxial Graphene Growth on SiC Wafers

D.K. Gaskill et al . 2”

Graphitization Epitaxial grapehene on SiC

Epitaxial graohene

W. A. de Heer et al (2007)

C. Berger, et al J. Phys. Chem.B 108 (52) (2004)

Towards wafer-size graphene layers by atmospheric pressure

graphitization of silicon carbide

K. V. Emtsev1, et al Nature materials (2009)

http://www.nature.com.proxy.libraries.rutgers.edu/nmat/journal/v8/n3/full/nmat2382.html


Chemical Vapor Deposition Epitaxial grapehene on metals Ir, Ru, Ni, Cu

Making Graphene


Gee Wizz: Mechanical

S. Bunch et al,Nano Letters‘08

STM studies of biological assays

Ultra - Filtration

• Young‟s modulus ~ 1 TPa

• Impermeable membrane

graphene


Gee Wizz: Chemical

F Schedin et al,Nature Materials ‘07

Single molecule detection

NO2, NH3, CO


Gee Wizz: Optical

Transmittance at Dirac point:

T=1-ap =97.2%

P. Blake et al, Nano Letters, „08

Graphene layers change their

opacity when a voltage is applied,

R.R. Nair et al, Science (2008).


What is it good for?

Bio -graphene • DNA on graphene protected from break-down by

enzymes.

•Differentiates between Single stranded and

double stranded.

• Neuron growth enhancement

Potential for Drug delivery, gene therapy

TEM Imaging and dynamics of light atoms

and molecules on graphene

J. Meyer et al,Nature 2008 (Berkeley)

Z. Tang, et al Small. (2010) (PNNA)

T. Mueller et al Nature Photonics 2010 Y. M. Lin et al Science 2010


Electronic structure

kx

ky

E

B0

kvkE F=)(

Dirac Point D(E)

E

D(E)

E

BnvenE Fn ||2)sgn( 2=

Landau Levels McLure 1956

Degeneracy = gsxgv =4

||12

)(22

Ev

EDFp

=

Flux Degeneracy = # of flux lines

0

Bn =


conductivity

DVg

Ch

arg

e i

nh

om

og

en

eit

y (

e-h

pu

dd

les):

E x

Graphene on SiO2

Martin, et.al, (2008)

Vgmin ~1-10V

nmin~ 1011 cm -2

(ΔEF~30-100meV)

e h

DOS

e-h puddles z smeared Dirac point

nmin minimum carrier density

SET microscopy


Graphene on SiO2 : STM

STM topography

Dirac point

STM spectroscopy

Ch

arg

e i

nh

om

og

en

eit

y (

e-h

pu

dd

les):

E x

e h

DOS

-400 -200 0 2000.0

0.2

0.4

0.6

0.8

1.0

dI/d

V (

a.u

.)

Sample Bias (mV)


Graphene on Graphite: STM

Graphite

– Clean

– Lattice matched

– Conductor

Topography z structure

Spectroscopy z Density of states B=0

Spectroscopy z Density of states B>0

STM – home built

– Temperature T=4 (2K)

– Magnetic field B=13 (15T)

– Scan range 10-10 -10-3 m


STM: Graphene on Graphite

-200 -100 0 100 2000.0

0.2

0.4

0.6

0.8

Sample bias (mV)

0.0 T

dI/d

V (

a.u

.)

topography B=0 spectroscopy B>0 spectroscopy

skip

Landau levels Linear DOS


-0.2 -0.1 0.0 0.1 0.2

0.0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

0T

dI/d

V

E(meV)

2T

4T

10T

8T

6T

Landau level spectroscopy

SiC: Miller et al Science 2009

G. Li , E.Y. A - Nature Physics, 3, 623 (2007)

G. Li, A. Luican, E. Y. A., Phys. Rev. Lett (2009)

1

-2 -1 2 3 4 -4 -3

-5 0


-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

-150

-100

-50

0

50

100

150

200

vF = 0.8 x106 m/s

2 T

4 T

6 T

8 T

10 T

En

erg

y (m

eV

)

sgn(n) (|n|B)1/2

ED = 16.6±0.5 meV

Massless Dirac Fermions

...2,1,0,2 == NNBevE Fj




Graphene on graphite other results

Electron-phonon interactions – Slow down of quasiparticles

e-e interactions – Quasiparticle lifetime

Gap at Dirac point – broken symmetry gap



K

’

K

meVpsEqp /91 t

smvF /108.0 6=

meVmvF 10~2=D

skip

-0.6 -0.4 -0.2 0.0 0.2 0.4

-0.8

-0.6

-0.4

-0.2

0.0

0.2

(v-v

0)/v

E(eV)


Quantum Hall effect in graphene on SiO2

K.S. Novoselov et al , Nature 2005

Vg

K. Novoselov et al Nature 2005

Y. Zhang et al , Nature 2005


Single particle

physics

14

10

6

2

0

-2

-6

-10

- 14

sxy (e

2/h)

Quantum Hall Effect

Each filled Landau level contributes g edge modes (g degeneracy)

Each edge mode contributes one quantum of Hall conductance

,..1,0,4

6,2)2/1(

==

==

Ng

Ng

D(E)

E

Number of edge modes is topological “Chern number”

2exy s =

Correlation-challenge

No FQHE in graphene on SiO2 (B< 45T)


•Substrate roughness

•Trapped charges

•Quench condensed ripples

Get rid of the substrate!

•X. Du, I. Skachako, A. Barker, E. Y. A. Nature Nanotech. 3, 491 (2008)

Suspended Graphene

• Bolotin et al , Solid State Communications (2008)

2 terminal

Hall bar Si

SiO2

L< 1 mm


-0.5 0.0 0.50

10

20

r (

k

)

n(1012

)cm-2

4K

Ballistic

-0.5 0.0 0.50

10

20

n(1012

cm-2)

100K

200K

250K

r(k

)

ballistic

•X. Du, I. Skachko, A. Barker, E. Y. A. Nature Nanotech. 3, 491 (2008)

Non-Suspended versus Suspended Graphene

Non-suspended

suspended

sr 1=


-0.5 0.0 0.50

10

20

r (

k

)

n(1012

)cm-2

4K

•X. Du, I. Skachako, A. Barker, E. Y. A. Nature Nanotech. 3, 491 (2008)

Non-Suspended versus Suspended Graphene

suspended

Ballistic

Suspended

s ~ n1/2 , lmfp ~ Lsample

nmin ~ 109 – 1010 cm-2

m ~ 105 - 106 -cm2/ V s

Non suspended

s ~ n , lmfp << Lsample nmin ~ 1011 cm-2

m ~ 104 cm2/ V s

Ballistic transport

Approaching Dirac point


Hall bar (6 lead)

Suspended Graphene and QHE Bolotin et al , Solid State Communications (2008)

Vd=0 Vs=VH .

works for large samples

… NOT for small samples

Hall angle = 90o

,..6,2

)2

1(4

22

==

eN

exy s

1mm

-6 -4 -2 0

-6

-4

-2

0

sxy

Hall conductivity

sxy (

e2/h

)

6

2

expect

actually

fraction

s

hope

Suspended Graphene:

No QHE in Hall bar

configuration

The Hall-bar Standard

No contact resistance

Separates sxy and rxx

Activation gaps


QHE in 2-terminal measurement

Vd=0 Vs=VH

Hall angle = 90o

-10 0

10

14

-14 -2

6

2

G(e

2/h

)

1T

2T

3T

4T

5T

6T

8T

10T

12T

-6

cW ~ 3L

X. Du et al. Nature Nanotechnology (08)

D. Abanin, L. Levitov, PRB (08)

2 lead


-2 -1 00

1

2

2T

6T

8T

12T

G

(e

2/h

)

-1/3

FQHE in 2-terminal measurement

X. Du, I. Skachko, F. Duerr, A. Luican, EYA, Nature 462, 192 (2009)

FQHE in graphene

Seen already at 2T

Persists up to 20K (in 12T)

=

FQHE

• Bolotin et al (Columbia) Nature 462 (2009)

• Geim & Novoselov (Manchester)


• Bolotin et al (Columbia) Nature 462 (2009)

• Geim & Novoselov (Manchester)

-2 -1 00

1

2

2T

6T

8T

12T

G

(e

2/h

)

-1/3

Suspended Graphene: two terminal measurement


FQHE in graphene

Seen already at 2T

Persists up to 20K (in 12T)

-1 00

1

1/3

G

(e2/h

)

40K

20K

10K

4K

1.2K

1/3

12T

=

FQHE

D( 12T)~ 4.4K

D( 12T)~ 0K

D. Abanin, et al, PRB (2010)

Alicea & Fisher (2006)

Normura & Macdonald, (2006)

Abanin, Lee, & Levitov, (2007);

Alicea & Fisher (2006)

Gusynin & Sharpov (2006)

= 1 valley split = 1 spin split

Ground state of neutral graphene in field

Conductor Insulator

Spin first DSpin > Dvalley

B

e

x

QH edge states

=+1

= 0 =

Valley first DSpin< Dvalley

B

e

x

QH edge states bulk edge bulk edge

=0 insulating

Checkelsky,

et al (08)

=1 valley split Zhang et al (07)

tilted field expt

=0 conducting

Abanin et al (07)

=+1

= 0 =

Magnetically induced insulating phase

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

105

106

107

108

109

1010

1T

2T

3T

4T

5T

6T

8T

10T

12T

R (

)

4.2K

||<0.1

B>1T 0.1 0.2 0.3 0.4 0.5

104

105

106

107

108

12T

10T

8T

6T

5T

3T

2T

1T

Rm

ax (

)

T-1/2

2/1)/*(

0max ~ TTeRR

T*(4T)~ 100K

Insulating phase Correlated electron state:

bulk antiferromagnet+no edge states

• CDW or SDW

Spin polarized bulk + “broken edges”



Supended CVD Graphene membrane

with: A. Reina, J. Kong (MIT) R. R. Nair, K. Novoselov, A. Geim (Manchester)

optical micrograph

STM- Landau levels

-2 -1 0 1 2

-100

0

100

200

Energ

y (m

V)

|n|1/2

vF=1.16x10

6 m/s

B=3 T

4.4 K

SEM

50 mm


θ=4° θ=0° θ=6° θ=3° θ=10°

Twist between top layers z Moiré pattern

•Period of superstructure :

Twisted graphene

a0 ≈ 2.46 Å

Lopes dos Santos et al PRL 99, 256802 (2007).


Moiré pattern on graphite surface

superstructure L=7.5nm

STM topography: Moiré superstructure

q=.79o

x4 x250

G. Li, et al Nature Physics (2010)

M1

Boundary of area with

superstructure

G

G

M2


-200 0 200

0.0

0.5

1.0

1.5

2.0

G

dI/dV

(a.u

.)

sample bias (mV)-200 0 200

0.0

0.5

1.0

1.5

2.0

dI/dV

(a.u

.)

sample bias (mV)

M1

M2

Moiré pattern on graphite surface

Two peak structure only in twisted region

G

M2

M1

M1

M2

G

Spectroscopy – Van Hove singularities

G. Li, et al Nature Physics (2010)


Electronic dispersion of twisted layers

PRL 99, 256802 (2007).

S. Shallcross, et al 2009

G. Mele PRB 2010

Bistrizer, MacDonald 2010

ΔE DK )2/sin(2 qKK =D


Van Hove singularities

ΔE

G. Li et al. Nature Physics 6, p109 (2010)

ΔE Density

of states

Twisted graphene

develops strong




ΔE


ΔE Density

of states

-0.2 -0.1 0.0 0.1 0.20.0

0.5

1.0

1.5

2.0

dI/

dV

(a.u

.)

sample bias (eV)

D=90 meV, q=.79o



ΔE


ΔE Density

of states

Twist engineering of electronic DOS


Summary

-200 -100 0 100 2000.0

0.2

0.4

0.6

0.8

Sample bias (mV)

0.0 T

dI/dV

(a.u

.)

-200 -100 0 100 200

0.0

0.2

0.4

0.6

0.8

1.0

D: (140,116) spi20182

dI/d

V (

a.u

.)

sample bias (mV)

m0H = 4 T T=4.36 K

D = 2. meV

SKIP -2 -1 0

0

1

2

2T

6T

8T

12T

G (

e2/h

)

-1/3

-0.2 -0.1 0.0 0.1 0.20.0

0.5

1.0

1.5

2.0

dI/

dV

(a

.u.)

sample bias (eV)

Gee Wizz Mechanical – ultra-strong, impermeable Chemical – ultra-sensitive nose Optical – gate controlled transmittance

Graphene on graphite Honeycomb structure Dirac fermions

Linear Density of states Well defined Dirac point

Direct observation of Landau levels

Suspended graphene

Exfoliated membranes Ballistic transport on micron length scales Fractional quantum Hall effect

CVD membranes Twist control of electronic properties


Thanks

Xu Du Adina Luican Ivan Skachko

Fabian Duerr

Guohong Li

Patrick Stanger Justin Meyerson Anthony

Barker

Collaborators: •MIT: J. Kong, A. Reina

•Manchester: A. Geim, K. Novoselov, R. Nair •Porto: J. los Santos

•BU: A.H. Castro Neto

•Princeton: D. Abanin

•MIT: L. Levitov

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