some things you might be interested in knowing about graphene

some things you might be interested in knowing

about Graphene

FEW EXAMPLES OF MOST RECENT WORK

MANCHESTER

Physics at the Dirac Point

(Lifshitz transition in bilayer)

Serge Morozovunpublished

-5 5

concentration (1010 cm-2)-10 0 10

10

resistivity (k)

0

20

5 K

200 K

Tem

pera

ture

suspended devices

2 m2 K

level degeneracy lifted lt 01T

SdH oscillations start lt 100Gquantum mobilities gt 1000000 cm2Vs

transport mobilities gt 1000000 cm2Vs remnant doping lt 109 cm-2

suspended devices

2 m

-1 1

n (1011cm-2)

-2 0 20

R (

k)

200

800

600

400

B=05T

zero B

T = 2K

GAP IS OPEN BY MAGNETIC FIELDfor some devices lt1T

(VALLEY GAP)

-5 5


10

resistivity (k)

0

20

5 K

200 K

Tem

pera

ture

suspended devices

2 m

fractional QHE

Manchester unpublished

first reported by Andreirsquos group Nature rsquo09Kimrsquos group Nature rsquo09 Laursquos group arxiv 2010

million mobilities but the quality of quantization

remains really bad

need 4-p

robe d

evices

-5 5


10

resistivity (k)

0

20

5 K

200 K

Tem

pera

ture

continues sharpening below 1Kcharge inhomogeneity lt 108 cm-2

suspended devices

2 m

-1 1

n (1011cm-2)

-2 0 20

(k

)

4

16

8

zero BT = 2K

12

can smoothly pass from one electron to one hole

Fermi energy scale lt 1 meV

14

10

(k

)

-5

n (108cm-2)0

~T

remnant doping lt 109 cm-2

-5 5


10

resistivity (k)

0

20

5 K

200 K

Tem

pera

ture

-5 5


10

resistivity (k)

0

20

5 K

200 K

Tem

pera

ture

resistivity Dirac point

PROBING DIRAC POINTbull NO ENERGY GAP

bull NO METAL-INSULATORTRANSITION

even with one electron per device

monolayer min moves closer to 4e2h

bilayer min remains gt 4e2h

50 150T (K)

0 100 200

max

imum

res

istiv

ity (

h4e

2 )

0

1

2

2 monolayers

2 bilayers

T approaches T=0 approx linearly

PROBING DIRAC POINT

MONOLAYERgradual gap opening

BILAYERmore complex behavior

PROBING DIRAC POINT


magnetoresistance at Dirac point

(k

)

5

15

(k)12 8

B =025 T

~3x

109 c

m-2 energy gap

induced by gateis less than T

=4

=-4

-10 10

gate-induced concentration (109 cm-2)

00

- m

in

e (

109 cm

-2)

5

10

5 K

50 K

100 K

150 K

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

(k)

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening

near Dirac point curves collapse on

a universal dependence

totalconcentration

measure concentration ofthermally excited carriers

first let us analyze

monolayer

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

(k)

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening

0

ther

mal

car

riers

(10

10 c

m-2)

5

1

50 150T (K)

0 100 200

T 2

monolayer


monolayer

number of carriers at energy ~kT

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

Tbilayer

0

ther

mal

car

riers

(10

10 c

m-2)

10

20

50 150T (K)

0 100 200

T 2

monolayer

thermalbroadening

(k)


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening

(k)

0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

~3x109 cm-2

DENSITYDIMINISHES

like a gap ~1 meV at the Dirac pointbut with a finite T-dependent DOS

within the gap


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

(k)

thermalbroadening

~3x109 cm-2

DENSITYDIMINISHES


within the gap


0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

(k)

thermalbroadening


within the gap


~3x109 cm-2

~1 meV

0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

PROBING DIRAC POINT

one of many possibilitiessymmetry-breaking e-e phase transition

Falkorsquos group arxiv 2010

OPEN FOR INTERPRETATION

cyclotron gaps between different Landau levels

0026m0

gap between zero and first LLdoes not want to close

with decreasing B down to 500G

MESSAGE TO TAKE AWAY

LIFSHITZ TRANSITIONMODIFIED BY SOMETHING()

DIRAC POINT PHYSICSIS ACCESSIBLE

TO STUDIES IN ALL DETAILS

million mobilities in 4-probe geometry should bring a lot more of new physics

Leaving the Carbon Flatland

Peter Blakeunpublished

vertical transport through one-atom-thick crystals

Many Other 2D Materials Possible

1m

0Aring 9Aring 16Aring 23Aring

05m

2D boron nitride in AFM

2D MoS2 in optics

1 m

1m

0Aring 8Aring 23Aring

2D NbSe2 in AFM

1 m

2D Bi2Sr2CaCu2Ox in SEM

SOME AREINSULATORS

Manchester PNAS 2005

spin tunneling devicesresonant tunneling devices

tunneling devices

SS

superconducting junctions

one-atom-thick barriersatomically smooth and continuous

(impossible by MBE)

2D CRYSTALS AS TUNNEL BARRIER

1 layer BN

can now find BN monolayersin an optical microscope

top Au contact

Au contact

boron nitrideAuAu

2m

7-layer BN

breakdown 2 Vnm

-04

tunn

el c

urre

nt (

A)

0

02

04

-02

voltage (V)-5 0 5

I (A)

4535voltage

40

01

001

1

exponentialdependence

monolayer

resistivity ~1 Mm2

-1

tunn

el c

urre

nt (

A)

0

05

1

-05

-025 025

voltage (V)-05 0 05

voltage-04 0400

(1

M)

2

resistivity ~1 km2

-80

tunn

el c

urre

nt (

A)

0

40

80

-40

-01 01voltage (V)

-02 0 02

-01 01voltage

0

04

02

(1k)

trilayer

NO temperature dependenceexcept for Zero Bias Anomaly

MONOLAYER BARRIERheight gap ~5eV

effective thickness ~5-6Aring

NO pin holes

AuAu


LAYER-BY-LAYER CONSTRUCTIONOF VARIOUS TUNNELING DEVICES

amp QUANTUM WELLS

NEW VENUEATOMICALLY SMOOTH CONTINUOUS

ONE- TWO FEW-ATOM-THICK TUNNEL BARRIERS

(beyond MBE any surface)

Pseudo-Magnetic Fields by Strain

Paco Guinea M Katsnelson amp AKG Nature Phys 2010

Electronic Properties under Strain

elastically stretched by gt 15

Manchester+Cambridge PRB 2009 Small 2009Honersquos group PNAS 2009

band structure changes littleno gap expected even at 25 stretch

Castro Neto PRB 2009

practically always rippled

non-uniform strain causes pseudo-magnetic field

Manchester PRL 2006

B+

B-

Non-Uniform Strain

[100]

[010][001]

Creating Uniform Pseudo-Magnetic Field

graphenedisk

graphenerectangular

UNIFORM FIELD

KKrsquoinsulating bulk

counter propagating edge currents

STRAIN ONLY

Nature Phys 2010 PRB 2010

field of 10T10 strain in m samples

spacing lattice size sample

straineff

e

hB

equivalent to magnetic fields of ~400T

Giant Pseudo-Magnetic FieldsM Crommiersquos group Science 2010 strained graphene bubbles

on Pt surface


Strain Engineering Can Open Really Large Gaps

Pseudo-Magnetic fieldcan be UNIFORM

Landau quantization and QHE in zero magnetic field

Magneto Oscillationsin Quantum Capacitance

Leonid Ponomarenko arxiv amp PRL 2010

Capacitance Measurements

100 m SiO2insulating Si

AuTi Al (top gate)

10 nm aluminium oxide

graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

T = 10 K

QUALITATIVE OBSERVATIONS Chen amp Appenzeller 2008

Xia et al Nature Nano 2009Giannazzo at al NanoLett 2009

~10000 cm2Vs


saturates to classical value Coxide

sharpness of the dip is determined by vF


AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

Coxide

T = 10 K

22π

2

Fv

E

dE

dn

~10000 cm2Vs



Capacitance Varies with Concentration

vF 11(plusmn01)middot106 ms


AuTi Al (top gate)


graphene

-04 -02 00 02 040

2

4

6

Cq (F

cm

2 )

EF (eV)

best fit 16 to 23 Fcm2

for several devices

smearingn 5middot1011 cm-2



QUANTITATIVE AGREEMENT

~10000 cm2Vs

22π

2

Fv

E

dE

dn

Magneto Capacitance Oscillations

250K

150K

100K

200K

-1 0 1

04

06B =16 T

C (F

cm

2)

Vtop gate

(V)

30K

12T

8T

4T

B =0T

T =10 K

-1 0 1

035

040

C (F

cm

2)

Vtop gate

(V)

pronouncedmagneto-oscillations

easily survive toroom T


Quantum Capacitanceis a Huge Effect in Graphene

Landau QuantizationSurvives at Room T in Modest Fields

(unlike transport this does not require gt30T)

CONCLUSION

GRAPHENE IS A GOLD MINEFOR NEW SCIENCEamp APPLICATIONS

does NOT feel at all like a mature research area

MUCH MORE TO COME

Misha Katsnelson(Nijmegen)

Rahul NairSergey Morozov(Chernogolovka)

F Schedin P Blake

Nuno Peres (Porto) Paco Guinea (Madrid) Leonid Levitov (Boston) Rui Yang Volodya Falrsquoko (Lancaster) Soeren Neubeck Ernie Hill Sasha Grigorenko

graphene reviews Nature Mat lsquo07 RMP rsquo09 Science lsquo09

Kostya Novoselov

D Elias A Ferrari(Cambridge)

LPonomarenko A Castro Neto(Boston)

Irina Grigorieva

ldquographene dreamsrdquosubstitute for Si

Manchester Science 2004de Heer et al JPhysChem 2004

see also Dresselhaus 1996

GRAPHENE ELECTRONICS

ballistic transport on submicron scale

high velocitygreat electrostaticsscales to nm sizes

BUTno pinch off

-100 -50 0 10050

Vg (V)

(k

)

0

2

4

6

SiO2

Si graphene

GRAPHENE NANO-CIRCUITS

)(

1

nm

eV

DE

E = vF h2D

not 1D2 as for electrons

but much larger 1Das for slow photons

10 nm

e-b lithography

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm

stable and robust down to a few nm in sizesustains large (~1 A per atom) currents


Manchester Science lsquo08also Dai et al Science lsquo08

e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K

PROBLEM no tools to sculpture at true nm scale

(same for any other nanoelectronics approach)


top-down molecular electronics

Slide 1

Slide 2

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Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

FEW EXAMPLES OF MOST RECENT WORK

MANCHESTER




-5 5


10

resistivity (k)

0

20

5 K

200 K

Tem

pera

ture

suspended devices

2 m2 K




suspended devices

2 m

-1 1

n (1011cm-2)

-2 0 20

R (

k)

200

800

600

400

B=05T

zero B

T = 2K


(VALLEY GAP)

-5 5


10

resistivity (k)

0

20

5 K

200 K

Tem

pera

ture

suspended devices

2 m

fractional QHE




remains really bad

need 4-p

robe d

evices

-5 5


10

resistivity (k)

0

20

5 K

200 K

Tem

pera

ture


suspended devices

2 m

-1 1

n (1011cm-2)

-2 0 20

(k

)

4

16

8

zero BT = 2K

12



14

10

(k

)

-5

n (108cm-2)0

~T


-5 5


10

resistivity (k)

0

20

5 K

200 K

Tem

pera

ture

-5 5


10

resistivity (k)

0

20

5 K

200 K

Tem

pera

ture







50 150T (K)

0 100 200

max

imum

res

istiv

ity (

h4e

2 )

0

1

2

2 monolayers

2 bilayers


PROBING DIRAC POINT



PROBING DIRAC POINT



(k

)

5

15

(k)12 8

B =025 T

~3x

109 c

m-2 energy gap


=4

=-4

-10 10


00

- m

in

e (

109 cm

-2)

5

10

5 K

50 K

100 K

150 K

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

(k)

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening



totalconcentration



monolayer

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

(k)

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening

0

ther

mal

car

riers

(10

10 c

m-2)

5

1

50 150T (K)

0 100 200

T 2

monolayer


monolayer


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

Tbilayer

0

ther

mal

car

riers

(10

10 c

m-2)

10

20

50 150T (K)

0 100 200

T 2

monolayer

thermalbroadening

(k)


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening

(k)

0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

~3x109 cm-2

DENSITYDIMINISHES


within the gap


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

(k)

thermalbroadening

~3x109 cm-2

DENSITYDIMINISHES


within the gap


0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

(k)

thermalbroadening


within the gap


~3x109 cm-2

~1 meV

0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

PROBING DIRAC POINT





0026m0












1m


05m


2D MoS2 in optics

1 m

1m


2D NbSe2 in AFM

1 m


SOME AREINSULATORS



tunneling devices

SS



(impossible by MBE)


1 layer BN


top Au contact

Au contact

boron nitrideAuAu

2m

7-layer BN

breakdown 2 Vnm

-04

tunn

el c

urre

nt (

A)

0

02

04

-02

voltage (V)-5 0 5

I (A)

4535voltage

40

01

001

1


monolayer

resistivity ~1 Mm2

-1

tunn

el c

urre

nt (

A)

0

05

1

-05

-025 025

voltage (V)-05 0 05

voltage-04 0400

(1

M)

2

resistivity ~1 km2

-80

tunn

el c

urre

nt (

A)

0

40

80

-40

-01 01voltage (V)

-02 0 02

-01 01voltage

0

04

02

(1k)

trilayer




NO pin holes

AuAu



amp QUANTUM WELLS













Manchester PRL 2006

B+

B-

Non-Uniform Strain

[100]

[010][001]


graphenedisk

graphenerectangular

UNIFORM FIELD



STRAIN ONLY




straineff

e

hB



on Pt surface









AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

T = 10 K



~10000 cm2Vs





AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

Coxide

T = 10 K

22π

2

Fv

E

dE

dn

~10000 cm2Vs






AuTi Al (top gate)


graphene

-04 -02 00 02 040

2

4

6

Cq (F

cm

2 )

EF (eV)


for several devices





~10000 cm2Vs

22π

2

Fv

E

dE

dn


250K

150K

100K

200K

-1 0 1

04

06B =16 T

C (F

cm

2)

Vtop gate

(V)

30K

12T

8T

4T

B =0T

T =10 K

-1 0 1

035

040

C (F

cm

2)

Vtop gate

(V)







CONCLUSION



MUCH MORE TO COME



F Schedin P Blake



Kostya Novoselov



Irina Grigorieva







BUTno pinch off

-100 -50 0 10050

Vg (V)

(k

)

0

2

4

6

SiO2

Si graphene


)(

1

nm

eV

DE

E = vF h2D



10 nm

e-b lithography

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm




e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43




-5 5


10

resistivity (k)

0

20

5 K

200 K

Tem

pera

ture

suspended devices

2 m2 K




suspended devices

2 m

-1 1

n (1011cm-2)

-2 0 20

R (

k)

200

800

600

400

B=05T

zero B

T = 2K


(VALLEY GAP)

-5 5


10

resistivity (k)

0

20

5 K

200 K

Tem

pera

ture

suspended devices

2 m

fractional QHE




remains really bad

need 4-p

robe d

evices

-5 5


10

resistivity (k)

0

20

5 K

200 K

Tem

pera

ture


suspended devices

2 m

-1 1

n (1011cm-2)

-2 0 20

(k

)

4

16

8

zero BT = 2K

12



14

10

(k

)

-5

n (108cm-2)0

~T


-5 5


10

resistivity (k)

0

20

5 K

200 K

Tem

pera

ture

-5 5


10

resistivity (k)

0

20

5 K

200 K

Tem

pera

ture







50 150T (K)

0 100 200

max

imum

res

istiv

ity (

h4e

2 )

0

1

2

2 monolayers

2 bilayers


PROBING DIRAC POINT



PROBING DIRAC POINT



(k

)

5

15

(k)12 8

B =025 T

~3x

109 c

m-2 energy gap


=4

=-4

-10 10


00

- m

in

e (

109 cm

-2)

5

10

5 K

50 K

100 K

150 K

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

(k)

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening



totalconcentration



monolayer

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

(k)

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening

0

ther

mal

car

riers

(10

10 c

m-2)

5

1

50 150T (K)

0 100 200

T 2

monolayer


monolayer


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

Tbilayer

0

ther

mal

car

riers

(10

10 c

m-2)

10

20

50 150T (K)

0 100 200

T 2

monolayer

thermalbroadening

(k)


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening

(k)

0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

~3x109 cm-2

DENSITYDIMINISHES


within the gap


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

(k)

thermalbroadening

~3x109 cm-2

DENSITYDIMINISHES


within the gap


0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

(k)

thermalbroadening


within the gap


~3x109 cm-2

~1 meV

0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

PROBING DIRAC POINT





0026m0












1m


05m


2D MoS2 in optics

1 m

1m


2D NbSe2 in AFM

1 m


SOME AREINSULATORS



tunneling devices

SS



(impossible by MBE)


1 layer BN


top Au contact

Au contact

boron nitrideAuAu

2m

7-layer BN

breakdown 2 Vnm

-04

tunn

el c

urre

nt (

A)

0

02

04

-02

voltage (V)-5 0 5

I (A)

4535voltage

40

01

001

1


monolayer

resistivity ~1 Mm2

-1

tunn

el c

urre

nt (

A)

0

05

1

-05

-025 025

voltage (V)-05 0 05

voltage-04 0400

(1

M)

2

resistivity ~1 km2

-80

tunn

el c

urre

nt (

A)

0

40

80

-40

-01 01voltage (V)

-02 0 02

-01 01voltage

0

04

02

(1k)

trilayer




NO pin holes

AuAu



amp QUANTUM WELLS













Manchester PRL 2006

B+

B-

Non-Uniform Strain

[100]

[010][001]


graphenedisk

graphenerectangular

UNIFORM FIELD



STRAIN ONLY




straineff

e

hB



on Pt surface









AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

T = 10 K



~10000 cm2Vs





AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

Coxide

T = 10 K

22π

2

Fv

E

dE

dn

~10000 cm2Vs






AuTi Al (top gate)


graphene

-04 -02 00 02 040

2

4

6

Cq (F

cm

2 )

EF (eV)


for several devices





~10000 cm2Vs

22π

2

Fv

E

dE

dn


250K

150K

100K

200K

-1 0 1

04

06B =16 T

C (F

cm

2)

Vtop gate

(V)

30K

12T

8T

4T

B =0T

T =10 K

-1 0 1

035

040

C (F

cm

2)

Vtop gate

(V)







CONCLUSION



MUCH MORE TO COME



F Schedin P Blake



Kostya Novoselov



Irina Grigorieva







BUTno pinch off

-100 -50 0 10050

Vg (V)

(k

)

0

2

4

6

SiO2

Si graphene


)(

1

nm

eV

DE

E = vF h2D



10 nm

e-b lithography

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm




e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

suspended devices

2 m

-1 1

n (1011cm-2)

-2 0 20

R (

k)

200

800

600

400

B=05T

zero B

T = 2K


(VALLEY GAP)

-5 5


10

resistivity (k)

0

20

5 K

200 K

Tem

pera

ture

suspended devices

2 m

fractional QHE




remains really bad

need 4-p

robe d

evices

-5 5


10

resistivity (k)

0

20

5 K

200 K

Tem

pera

ture


suspended devices

2 m

-1 1

n (1011cm-2)

-2 0 20

(k

)

4

16

8

zero BT = 2K

12



14

10

(k

)

-5

n (108cm-2)0

~T


-5 5


10

resistivity (k)

0

20

5 K

200 K

Tem

pera

ture

-5 5


10

resistivity (k)

0

20

5 K

200 K

Tem

pera

ture







50 150T (K)

0 100 200

max

imum

res

istiv

ity (

h4e

2 )

0

1

2

2 monolayers

2 bilayers


PROBING DIRAC POINT



PROBING DIRAC POINT



(k

)

5

15

(k)12 8

B =025 T

~3x

109 c

m-2 energy gap


=4

=-4

-10 10


00

- m

in

e (

109 cm

-2)

5

10

5 K

50 K

100 K

150 K

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

(k)

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening



totalconcentration



monolayer

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

(k)

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening

0

ther

mal

car

riers

(10

10 c

m-2)

5

1

50 150T (K)

0 100 200

T 2

monolayer


monolayer


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

Tbilayer

0

ther

mal

car

riers

(10

10 c

m-2)

10

20

50 150T (K)

0 100 200

T 2

monolayer

thermalbroadening

(k)


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening

(k)

0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

~3x109 cm-2

DENSITYDIMINISHES


within the gap


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

(k)

thermalbroadening

~3x109 cm-2

DENSITYDIMINISHES


within the gap


0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

(k)

thermalbroadening


within the gap


~3x109 cm-2

~1 meV

0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

PROBING DIRAC POINT





0026m0












1m


05m


2D MoS2 in optics

1 m

1m


2D NbSe2 in AFM

1 m


SOME AREINSULATORS



tunneling devices

SS



(impossible by MBE)


1 layer BN


top Au contact

Au contact

boron nitrideAuAu

2m

7-layer BN

breakdown 2 Vnm

-04

tunn

el c

urre

nt (

A)

0

02

04

-02

voltage (V)-5 0 5

I (A)

4535voltage

40

01

001

1


monolayer

resistivity ~1 Mm2

-1

tunn

el c

urre

nt (

A)

0

05

1

-05

-025 025

voltage (V)-05 0 05

voltage-04 0400

(1

M)

2

resistivity ~1 km2

-80

tunn

el c

urre

nt (

A)

0

40

80

-40

-01 01voltage (V)

-02 0 02

-01 01voltage

0

04

02

(1k)

trilayer




NO pin holes

AuAu



amp QUANTUM WELLS













Manchester PRL 2006

B+

B-

Non-Uniform Strain

[100]

[010][001]


graphenedisk

graphenerectangular

UNIFORM FIELD



STRAIN ONLY




straineff

e

hB



on Pt surface









AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

T = 10 K



~10000 cm2Vs





AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

Coxide

T = 10 K

22π

2

Fv

E

dE

dn

~10000 cm2Vs






AuTi Al (top gate)


graphene

-04 -02 00 02 040

2

4

6

Cq (F

cm

2 )

EF (eV)


for several devices





~10000 cm2Vs

22π

2

Fv

E

dE

dn


250K

150K

100K

200K

-1 0 1

04

06B =16 T

C (F

cm

2)

Vtop gate

(V)

30K

12T

8T

4T

B =0T

T =10 K

-1 0 1

035

040

C (F

cm

2)

Vtop gate

(V)







CONCLUSION



MUCH MORE TO COME



F Schedin P Blake



Kostya Novoselov



Irina Grigorieva







BUTno pinch off

-100 -50 0 10050

Vg (V)

(k

)

0

2

4

6

SiO2

Si graphene


)(

1

nm

eV

DE

E = vF h2D



10 nm

e-b lithography

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm




e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

suspended devices

2 m

fractional QHE




remains really bad

need 4-p

robe d

evices

-5 5


10

resistivity (k)

0

20

5 K

200 K

Tem

pera

ture


suspended devices

2 m

-1 1

n (1011cm-2)

-2 0 20

(k

)

4

16

8

zero BT = 2K

12



14

10

(k

)

-5

n (108cm-2)0

~T


-5 5


10

resistivity (k)

0

20

5 K

200 K

Tem

pera

ture

-5 5


10

resistivity (k)

0

20

5 K

200 K

Tem

pera

ture







50 150T (K)

0 100 200

max

imum

res

istiv

ity (

h4e

2 )

0

1

2

2 monolayers

2 bilayers


PROBING DIRAC POINT



PROBING DIRAC POINT



(k

)

5

15

(k)12 8

B =025 T

~3x

109 c

m-2 energy gap


=4

=-4

-10 10


00

- m

in

e (

109 cm

-2)

5

10

5 K

50 K

100 K

150 K

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

(k)

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening



totalconcentration



monolayer

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

(k)

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening

0

ther

mal

car

riers

(10

10 c

m-2)

5

1

50 150T (K)

0 100 200

T 2

monolayer


monolayer


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

Tbilayer

0

ther

mal

car

riers

(10

10 c

m-2)

10

20

50 150T (K)

0 100 200

T 2

monolayer

thermalbroadening

(k)


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening

(k)

0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

~3x109 cm-2

DENSITYDIMINISHES


within the gap


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

(k)

thermalbroadening

~3x109 cm-2

DENSITYDIMINISHES


within the gap


0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

(k)

thermalbroadening


within the gap


~3x109 cm-2

~1 meV

0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

PROBING DIRAC POINT





0026m0












1m


05m


2D MoS2 in optics

1 m

1m


2D NbSe2 in AFM

1 m


SOME AREINSULATORS



tunneling devices

SS



(impossible by MBE)


1 layer BN


top Au contact

Au contact

boron nitrideAuAu

2m

7-layer BN

breakdown 2 Vnm

-04

tunn

el c

urre

nt (

A)

0

02

04

-02

voltage (V)-5 0 5

I (A)

4535voltage

40

01

001

1


monolayer

resistivity ~1 Mm2

-1

tunn

el c

urre

nt (

A)

0

05

1

-05

-025 025

voltage (V)-05 0 05

voltage-04 0400

(1

M)

2

resistivity ~1 km2

-80

tunn

el c

urre

nt (

A)

0

40

80

-40

-01 01voltage (V)

-02 0 02

-01 01voltage

0

04

02

(1k)

trilayer




NO pin holes

AuAu



amp QUANTUM WELLS













Manchester PRL 2006

B+

B-

Non-Uniform Strain

[100]

[010][001]


graphenedisk

graphenerectangular

UNIFORM FIELD



STRAIN ONLY




straineff

e

hB



on Pt surface









AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

T = 10 K



~10000 cm2Vs





AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

Coxide

T = 10 K

22π

2

Fv

E

dE

dn

~10000 cm2Vs






AuTi Al (top gate)


graphene

-04 -02 00 02 040

2

4

6

Cq (F

cm

2 )

EF (eV)


for several devices





~10000 cm2Vs

22π

2

Fv

E

dE

dn


250K

150K

100K

200K

-1 0 1

04

06B =16 T

C (F

cm

2)

Vtop gate

(V)

30K

12T

8T

4T

B =0T

T =10 K

-1 0 1

035

040

C (F

cm

2)

Vtop gate

(V)







CONCLUSION



MUCH MORE TO COME



F Schedin P Blake



Kostya Novoselov



Irina Grigorieva







BUTno pinch off

-100 -50 0 10050

Vg (V)

(k

)

0

2

4

6

SiO2

Si graphene


)(

1

nm

eV

DE

E = vF h2D



10 nm

e-b lithography

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm




e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43


suspended devices

2 m

-1 1

n (1011cm-2)

-2 0 20

(k

)

4

16

8

zero BT = 2K

12



14

10

(k

)

-5

n (108cm-2)0

~T


-5 5


10

resistivity (k)

0

20

5 K

200 K

Tem

pera

ture

-5 5


10

resistivity (k)

0

20

5 K

200 K

Tem

pera

ture







50 150T (K)

0 100 200

max

imum

res

istiv

ity (

h4e

2 )

0

1

2

2 monolayers

2 bilayers


PROBING DIRAC POINT



PROBING DIRAC POINT



(k

)

5

15

(k)12 8

B =025 T

~3x

109 c

m-2 energy gap


=4

=-4

-10 10


00

- m

in

e (

109 cm

-2)

5

10

5 K

50 K

100 K

150 K

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

(k)

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening



totalconcentration



monolayer

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

(k)

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening

0

ther

mal

car

riers

(10

10 c

m-2)

5

1

50 150T (K)

0 100 200

T 2

monolayer


monolayer


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

Tbilayer

0

ther

mal

car

riers

(10

10 c

m-2)

10

20

50 150T (K)

0 100 200

T 2

monolayer

thermalbroadening

(k)


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening

(k)

0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

~3x109 cm-2

DENSITYDIMINISHES


within the gap


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

(k)

thermalbroadening

~3x109 cm-2

DENSITYDIMINISHES


within the gap


0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

(k)

thermalbroadening


within the gap


~3x109 cm-2

~1 meV

0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

PROBING DIRAC POINT





0026m0












1m


05m


2D MoS2 in optics

1 m

1m


2D NbSe2 in AFM

1 m


SOME AREINSULATORS



tunneling devices

SS



(impossible by MBE)


1 layer BN


top Au contact

Au contact

boron nitrideAuAu

2m

7-layer BN

breakdown 2 Vnm

-04

tunn

el c

urre

nt (

A)

0

02

04

-02

voltage (V)-5 0 5

I (A)

4535voltage

40

01

001

1


monolayer

resistivity ~1 Mm2

-1

tunn

el c

urre

nt (

A)

0

05

1

-05

-025 025

voltage (V)-05 0 05

voltage-04 0400

(1

M)

2

resistivity ~1 km2

-80

tunn

el c

urre

nt (

A)

0

40

80

-40

-01 01voltage (V)

-02 0 02

-01 01voltage

0

04

02

(1k)

trilayer




NO pin holes

AuAu



amp QUANTUM WELLS













Manchester PRL 2006

B+

B-

Non-Uniform Strain

[100]

[010][001]


graphenedisk

graphenerectangular

UNIFORM FIELD



STRAIN ONLY




straineff

e

hB



on Pt surface









AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

T = 10 K



~10000 cm2Vs





AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

Coxide

T = 10 K

22π

2

Fv

E

dE

dn

~10000 cm2Vs






AuTi Al (top gate)


graphene

-04 -02 00 02 040

2

4

6

Cq (F

cm

2 )

EF (eV)


for several devices





~10000 cm2Vs

22π

2

Fv

E

dE

dn


250K

150K

100K

200K

-1 0 1

04

06B =16 T

C (F

cm

2)

Vtop gate

(V)

30K

12T

8T

4T

B =0T

T =10 K

-1 0 1

035

040

C (F

cm

2)

Vtop gate

(V)







CONCLUSION



MUCH MORE TO COME



F Schedin P Blake



Kostya Novoselov



Irina Grigorieva







BUTno pinch off

-100 -50 0 10050

Vg (V)

(k

)

0

2

4

6

SiO2

Si graphene


)(

1

nm

eV

DE

E = vF h2D



10 nm

e-b lithography

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm




e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

-5 5


10

resistivity (k)

0

20

5 K

200 K

Tem

pera

ture







50 150T (K)

0 100 200

max

imum

res

istiv

ity (

h4e

2 )

0

1

2

2 monolayers

2 bilayers


PROBING DIRAC POINT



PROBING DIRAC POINT



(k

)

5

15

(k)12 8

B =025 T

~3x

109 c

m-2 energy gap


=4

=-4

-10 10


00

- m

in

e (

109 cm

-2)

5

10

5 K

50 K

100 K

150 K

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

(k)

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening



totalconcentration



monolayer

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

(k)

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening

0

ther

mal

car

riers

(10

10 c

m-2)

5

1

50 150T (K)

0 100 200

T 2

monolayer


monolayer


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

Tbilayer

0

ther

mal

car

riers

(10

10 c

m-2)

10

20

50 150T (K)

0 100 200

T 2

monolayer

thermalbroadening

(k)


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening

(k)

0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

~3x109 cm-2

DENSITYDIMINISHES


within the gap


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

(k)

thermalbroadening

~3x109 cm-2

DENSITYDIMINISHES


within the gap


0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

(k)

thermalbroadening


within the gap


~3x109 cm-2

~1 meV

0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

PROBING DIRAC POINT





0026m0












1m


05m


2D MoS2 in optics

1 m

1m


2D NbSe2 in AFM

1 m


SOME AREINSULATORS



tunneling devices

SS



(impossible by MBE)


1 layer BN


top Au contact

Au contact

boron nitrideAuAu

2m

7-layer BN

breakdown 2 Vnm

-04

tunn

el c

urre

nt (

A)

0

02

04

-02

voltage (V)-5 0 5

I (A)

4535voltage

40

01

001

1


monolayer

resistivity ~1 Mm2

-1

tunn

el c

urre

nt (

A)

0

05

1

-05

-025 025

voltage (V)-05 0 05

voltage-04 0400

(1

M)

2

resistivity ~1 km2

-80

tunn

el c

urre

nt (

A)

0

40

80

-40

-01 01voltage (V)

-02 0 02

-01 01voltage

0

04

02

(1k)

trilayer




NO pin holes

AuAu



amp QUANTUM WELLS













Manchester PRL 2006

B+

B-

Non-Uniform Strain

[100]

[010][001]


graphenedisk

graphenerectangular

UNIFORM FIELD



STRAIN ONLY




straineff

e

hB



on Pt surface









AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

T = 10 K



~10000 cm2Vs





AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

Coxide

T = 10 K

22π

2

Fv

E

dE

dn

~10000 cm2Vs






AuTi Al (top gate)


graphene

-04 -02 00 02 040

2

4

6

Cq (F

cm

2 )

EF (eV)


for several devices





~10000 cm2Vs

22π

2

Fv

E

dE

dn


250K

150K

100K

200K

-1 0 1

04

06B =16 T

C (F

cm

2)

Vtop gate

(V)

30K

12T

8T

4T

B =0T

T =10 K

-1 0 1

035

040

C (F

cm

2)

Vtop gate

(V)







CONCLUSION



MUCH MORE TO COME



F Schedin P Blake



Kostya Novoselov



Irina Grigorieva







BUTno pinch off

-100 -50 0 10050

Vg (V)

(k

)

0

2

4

6

SiO2

Si graphene


)(

1

nm

eV

DE

E = vF h2D



10 nm

e-b lithography

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm




e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

PROBING DIRAC POINT



PROBING DIRAC POINT



(k

)

5

15

(k)12 8

B =025 T

~3x

109 c

m-2 energy gap


=4

=-4

-10 10


00

- m

in

e (

109 cm

-2)

5

10

5 K

50 K

100 K

150 K

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

(k)

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening



totalconcentration



monolayer

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

(k)

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening

0

ther

mal

car

riers

(10

10 c

m-2)

5

1

50 150T (K)

0 100 200

T 2

monolayer


monolayer


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

Tbilayer

0

ther

mal

car

riers

(10

10 c

m-2)

10

20

50 150T (K)

0 100 200

T 2

monolayer

thermalbroadening

(k)


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening

(k)

0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

~3x109 cm-2

DENSITYDIMINISHES


within the gap


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

(k)

thermalbroadening

~3x109 cm-2

DENSITYDIMINISHES


within the gap


0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

(k)

thermalbroadening


within the gap


~3x109 cm-2

~1 meV

0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

PROBING DIRAC POINT





0026m0












1m


05m


2D MoS2 in optics

1 m

1m


2D NbSe2 in AFM

1 m


SOME AREINSULATORS



tunneling devices

SS



(impossible by MBE)


1 layer BN


top Au contact

Au contact

boron nitrideAuAu

2m

7-layer BN

breakdown 2 Vnm

-04

tunn

el c

urre

nt (

A)

0

02

04

-02

voltage (V)-5 0 5

I (A)

4535voltage

40

01

001

1


monolayer

resistivity ~1 Mm2

-1

tunn

el c

urre

nt (

A)

0

05

1

-05

-025 025

voltage (V)-05 0 05

voltage-04 0400

(1

M)

2

resistivity ~1 km2

-80

tunn

el c

urre

nt (

A)

0

40

80

-40

-01 01voltage (V)

-02 0 02

-01 01voltage

0

04

02

(1k)

trilayer




NO pin holes

AuAu



amp QUANTUM WELLS













Manchester PRL 2006

B+

B-

Non-Uniform Strain

[100]

[010][001]


graphenedisk

graphenerectangular

UNIFORM FIELD



STRAIN ONLY




straineff

e

hB



on Pt surface









AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

T = 10 K



~10000 cm2Vs





AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

Coxide

T = 10 K

22π

2

Fv

E

dE

dn

~10000 cm2Vs






AuTi Al (top gate)


graphene

-04 -02 00 02 040

2

4

6

Cq (F

cm

2 )

EF (eV)


for several devices





~10000 cm2Vs

22π

2

Fv

E

dE

dn


250K

150K

100K

200K

-1 0 1

04

06B =16 T

C (F

cm

2)

Vtop gate

(V)

30K

12T

8T

4T

B =0T

T =10 K

-1 0 1

035

040

C (F

cm

2)

Vtop gate

(V)







CONCLUSION



MUCH MORE TO COME



F Schedin P Blake



Kostya Novoselov



Irina Grigorieva







BUTno pinch off

-100 -50 0 10050

Vg (V)

(k

)

0

2

4

6

SiO2

Si graphene


)(

1

nm

eV

DE

E = vF h2D



10 nm

e-b lithography

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm




e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

PROBING DIRAC POINT



(k

)

5

15

(k)12 8

B =025 T

~3x

109 c

m-2 energy gap


=4

=-4

-10 10


00

- m

in

e (

109 cm

-2)

5

10

5 K

50 K

100 K

150 K

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

(k)

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening



totalconcentration



monolayer

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

(k)

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening

0

ther

mal

car

riers

(10

10 c

m-2)

5

1

50 150T (K)

0 100 200

T 2

monolayer


monolayer


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

Tbilayer

0

ther

mal

car

riers

(10

10 c

m-2)

10

20

50 150T (K)

0 100 200

T 2

monolayer

thermalbroadening

(k)


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening

(k)

0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

~3x109 cm-2

DENSITYDIMINISHES


within the gap


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

(k)

thermalbroadening

~3x109 cm-2

DENSITYDIMINISHES


within the gap


0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

(k)

thermalbroadening


within the gap


~3x109 cm-2

~1 meV

0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

PROBING DIRAC POINT





0026m0












1m


05m


2D MoS2 in optics

1 m

1m


2D NbSe2 in AFM

1 m


SOME AREINSULATORS



tunneling devices

SS



(impossible by MBE)


1 layer BN


top Au contact

Au contact

boron nitrideAuAu

2m

7-layer BN

breakdown 2 Vnm

-04

tunn

el c

urre

nt (

A)

0

02

04

-02

voltage (V)-5 0 5

I (A)

4535voltage

40

01

001

1


monolayer

resistivity ~1 Mm2

-1

tunn

el c

urre

nt (

A)

0

05

1

-05

-025 025

voltage (V)-05 0 05

voltage-04 0400

(1

M)

2

resistivity ~1 km2

-80

tunn

el c

urre

nt (

A)

0

40

80

-40

-01 01voltage (V)

-02 0 02

-01 01voltage

0

04

02

(1k)

trilayer




NO pin holes

AuAu



amp QUANTUM WELLS













Manchester PRL 2006

B+

B-

Non-Uniform Strain

[100]

[010][001]


graphenedisk

graphenerectangular

UNIFORM FIELD



STRAIN ONLY




straineff

e

hB



on Pt surface









AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

T = 10 K



~10000 cm2Vs





AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

Coxide

T = 10 K

22π

2

Fv

E

dE

dn

~10000 cm2Vs






AuTi Al (top gate)


graphene

-04 -02 00 02 040

2

4

6

Cq (F

cm

2 )

EF (eV)


for several devices





~10000 cm2Vs

22π

2

Fv

E

dE

dn


250K

150K

100K

200K

-1 0 1

04

06B =16 T

C (F

cm

2)

Vtop gate

(V)

30K

12T

8T

4T

B =0T

T =10 K

-1 0 1

035

040

C (F

cm

2)

Vtop gate

(V)







CONCLUSION



MUCH MORE TO COME



F Schedin P Blake



Kostya Novoselov



Irina Grigorieva







BUTno pinch off

-100 -50 0 10050

Vg (V)

(k

)

0

2

4

6

SiO2

Si graphene


)(

1

nm

eV

DE

E = vF h2D



10 nm

e-b lithography

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm




e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

-10 10


00

- m

in

e (

109 cm

-2)

5

10

5 K

50 K

100 K

150 K

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

(k)

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening



totalconcentration



monolayer

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

(k)

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening

0

ther

mal

car

riers

(10

10 c

m-2)

5

1

50 150T (K)

0 100 200

T 2

monolayer


monolayer


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

Tbilayer

0

ther

mal

car

riers

(10

10 c

m-2)

10

20

50 150T (K)

0 100 200

T 2

monolayer

thermalbroadening

(k)


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening

(k)

0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

~3x109 cm-2

DENSITYDIMINISHES


within the gap


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

(k)

thermalbroadening

~3x109 cm-2

DENSITYDIMINISHES


within the gap


0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

(k)

thermalbroadening


within the gap


~3x109 cm-2

~1 meV

0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

PROBING DIRAC POINT





0026m0












1m


05m


2D MoS2 in optics

1 m

1m


2D NbSe2 in AFM

1 m


SOME AREINSULATORS



tunneling devices

SS



(impossible by MBE)


1 layer BN


top Au contact

Au contact

boron nitrideAuAu

2m

7-layer BN

breakdown 2 Vnm

-04

tunn

el c

urre

nt (

A)

0

02

04

-02

voltage (V)-5 0 5

I (A)

4535voltage

40

01

001

1


monolayer

resistivity ~1 Mm2

-1

tunn

el c

urre

nt (

A)

0

05

1

-05

-025 025

voltage (V)-05 0 05

voltage-04 0400

(1

M)

2

resistivity ~1 km2

-80

tunn

el c

urre

nt (

A)

0

40

80

-40

-01 01voltage (V)

-02 0 02

-01 01voltage

0

04

02

(1k)

trilayer




NO pin holes

AuAu



amp QUANTUM WELLS













Manchester PRL 2006

B+

B-

Non-Uniform Strain

[100]

[010][001]


graphenedisk

graphenerectangular

UNIFORM FIELD



STRAIN ONLY




straineff

e

hB



on Pt surface









AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

T = 10 K



~10000 cm2Vs





AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

Coxide

T = 10 K

22π

2

Fv

E

dE

dn

~10000 cm2Vs






AuTi Al (top gate)


graphene

-04 -02 00 02 040

2

4

6

Cq (F

cm

2 )

EF (eV)


for several devices





~10000 cm2Vs

22π

2

Fv

E

dE

dn


250K

150K

100K

200K

-1 0 1

04

06B =16 T

C (F

cm

2)

Vtop gate

(V)

30K

12T

8T

4T

B =0T

T =10 K

-1 0 1

035

040

C (F

cm

2)

Vtop gate

(V)







CONCLUSION



MUCH MORE TO COME



F Schedin P Blake



Kostya Novoselov



Irina Grigorieva







BUTno pinch off

-100 -50 0 10050

Vg (V)

(k

)

0

2

4

6

SiO2

Si graphene


)(

1

nm

eV

DE

E = vF h2D



10 nm

e-b lithography

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm




e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

(k)

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening

0

ther

mal

car

riers

(10

10 c

m-2)

5

1

50 150T (K)

0 100 200

T 2

monolayer


monolayer


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

Tbilayer

0

ther

mal

car

riers

(10

10 c

m-2)

10

20

50 150T (K)

0 100 200

T 2

monolayer

thermalbroadening

(k)


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening

(k)

0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

~3x109 cm-2

DENSITYDIMINISHES


within the gap


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

(k)

thermalbroadening

~3x109 cm-2

DENSITYDIMINISHES


within the gap


0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

(k)

thermalbroadening


within the gap


~3x109 cm-2

~1 meV

0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

PROBING DIRAC POINT





0026m0












1m


05m


2D MoS2 in optics

1 m

1m


2D NbSe2 in AFM

1 m


SOME AREINSULATORS



tunneling devices

SS



(impossible by MBE)


1 layer BN


top Au contact

Au contact

boron nitrideAuAu

2m

7-layer BN

breakdown 2 Vnm

-04

tunn

el c

urre

nt (

A)

0

02

04

-02

voltage (V)-5 0 5

I (A)

4535voltage

40

01

001

1


monolayer

resistivity ~1 Mm2

-1

tunn

el c

urre

nt (

A)

0

05

1

-05

-025 025

voltage (V)-05 0 05

voltage-04 0400

(1

M)

2

resistivity ~1 km2

-80

tunn

el c

urre

nt (

A)

0

40

80

-40

-01 01voltage (V)

-02 0 02

-01 01voltage

0

04

02

(1k)

trilayer




NO pin holes

AuAu



amp QUANTUM WELLS













Manchester PRL 2006

B+

B-

Non-Uniform Strain

[100]

[010][001]


graphenedisk

graphenerectangular

UNIFORM FIELD



STRAIN ONLY




straineff

e

hB



on Pt surface









AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

T = 10 K



~10000 cm2Vs





AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

Coxide

T = 10 K

22π

2

Fv

E

dE

dn

~10000 cm2Vs






AuTi Al (top gate)


graphene

-04 -02 00 02 040

2

4

6

Cq (F

cm

2 )

EF (eV)


for several devices





~10000 cm2Vs

22π

2

Fv

E

dE

dn


250K

150K

100K

200K

-1 0 1

04

06B =16 T

C (F

cm

2)

Vtop gate

(V)

30K

12T

8T

4T

B =0T

T =10 K

-1 0 1

035

040

C (F

cm

2)

Vtop gate

(V)







CONCLUSION



MUCH MORE TO COME



F Schedin P Blake



Kostya Novoselov



Irina Grigorieva







BUTno pinch off

-100 -50 0 10050

Vg (V)

(k

)

0

2

4

6

SiO2

Si graphene


)(

1

nm

eV

DE

E = vF h2D



10 nm

e-b lithography

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm




e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

Tbilayer

0

ther

mal

car

riers

(10

10 c

m-2)

10

20

50 150T (K)

0 100 200

T 2

monolayer

thermalbroadening

(k)


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening

(k)

0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

~3x109 cm-2

DENSITYDIMINISHES


within the gap


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

(k)

thermalbroadening

~3x109 cm-2

DENSITYDIMINISHES


within the gap


0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

(k)

thermalbroadening


within the gap


~3x109 cm-2

~1 meV

0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

PROBING DIRAC POINT





0026m0












1m


05m


2D MoS2 in optics

1 m

1m


2D NbSe2 in AFM

1 m


SOME AREINSULATORS



tunneling devices

SS



(impossible by MBE)


1 layer BN


top Au contact

Au contact

boron nitrideAuAu

2m

7-layer BN

breakdown 2 Vnm

-04

tunn

el c

urre

nt (

A)

0

02

04

-02

voltage (V)-5 0 5

I (A)

4535voltage

40

01

001

1


monolayer

resistivity ~1 Mm2

-1

tunn

el c

urre

nt (

A)

0

05

1

-05

-025 025

voltage (V)-05 0 05

voltage-04 0400

(1

M)

2

resistivity ~1 km2

-80

tunn

el c

urre

nt (

A)

0

40

80

-40

-01 01voltage (V)

-02 0 02

-01 01voltage

0

04

02

(1k)

trilayer




NO pin holes

AuAu



amp QUANTUM WELLS













Manchester PRL 2006

B+

B-

Non-Uniform Strain

[100]

[010][001]


graphenedisk

graphenerectangular

UNIFORM FIELD



STRAIN ONLY




straineff

e

hB



on Pt surface









AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

T = 10 K



~10000 cm2Vs





AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

Coxide

T = 10 K

22π

2

Fv

E

dE

dn

~10000 cm2Vs






AuTi Al (top gate)


graphene

-04 -02 00 02 040

2

4

6

Cq (F

cm

2 )

EF (eV)


for several devices





~10000 cm2Vs

22π

2

Fv

E

dE

dn


250K

150K

100K

200K

-1 0 1

04

06B =16 T

C (F

cm

2)

Vtop gate

(V)

30K

12T

8T

4T

B =0T

T =10 K

-1 0 1

035

040

C (F

cm

2)

Vtop gate

(V)







CONCLUSION



MUCH MORE TO COME



F Schedin P Blake



Kostya Novoselov



Irina Grigorieva







BUTno pinch off

-100 -50 0 10050

Vg (V)

(k

)

0

2

4

6

SiO2

Si graphene


)(

1

nm

eV

DE

E = vF h2D



10 nm

e-b lithography

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm




e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

thermalbroadening

(k)

0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

~3x109 cm-2

DENSITYDIMINISHES


within the gap


PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

(k)

thermalbroadening

~3x109 cm-2

DENSITYDIMINISHES


within the gap


0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

(k)

thermalbroadening


within the gap


~3x109 cm-2

~1 meV

0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

PROBING DIRAC POINT





0026m0












1m


05m


2D MoS2 in optics

1 m

1m


2D NbSe2 in AFM

1 m


SOME AREINSULATORS



tunneling devices

SS



(impossible by MBE)


1 layer BN


top Au contact

Au contact

boron nitrideAuAu

2m

7-layer BN

breakdown 2 Vnm

-04

tunn

el c

urre

nt (

A)

0

02

04

-02

voltage (V)-5 0 5

I (A)

4535voltage

40

01

001

1


monolayer

resistivity ~1 Mm2

-1

tunn

el c

urre

nt (

A)

0

05

1

-05

-025 025

voltage (V)-05 0 05

voltage-04 0400

(1

M)

2

resistivity ~1 km2

-80

tunn

el c

urre

nt (

A)

0

40

80

-40

-01 01voltage (V)

-02 0 02

-01 01voltage

0

04

02

(1k)

trilayer




NO pin holes

AuAu



amp QUANTUM WELLS













Manchester PRL 2006

B+

B-

Non-Uniform Strain

[100]

[010][001]


graphenedisk

graphenerectangular

UNIFORM FIELD



STRAIN ONLY




straineff

e

hB



on Pt surface









AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

T = 10 K



~10000 cm2Vs





AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

Coxide

T = 10 K

22π

2

Fv

E

dE

dn

~10000 cm2Vs






AuTi Al (top gate)


graphene

-04 -02 00 02 040

2

4

6

Cq (F

cm

2 )

EF (eV)


for several devices





~10000 cm2Vs

22π

2

Fv

E

dE

dn


250K

150K

100K

200K

-1 0 1

04

06B =16 T

C (F

cm

2)

Vtop gate

(V)

30K

12T

8T

4T

B =0T

T =10 K

-1 0 1

035

040

C (F

cm

2)

Vtop gate

(V)







CONCLUSION



MUCH MORE TO COME



F Schedin P Blake



Kostya Novoselov



Irina Grigorieva







BUTno pinch off

-100 -50 0 10050

Vg (V)

(k

)

0

2

4

6

SiO2

Si graphene


)(

1

nm

eV

DE

E = vF h2D



10 nm

e-b lithography

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm




e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

(k)

thermalbroadening

~3x109 cm-2

DENSITYDIMINISHES


within the gap


0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

(k)

thermalbroadening


within the gap


~3x109 cm-2

~1 meV

0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

PROBING DIRAC POINT





0026m0












1m


05m


2D MoS2 in optics

1 m

1m


2D NbSe2 in AFM

1 m


SOME AREINSULATORS



tunneling devices

SS



(impossible by MBE)


1 layer BN


top Au contact

Au contact

boron nitrideAuAu

2m

7-layer BN

breakdown 2 Vnm

-04

tunn

el c

urre

nt (

A)

0

02

04

-02

voltage (V)-5 0 5

I (A)

4535voltage

40

01

001

1


monolayer

resistivity ~1 Mm2

-1

tunn

el c

urre

nt (

A)

0

05

1

-05

-025 025

voltage (V)-05 0 05

voltage-04 0400

(1

M)

2

resistivity ~1 km2

-80

tunn

el c

urre

nt (

A)

0

40

80

-40

-01 01voltage (V)

-02 0 02

-01 01voltage

0

04

02

(1k)

trilayer




NO pin holes

AuAu



amp QUANTUM WELLS













Manchester PRL 2006

B+

B-

Non-Uniform Strain

[100]

[010][001]


graphenedisk

graphenerectangular

UNIFORM FIELD



STRAIN ONLY




straineff

e

hB



on Pt surface









AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

T = 10 K



~10000 cm2Vs





AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

Coxide

T = 10 K

22π

2

Fv

E

dE

dn

~10000 cm2Vs






AuTi Al (top gate)


graphene

-04 -02 00 02 040

2

4

6

Cq (F

cm

2 )

EF (eV)


for several devices





~10000 cm2Vs

22π

2

Fv

E

dE

dn


250K

150K

100K

200K

-1 0 1

04

06B =16 T

C (F

cm

2)

Vtop gate

(V)

30K

12T

8T

4T

B =0T

T =10 K

-1 0 1

035

040

C (F

cm

2)

Vtop gate

(V)







CONCLUSION



MUCH MORE TO COME



F Schedin P Blake



Kostya Novoselov



Irina Grigorieva







BUTno pinch off

-100 -50 0 10050

Vg (V)

(k

)

0

2

4

6

SiO2

Si graphene


)(

1

nm

eV

DE

E = vF h2D



10 nm

e-b lithography

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm




e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

PROBING DIRAC POINT

-5 5

n (1010 cm-2)-10 0 10

10

0

20

5 K

200 K

Tem

pera

ture

(k)

thermalbroadening


within the gap


~3x109 cm-2

~1 meV

0

ther

mal

car

riers

(10

10 c

m-2)

1

2

10 20T (K)

0 30

3

bilayer

PROBING DIRAC POINT





0026m0












1m


05m


2D MoS2 in optics

1 m

1m


2D NbSe2 in AFM

1 m


SOME AREINSULATORS



tunneling devices

SS



(impossible by MBE)


1 layer BN


top Au contact

Au contact

boron nitrideAuAu

2m

7-layer BN

breakdown 2 Vnm

-04

tunn

el c

urre

nt (

A)

0

02

04

-02

voltage (V)-5 0 5

I (A)

4535voltage

40

01

001

1


monolayer

resistivity ~1 Mm2

-1

tunn

el c

urre

nt (

A)

0

05

1

-05

-025 025

voltage (V)-05 0 05

voltage-04 0400

(1

M)

2

resistivity ~1 km2

-80

tunn

el c

urre

nt (

A)

0

40

80

-40

-01 01voltage (V)

-02 0 02

-01 01voltage

0

04

02

(1k)

trilayer




NO pin holes

AuAu



amp QUANTUM WELLS













Manchester PRL 2006

B+

B-

Non-Uniform Strain

[100]

[010][001]


graphenedisk

graphenerectangular

UNIFORM FIELD



STRAIN ONLY




straineff

e

hB



on Pt surface









AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

T = 10 K



~10000 cm2Vs





AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

Coxide

T = 10 K

22π

2

Fv

E

dE

dn

~10000 cm2Vs






AuTi Al (top gate)


graphene

-04 -02 00 02 040

2

4

6

Cq (F

cm

2 )

EF (eV)


for several devices





~10000 cm2Vs

22π

2

Fv

E

dE

dn


250K

150K

100K

200K

-1 0 1

04

06B =16 T

C (F

cm

2)

Vtop gate

(V)

30K

12T

8T

4T

B =0T

T =10 K

-1 0 1

035

040

C (F

cm

2)

Vtop gate

(V)







CONCLUSION



MUCH MORE TO COME



F Schedin P Blake



Kostya Novoselov



Irina Grigorieva







BUTno pinch off

-100 -50 0 10050

Vg (V)

(k

)

0

2

4

6

SiO2

Si graphene


)(

1

nm

eV

DE

E = vF h2D



10 nm

e-b lithography

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm




e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

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Slide 19

Slide 20

Slide 21

Slide 22

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Slide 24

Slide 25

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Slide 27

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Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

PROBING DIRAC POINT





0026m0












1m


05m


2D MoS2 in optics

1 m

1m


2D NbSe2 in AFM

1 m


SOME AREINSULATORS



tunneling devices

SS



(impossible by MBE)


1 layer BN


top Au contact

Au contact

boron nitrideAuAu

2m

7-layer BN

breakdown 2 Vnm

-04

tunn

el c

urre

nt (

A)

0

02

04

-02

voltage (V)-5 0 5

I (A)

4535voltage

40

01

001

1


monolayer

resistivity ~1 Mm2

-1

tunn

el c

urre

nt (

A)

0

05

1

-05

-025 025

voltage (V)-05 0 05

voltage-04 0400

(1

M)

2

resistivity ~1 km2

-80

tunn

el c

urre

nt (

A)

0

40

80

-40

-01 01voltage (V)

-02 0 02

-01 01voltage

0

04

02

(1k)

trilayer




NO pin holes

AuAu



amp QUANTUM WELLS













Manchester PRL 2006

B+

B-

Non-Uniform Strain

[100]

[010][001]


graphenedisk

graphenerectangular

UNIFORM FIELD



STRAIN ONLY




straineff

e

hB



on Pt surface









AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

T = 10 K



~10000 cm2Vs





AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

Coxide

T = 10 K

22π

2

Fv

E

dE

dn

~10000 cm2Vs






AuTi Al (top gate)


graphene

-04 -02 00 02 040

2

4

6

Cq (F

cm

2 )

EF (eV)


for several devices





~10000 cm2Vs

22π

2

Fv

E

dE

dn


250K

150K

100K

200K

-1 0 1

04

06B =16 T

C (F

cm

2)

Vtop gate

(V)

30K

12T

8T

4T

B =0T

T =10 K

-1 0 1

035

040

C (F

cm

2)

Vtop gate

(V)







CONCLUSION



MUCH MORE TO COME



F Schedin P Blake



Kostya Novoselov



Irina Grigorieva







BUTno pinch off

-100 -50 0 10050

Vg (V)

(k

)

0

2

4

6

SiO2

Si graphene


)(

1

nm

eV

DE

E = vF h2D



10 nm

e-b lithography

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm




e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43










1m


05m


2D MoS2 in optics

1 m

1m


2D NbSe2 in AFM

1 m


SOME AREINSULATORS



tunneling devices

SS



(impossible by MBE)


1 layer BN


top Au contact

Au contact

boron nitrideAuAu

2m

7-layer BN

breakdown 2 Vnm

-04

tunn

el c

urre

nt (

A)

0

02

04

-02

voltage (V)-5 0 5

I (A)

4535voltage

40

01

001

1


monolayer

resistivity ~1 Mm2

-1

tunn

el c

urre

nt (

A)

0

05

1

-05

-025 025

voltage (V)-05 0 05

voltage-04 0400

(1

M)

2

resistivity ~1 km2

-80

tunn

el c

urre

nt (

A)

0

40

80

-40

-01 01voltage (V)

-02 0 02

-01 01voltage

0

04

02

(1k)

trilayer




NO pin holes

AuAu



amp QUANTUM WELLS













Manchester PRL 2006

B+

B-

Non-Uniform Strain

[100]

[010][001]


graphenedisk

graphenerectangular

UNIFORM FIELD



STRAIN ONLY




straineff

e

hB



on Pt surface









AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

T = 10 K



~10000 cm2Vs





AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

Coxide

T = 10 K

22π

2

Fv

E

dE

dn

~10000 cm2Vs






AuTi Al (top gate)


graphene

-04 -02 00 02 040

2

4

6

Cq (F

cm

2 )

EF (eV)


for several devices





~10000 cm2Vs

22π

2

Fv

E

dE

dn


250K

150K

100K

200K

-1 0 1

04

06B =16 T

C (F

cm

2)

Vtop gate

(V)

30K

12T

8T

4T

B =0T

T =10 K

-1 0 1

035

040

C (F

cm

2)

Vtop gate

(V)







CONCLUSION



MUCH MORE TO COME



F Schedin P Blake



Kostya Novoselov



Irina Grigorieva







BUTno pinch off

-100 -50 0 10050

Vg (V)

(k

)

0

2

4

6

SiO2

Si graphene


)(

1

nm

eV

DE

E = vF h2D



10 nm

e-b lithography

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm




e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43


tunneling devices

SS



(impossible by MBE)


1 layer BN


top Au contact

Au contact

boron nitrideAuAu

2m

7-layer BN

breakdown 2 Vnm

-04

tunn

el c

urre

nt (

A)

0

02

04

-02

voltage (V)-5 0 5

I (A)

4535voltage

40

01

001

1


monolayer

resistivity ~1 Mm2

-1

tunn

el c

urre

nt (

A)

0

05

1

-05

-025 025

voltage (V)-05 0 05

voltage-04 0400

(1

M)

2

resistivity ~1 km2

-80

tunn

el c

urre

nt (

A)

0

40

80

-40

-01 01voltage (V)

-02 0 02

-01 01voltage

0

04

02

(1k)

trilayer




NO pin holes

AuAu



amp QUANTUM WELLS













Manchester PRL 2006

B+

B-

Non-Uniform Strain

[100]

[010][001]


graphenedisk

graphenerectangular

UNIFORM FIELD



STRAIN ONLY




straineff

e

hB



on Pt surface









AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

T = 10 K



~10000 cm2Vs





AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

Coxide

T = 10 K

22π

2

Fv

E

dE

dn

~10000 cm2Vs






AuTi Al (top gate)


graphene

-04 -02 00 02 040

2

4

6

Cq (F

cm

2 )

EF (eV)


for several devices





~10000 cm2Vs

22π

2

Fv

E

dE

dn


250K

150K

100K

200K

-1 0 1

04

06B =16 T

C (F

cm

2)

Vtop gate

(V)

30K

12T

8T

4T

B =0T

T =10 K

-1 0 1

035

040

C (F

cm

2)

Vtop gate

(V)







CONCLUSION



MUCH MORE TO COME



F Schedin P Blake



Kostya Novoselov



Irina Grigorieva







BUTno pinch off

-100 -50 0 10050

Vg (V)

(k

)

0

2

4

6

SiO2

Si graphene


)(

1

nm

eV

DE

E = vF h2D



10 nm

e-b lithography

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm




e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43


1 layer BN


top Au contact

Au contact

boron nitrideAuAu

2m

7-layer BN

breakdown 2 Vnm

-04

tunn

el c

urre

nt (

A)

0

02

04

-02

voltage (V)-5 0 5

I (A)

4535voltage

40

01

001

1


monolayer

resistivity ~1 Mm2

-1

tunn

el c

urre

nt (

A)

0

05

1

-05

-025 025

voltage (V)-05 0 05

voltage-04 0400

(1

M)

2

resistivity ~1 km2

-80

tunn

el c

urre

nt (

A)

0

40

80

-40

-01 01voltage (V)

-02 0 02

-01 01voltage

0

04

02

(1k)

trilayer




NO pin holes

AuAu



amp QUANTUM WELLS













Manchester PRL 2006

B+

B-

Non-Uniform Strain

[100]

[010][001]


graphenedisk

graphenerectangular

UNIFORM FIELD



STRAIN ONLY




straineff

e

hB



on Pt surface









AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

T = 10 K



~10000 cm2Vs





AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

Coxide

T = 10 K

22π

2

Fv

E

dE

dn

~10000 cm2Vs






AuTi Al (top gate)


graphene

-04 -02 00 02 040

2

4

6

Cq (F

cm

2 )

EF (eV)


for several devices





~10000 cm2Vs

22π

2

Fv

E

dE

dn


250K

150K

100K

200K

-1 0 1

04

06B =16 T

C (F

cm

2)

Vtop gate

(V)

30K

12T

8T

4T

B =0T

T =10 K

-1 0 1

035

040

C (F

cm

2)

Vtop gate

(V)







CONCLUSION



MUCH MORE TO COME



F Schedin P Blake



Kostya Novoselov



Irina Grigorieva







BUTno pinch off

-100 -50 0 10050

Vg (V)

(k

)

0

2

4

6

SiO2

Si graphene


)(

1

nm

eV

DE

E = vF h2D



10 nm

e-b lithography

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm




e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43

7-layer BN

breakdown 2 Vnm

-04

tunn

el c

urre

nt (

A)

0

02

04

-02

voltage (V)-5 0 5

I (A)

4535voltage

40

01

001

1


monolayer

resistivity ~1 Mm2

-1

tunn

el c

urre

nt (

A)

0

05

1

-05

-025 025

voltage (V)-05 0 05

voltage-04 0400

(1

M)

2

resistivity ~1 km2

-80

tunn

el c

urre

nt (

A)

0

40

80

-40

-01 01voltage (V)

-02 0 02

-01 01voltage

0

04

02

(1k)

trilayer




NO pin holes

AuAu



amp QUANTUM WELLS













Manchester PRL 2006

B+

B-

Non-Uniform Strain

[100]

[010][001]


graphenedisk

graphenerectangular

UNIFORM FIELD



STRAIN ONLY




straineff

e

hB



on Pt surface









AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

T = 10 K



~10000 cm2Vs





AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

Coxide

T = 10 K

22π

2

Fv

E

dE

dn

~10000 cm2Vs






AuTi Al (top gate)


graphene

-04 -02 00 02 040

2

4

6

Cq (F

cm

2 )

EF (eV)


for several devices





~10000 cm2Vs

22π

2

Fv

E

dE

dn


250K

150K

100K

200K

-1 0 1

04

06B =16 T

C (F

cm

2)

Vtop gate

(V)

30K

12T

8T

4T

B =0T

T =10 K

-1 0 1

035

040

C (F

cm

2)

Vtop gate

(V)







CONCLUSION



MUCH MORE TO COME



F Schedin P Blake



Kostya Novoselov



Irina Grigorieva







BUTno pinch off

-100 -50 0 10050

Vg (V)

(k

)

0

2

4

6

SiO2

Si graphene


)(

1

nm

eV

DE

E = vF h2D



10 nm

e-b lithography

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm




e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43



amp QUANTUM WELLS













Manchester PRL 2006

B+

B-

Non-Uniform Strain

[100]

[010][001]


graphenedisk

graphenerectangular

UNIFORM FIELD



STRAIN ONLY




straineff

e

hB



on Pt surface









AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

T = 10 K



~10000 cm2Vs





AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

Coxide

T = 10 K

22π

2

Fv

E

dE

dn

~10000 cm2Vs






AuTi Al (top gate)


graphene

-04 -02 00 02 040

2

4

6

Cq (F

cm

2 )

EF (eV)


for several devices





~10000 cm2Vs

22π

2

Fv

E

dE

dn


250K

150K

100K

200K

-1 0 1

04

06B =16 T

C (F

cm

2)

Vtop gate

(V)

30K

12T

8T

4T

B =0T

T =10 K

-1 0 1

035

040

C (F

cm

2)

Vtop gate

(V)







CONCLUSION



MUCH MORE TO COME



F Schedin P Blake



Kostya Novoselov



Irina Grigorieva







BUTno pinch off

-100 -50 0 10050

Vg (V)

(k

)

0

2

4

6

SiO2

Si graphene


)(

1

nm

eV

DE

E = vF h2D



10 nm

e-b lithography

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm




e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

Slide 26

Slide 27

Slide 28

Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43










Manchester PRL 2006

B+

B-

Non-Uniform Strain

[100]

[010][001]


graphenedisk

graphenerectangular

UNIFORM FIELD



STRAIN ONLY




straineff

e

hB



on Pt surface









AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

T = 10 K



~10000 cm2Vs





AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

Coxide

T = 10 K

22π

2

Fv

E

dE

dn

~10000 cm2Vs






AuTi Al (top gate)


graphene

-04 -02 00 02 040

2

4

6

Cq (F

cm

2 )

EF (eV)


for several devices





~10000 cm2Vs

22π

2

Fv

E

dE

dn


250K

150K

100K

200K

-1 0 1

04

06B =16 T

C (F

cm

2)

Vtop gate

(V)

30K

12T

8T

4T

B =0T

T =10 K

-1 0 1

035

040

C (F

cm

2)

Vtop gate

(V)







CONCLUSION



MUCH MORE TO COME



F Schedin P Blake



Kostya Novoselov



Irina Grigorieva







BUTno pinch off

-100 -50 0 10050

Vg (V)

(k

)

0

2

4

6

SiO2

Si graphene


)(

1

nm

eV

DE

E = vF h2D



10 nm

e-b lithography

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm




e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

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Slide 43

[100]

[010][001]


graphenedisk

graphenerectangular

UNIFORM FIELD



STRAIN ONLY




straineff

e

hB



on Pt surface









AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

T = 10 K



~10000 cm2Vs





AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

Coxide

T = 10 K

22π

2

Fv

E

dE

dn

~10000 cm2Vs






AuTi Al (top gate)


graphene

-04 -02 00 02 040

2

4

6

Cq (F

cm

2 )

EF (eV)


for several devices





~10000 cm2Vs

22π

2

Fv

E

dE

dn


250K

150K

100K

200K

-1 0 1

04

06B =16 T

C (F

cm

2)

Vtop gate

(V)

30K

12T

8T

4T

B =0T

T =10 K

-1 0 1

035

040

C (F

cm

2)

Vtop gate

(V)







CONCLUSION



MUCH MORE TO COME



F Schedin P Blake



Kostya Novoselov



Irina Grigorieva







BUTno pinch off

-100 -50 0 10050

Vg (V)

(k

)

0

2

4

6

SiO2

Si graphene


)(

1

nm

eV

DE

E = vF h2D



10 nm

e-b lithography

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm




e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

Slide 2

Slide 3

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Slide 43



on Pt surface









AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

T = 10 K



~10000 cm2Vs





AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

Coxide

T = 10 K

22π

2

Fv

E

dE

dn

~10000 cm2Vs






AuTi Al (top gate)


graphene

-04 -02 00 02 040

2

4

6

Cq (F

cm

2 )

EF (eV)


for several devices





~10000 cm2Vs

22π

2

Fv

E

dE

dn


250K

150K

100K

200K

-1 0 1

04

06B =16 T

C (F

cm

2)

Vtop gate

(V)

30K

12T

8T

4T

B =0T

T =10 K

-1 0 1

035

040

C (F

cm

2)

Vtop gate

(V)







CONCLUSION



MUCH MORE TO COME



F Schedin P Blake



Kostya Novoselov



Irina Grigorieva







BUTno pinch off

-100 -50 0 10050

Vg (V)

(k

)

0

2

4

6

SiO2

Si graphene


)(

1

nm

eV

DE

E = vF h2D



10 nm

e-b lithography

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm




e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

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Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43









AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

T = 10 K



~10000 cm2Vs





AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

Coxide

T = 10 K

22π

2

Fv

E

dE

dn

~10000 cm2Vs






AuTi Al (top gate)


graphene

-04 -02 00 02 040

2

4

6

Cq (F

cm

2 )

EF (eV)


for several devices





~10000 cm2Vs

22π

2

Fv

E

dE

dn


250K

150K

100K

200K

-1 0 1

04

06B =16 T

C (F

cm

2)

Vtop gate

(V)

30K

12T

8T

4T

B =0T

T =10 K

-1 0 1

035

040

C (F

cm

2)

Vtop gate

(V)







CONCLUSION



MUCH MORE TO COME



F Schedin P Blake



Kostya Novoselov



Irina Grigorieva







BUTno pinch off

-100 -50 0 10050

Vg (V)

(k

)

0

2

4

6

SiO2

Si graphene


)(

1

nm

eV

DE

E = vF h2D



10 nm

e-b lithography

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm




e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

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Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43





AuTi Al (top gate)


graphene

-2 0 2030

035

040

045

C (F

cm

2 )

Vtop gate

(V)

Coxide

T = 10 K

22π

2

Fv

E

dE

dn

~10000 cm2Vs






AuTi Al (top gate)


graphene

-04 -02 00 02 040

2

4

6

Cq (F

cm

2 )

EF (eV)


for several devices





~10000 cm2Vs

22π

2

Fv

E

dE

dn


250K

150K

100K

200K

-1 0 1

04

06B =16 T

C (F

cm

2)

Vtop gate

(V)

30K

12T

8T

4T

B =0T

T =10 K

-1 0 1

035

040

C (F

cm

2)

Vtop gate

(V)







CONCLUSION



MUCH MORE TO COME



F Schedin P Blake



Kostya Novoselov



Irina Grigorieva







BUTno pinch off

-100 -50 0 10050

Vg (V)

(k

)

0

2

4

6

SiO2

Si graphene


)(

1

nm

eV

DE

E = vF h2D



10 nm

e-b lithography

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm




e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

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Slide 29

Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43




AuTi Al (top gate)


graphene

-04 -02 00 02 040

2

4

6

Cq (F

cm

2 )

EF (eV)


for several devices





~10000 cm2Vs

22π

2

Fv

E

dE

dn


250K

150K

100K

200K

-1 0 1

04

06B =16 T

C (F

cm

2)

Vtop gate

(V)

30K

12T

8T

4T

B =0T

T =10 K

-1 0 1

035

040

C (F

cm

2)

Vtop gate

(V)







CONCLUSION



MUCH MORE TO COME



F Schedin P Blake



Kostya Novoselov



Irina Grigorieva







BUTno pinch off

-100 -50 0 10050

Vg (V)

(k

)

0

2

4

6

SiO2

Si graphene


)(

1

nm

eV

DE

E = vF h2D



10 nm

e-b lithography

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm




e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

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Slide 32

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Slide 34

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Slide 36

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Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43


250K

150K

100K

200K

-1 0 1

04

06B =16 T

C (F

cm

2)

Vtop gate

(V)

30K

12T

8T

4T

B =0T

T =10 K

-1 0 1

035

040

C (F

cm

2)

Vtop gate

(V)







CONCLUSION



MUCH MORE TO COME



F Schedin P Blake



Kostya Novoselov



Irina Grigorieva







BUTno pinch off

-100 -50 0 10050

Vg (V)

(k

)

0

2

4

6

SiO2

Si graphene


)(

1

nm

eV

DE

E = vF h2D



10 nm

e-b lithography

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm




e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

Slide 19

Slide 20

Slide 21

Slide 22

Slide 23

Slide 24

Slide 25

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Slide 28

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Slide 30

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Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43





CONCLUSION



MUCH MORE TO COME



F Schedin P Blake



Kostya Novoselov



Irina Grigorieva







BUTno pinch off

-100 -50 0 10050

Vg (V)

(k

)

0

2

4

6

SiO2

Si graphene


)(

1

nm

eV

DE

E = vF h2D



10 nm

e-b lithography

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm




e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

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Slide 20

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Slide 30

Slide 31

Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43



F Schedin P Blake



Kostya Novoselov



Irina Grigorieva







BUTno pinch off

-100 -50 0 10050

Vg (V)

(k

)

0

2

4

6

SiO2

Si graphene


)(

1

nm

eV

DE

E = vF h2D



10 nm

e-b lithography

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm




e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

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Slide 32

Slide 33

Slide 34

Slide 35

Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43







BUTno pinch off

-100 -50 0 10050

Vg (V)

(k

)

0

2

4

6

SiO2

Si graphene


)(

1

nm

eV

DE

E = vF h2D



10 nm

e-b lithography

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm




e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

Slide 14

Slide 15

Slide 16

Slide 17

Slide 18

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Slide 36

Slide 37

Slide 38

Slide 39

Slide 40

Slide 41

Slide 42

Slide 43


)(

1

nm

eV

DE

E = vF h2D



10 nm

e-b lithography

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm




e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

Slide 7

Slide 8

Slide 9

Slide 10

Slide 11

Slide 12

Slide 13

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Slide 42

Slide 43

E = vF h2D

gate (V)

(S

)0 0402

2

0

6

4

few nm300 K

10 nm




e-b lithography

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

Slide 6

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Slide 41

Slide 42

Slide 43

10 nm

10 nm


gate (V)

(S

)0 0402

2

0

6

4

1-10 nm300 K





Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

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some things you might be interested in knowing about graphene

Documents

t k0100200 t

dirac pointbut

kt12probing dirac point

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