Manipulating Graphene at the Atomic-scale

(I) Atomic-scale Gating

-- Tunable charge centers

(II) Nanoribbon Edge States

-- Controllable edge functionalization

Mike CrommieDept. of Physics, UC Berkeley

Materials Science Division, LBNL

V+

-- - - - - -

+ + + + +

Macroscopic:Electrode

-+ + +

Microscopic:Charged Impurity

-

Klein Tunneling

(I) Atomic-scale Gating

V Ve- e-

Coulomb Impurity

2mc2

Non-relativistic Case (Hydrogen)

2 2 2

22 2

rP L Ze

Em mr r

Veff

++Ze

2Ze

Vr

r

Veff

k

E

Electron

Positron

r

Veff

k

E

Electron band

Hole band

Ultra-relativistic Case for Graphene

Z < Zc (subcritical)

Physics of a Coulomb Impurity

|Z| invariant

r

ZepvE

F

2

Critical Charge: Zc = g

g

2

2mc2

Non-relativistic Case (Hydrogen)

2 2 2

22 2

rP L Ze

Em mr r

Veff

++Ze

2Ze

Vr

r

Veff

k

E

Electron

Positron

r

Veff

k

E

Ultra-relativistic Case for Graphene

Z > Zc (supercritical)

Physics of a Coulomb Impurity

|Z| invariant

r

ZepvE

F

2

Electron band

Hole band

Critical Charge: Zc = g

g

2

Pereira et al., PRL 99, 166802 (2007)

Shytov et al., PRL 99, 246802 (2007)

Subcritical (Z < Zc)

Predicted quasi-bound-states(atomic collapse states)

Predicted Behavior for Dirac Fermions Near Coulomb Potential

Energy

Q > 0

holes electrons

Charge asymmetry

(Solution to Dirac Equation using a Continuum Model)

+Q = + Z |e| > 0

Supercritical (Z > Zc)

Deposit Cobalt Atoms onto Graphene / SiO2 Device

cobalt

V.W. Brar, et al., Nature Physics 7, 43 (2011)

Spectroscopy at Site of Cobalt Atom on Graphene

Gated Cobalt Atom Spectroscopy

E

Atomic Resonances, Gate-induced Charging

EF

LDO

S

Vg

Graphene flake

doped Si bottom gateSiO2

STMtip

Vbcobalt

+

+

E

k

=

E

DOS

cobalt

graphene impurity

V.W. Brar, et al., Nature Physics 7, 43 (2011)

Off-atom Problems: Bi-stability and Inhomogeneity

10nm10nm

Graph. / SiO2 Rough Topography Graph. / SiO2 Charge Inhomogeneity

Charge bi-stability: Co on Graphene

/C60/C60

Teichmann, et al., PRL 101,076103 (2008)

Pradhan, et al., PRL 94,076801 (2005)

Si/GaAs

Previous Impurities in Semiconductors

V.W. Brar, et al., Nat. Phys. 7, 43 (2011)

Dean C. R. et al., Nat Nano 5, 722 (2010)

Doped Si bottom gate

SiO2

BN flake

CVD Graphene

Vb

VG

A New Substrate Solves these Problems (BN)

BN substrate in new STM geometry

Crommie, Zettl

Less Inhomogeneity for Graphene on BN

R. Decker, et al., Nano Letters 11, 2291 (2011)

Similar to: J. Xue, et al., Nature Mat. 10, 282 (2011)

Moiré Patterns

R. Decker, et al., Nano Letters 11, 2291 (2011)

kBN

4 nm4 nm 4 nm 4 nm

a b c d

θ = 21°± 1° θ = 7°± 1° θ = 0°± 1°θ = 4°± 1°

Graph./BN

Vg=50

Vg=35

Vg=25

Vg=15

Vg=10

Vg=5

Vg=-10

Vg=0

Vg=-20

Vg=-30

Vg=-50

Graphene /BN

Gate-dependent STM Spect.

General spectral line-shape: V. W. Brar, et al., PRL 104, 036805 (2010)

Atomic Manipulation on Graphene/BN: Co Trimers

Trimers:no chargebi-stability

Q = +1 |e| State (charged)

Vg = -20V , Vs = +0.3V

Co Trimer

Q = 0 State (uncharged)

Vg = +45V , Vs = +0.3V

Co Trimer

Graphene Graphene

Co Trimer Provides aStable Charged State

Trimers Are Stable, Tunable Charge Centers

STM dI/dV

images

dI/dV Spectra on Graphene around Charged Co Trimer

Co Trimer

Distance dependent spectra around charged Co trimer

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

No

rma

lize

d d

I/d

V (

a.u

.)

Sample Bias (eV)

1.60nm

2.22nm

3.48nm

6.35nm

• LDOS Asymmetry• No Bound-state

Q = +1 |e|

Comparing Experiment to Predictions for Dirac Fermions

THEORYEXPERIMENT

Interband Dielectric Constant: g = 3.0 ± 1.0

D. A. Siegel, et al., PNAS 108, 11365 (2011): g < 6

D. C. Elias, et al., Nat Phys. advance online pub. (2011): g = 2 - 5

J. P. Reed, et al., Science 330, 805 (2010): g = 15

T. Ando, J. of the Phys. Soc. of Japan 75, 074716 (2006): g ≈ 2

E. H. Hwang and S. Das Sarma, PRB 75, 205418 (2007): g ≈ 2

Previous Theory for g : Previous Experiment for g:

Spatial Dependence Reflects Charge Asymmetry

Y. Wang, et al., submitted for publication

Cobalt Trimer:Sub-critical Impurity

Holes

Electrons

g = 3.0 ± 1.0

(II) Nanoribbons: Controlling the Edge

DO

S

E

DO

S

E

……

Armchair

… …

Zigzag

D(e

V)

Zigzag

D(e

V)

Armchair

Spin-polarized

w

Y.-W. Son et al, Phys.Rev. Lett.

97, 216803 (2006)

A. Yamashiro et al, Phys.Rev. B

68, 193410 (2003)

J. Heyd et al, J. Chem. Phys. 118,

8207 (2003)

K. Nakada, et al., PRB 54, 17954

(1996)

M. Fujita, et al., J. Phys. Soc.

Jpn 65, 1920 (1996)

Tunable GapsEdge-statesSpin

GNRsGraphene GNR

Some Previous Nanoribbon Investigations

Ritter and Lyding, Nat. Mat. 8, 235 (2009)

Lithography: Transport Graphene platelet on Si(100)

Jinming Cao et al., Nature 466, 470 (2010)

Armchair GNRs grown on Au

Y. Kobayash et al., PRB 71, 193406 (2005)

Graphite Step edge

Some Previous Edge Investigations

Graphene Edges on SiC & Cu

C. Park, et al., PNAS, doi:10.1073 (2011)

H. Yang, et al., Nano Lett. 10, 943 (2010)

J. Tian, et al., Nano Lett. 11, 3663 (2011)

SiC

Cu

M. Y. Han et al., PRL 98, 206805 (2007)

GNRs from Unzipped Nanotubes

Jiao, et al, Nat. Nanotechnol 5, 321 (2010)

1000 Å

GNR on Au(111)

C. Tao, et al., Nature Physics 7, 616 (2011)

(8, 1) GNR

0.0 Å

5.5 Å

48 Å × 48 Å θ = 5.8°

Different Chiralities Observed

Width = 19.8 nm

C. Tao, et al., Nature Physics 7, 616 (2011)

(1, 1) Armchair

(1, 0) Zigzag

(n, m)

θ

STM Spectroscopy of Nanoribbon Edge State

Au(111)

(8, 1) GNR

0.0 Å

5.5 Å

48 Å × 48 Å

Perpendicular to edge

0 Å

2.2 Å

4.4 Å

6.6 Å

8.8 Å

11.0 Å

13.2 Å

15.4 Å

19.8 Å

24.2 Å

-8.8 Å

Vs (V)

dI/d

V(a

rb.

un

its)

dI/d

V (a. u

.)Vs (V)

Δ0.8

0.00 0.04

0.6

width = 19.8 nm

Gap Width Dependence

ExperimentTheory

C. Tao, et al., Nature Physics 7, 616 (2011)

a b20 nm 20 nmGNR / Au(111) before H2

plasma EtchingGNR / Au(111) after H2 plasma Etching

0 10 20 30

0.0

0.3

0.6

(nm

)

(nm)0 10 20 30

0.0

0.3

0.6

(nm

)

(nm)

Control GNR Edge Through H2 Plasma Etch

Room temperature STM

Crommie, Dai, Louie, Zettl (unpublished)

a

b

dc

d

e

c

e

5 nm

1 nm

5 nm

1 nm

1 nm

Nano-scale Structure of Edge

Zigzag edge

(2, 1) Chiral edge

Armchair edge

Can Find Edge Symmetry, But What is H-Composition?

What is Hydrogen Edge Structure?

Calculate Thermodynamic Stability

of Different Edge Structures

O. Yazyev, S. G. Louie & co-workersPrevious Work:Wassman, Seitsonen, Marco Saitta, Lazzeri, Mauri, PRL 101, 096402 (2008)

Comparing Exp. Edge to Theory w/ Proper H-structure

d

c

e

1 nm

f

g

h

1 nm

1 nm 1 nm

1 nm

1 nm

EXPERIMENT THEORY

Experiment

Theory

Armchair GNR

Edge

Experiment

Theory

Zigzag GNR

Edge

Averaged Linescans

Conclusion

Future:

Atomic Collapse Pseudo-field and SpinSPSTM of GNRs

I) Dirac Fermion Screening of Tunable Charge Impurities

II) Controlling GNR Edges through Chemical Functionalization

Collaborators:

Tunable ChargeCenters

Victor Brar, Regis Decker, Yang Wang, Q. Wu, H. Tsai,

Will Regan, A. Shytov

NanoribbonEdges

Chenggang Tao, Yen-Chia Chen, Liying Jiao, Juanjuan Feng,

Xiaowei Zhang, R. Capaz, Oleg Yazyev

co-PI’s M. F. Crommie, A. Zettl, S. G. Louie, J. M. Tour, H. Dai, L. Levitov

STUDENTS + POSTDOCS + VISITORS

The End