Large band gaps, ferromagnetism, and

anomalous magnetoresistance oscillations

derived from edge states;

Nanoribbons and Antidot-lattice graphenes

Junji HaruyamaAoyama Gakuin University, Tokyo, Japan

Contents

1. Introduction

２．GNRs fabricated by unzipping of carbon

nanotubes and 3-stepped annealing

Low defects and 7-times larger energy band gaps

３．Antidot-lattice graphenes fabricated using nano-

porous alumina templates as etching masks

Anomalous magnetoresistance oscillations

Room-temperature Ferromagnetism

Non-lithographic

（10 layers）

（Monolyer）

４．Future plans: (Quantum ) Spin-Hall effect

Nature Nanotech &

Latest Highlights

PRL

Submitted to Nature

Arm Chair

zigzag

zigzag

Edge atomic structures of Graphene (Graphite)

Arm

chair

(超伝導・強磁性)電極

ジグザグ端

(超伝導・強磁性)電極

Graphene nanoribbon

Flat band

Arm chair Zigzag

Tight-binding

Band gap

K.Nakata et al., Phys. Rev. B 54,

17954 (1996)

Strong Electron localization

High EDOS

Spin polarization

Edge states of Graphene (Graphite)

Spin polarization and ferromagnetism at

zigzag edges with hydrogen termination

Kusakabe and Maruyama,

Phys. Rev. B 67, 092406

(2003)

Up spin Down spin

Hydrogen

local-spin-density

approximation

Why graphene edges are important and

interesting??

1. Band gap engineering

3. All carbon magnetism (magnets)

4. Spin Current & (Quantum) Spin Hall Effect

2. Electron correlation with localized edge electrons

So many theoretical reports, but no experimental reports

Large damages by lithographic methods

Non-lithographic methods

Contents

1. Introduction

Non-lithographic

２．GNRs fabricated by unzipping of carbon

nanotubes and 3-stepped annealing

Low defects and 7-times larger energy band gaps

Nature Nanotech &

Latest Highlights

Advance online publication

Nanoelectronics

Article by Shimizu et al.

Graphene nanoribbons manufactured by

annealing unzipped carbon nanotubes have

been measured to have a large energy

bandgap.

Latest highlights

Current issue

Quantum tunnelling through single bases FREE

RNA nanotechnology: Best of both worlds

Current issue table of contents

Impact Factor 26.309

December 2010 - Vol 5 No 12

Nature Nanotechnology | News and Views

Nanoelectronics: Graphene gets a better gapStephan RocheJournal name: Nature Nanotechnology Volume: 6, Pages: 8–9 Year published: (2011)

DOI:doi:10.1038/nnano.2011.262 Published online 23 December 2010

Introduction of energy band gaps

Absence of energy band gaps

Destruction of symmetry in bilayer graphenes

Voltages, Carrier doping, Substrate

Carrier confinement into 1D space GNRs

Semi metal, Zero- gap

semiconductor

Han, Kim et al., Phys. Rev. Lett., 104,

056801 (2010)

Disordered Graphene Nano-ribbon(Lithographic)

Hopping conductance

Stochastic Coulomb diamond

Large difference between & EaLarge transport gaps

Ec=e2/2C

J.Tour et al.,

Nature 458, 872

(2009)

Rice University, Smalley Institute for Nanoscale Science and Technology

①Formation of GNRs on substrate by air blow

②３stepped annealing（high vacuum, H2）

Our originality

Low-defect GNR formed by unzipping of MWCNTs

1μm

200nm

As-depo

Our originality①Formation of GNRs on substrate by air blow

②by air blowing to droplet①by brushing

AFM

Brush Air blow

Isolated 47 58

Rectangle 14 26

Monolayer 5 15

Formation of GNRs on Si-substrate by air blow

Number of GNRs within 5mm2-substrate

②3-stepped annealing during FET formation process

Our originality for deoxidization and carrier doping

Right after formation of GNRs on substrate High vacuum・ 800 C

Right before formation of EB mark H2 atmosphere・800 C

Right before formation of FET electrode High vacuum ・300 C

For deoxidization & Recovery of defects

For carrier doping

For cleaning

for long time

Nature Nanotech(Dec.19, 2010)

HRTEM

Raman

AFM

As-grown

nanoribbon

FET

Quality of GNRs: low defects

Before

annealing

After

annealing

AIST

Suenaga

Electronic transport for 4 different-type GNRs

W Width (nm)

N Layer number

Nature Nanotech(Dec.19, 2010)

Correlation of ambipolar feature with

annealing time at high vacuum

Deoxidization：p-type Ambipolar

t = 0

t = 24h

Electronic transport：Zero-bias

anomaly & Transport gap

VBG = 1V

Small transport gap

Low defects

W=75nm

N=1

Nature Nanotech(Dec.19, 2010)

Single-electron Spectroscopy

No stochastic diamonds

Disordered GNRsLow-defects GNR

Nature Nanotechnology

Coulomb diamonds

Stochastic diamonds due to

defects (Q-dots connected in

series)Low defects

W=75nm

N=1

Energy band gap in thermal-

activation relationships

7-times larger Ea

No hopping conductance

Transport gap close to Ea values

Nature Nanotech(Dec.19, 2010)

55m

eV

Louie et al., UC Berkeley

Theory for energy band gaps of GNRs

with arm chair edge

GWA

LDA

3 eV for W=1nm

Ea30 meV

for

W100nm

Q1: The large band gaps are relevant for large-width GNRs?

le 300nm

W < 300nm

Remaining

1D

Contents

1. Introduction

２．GNRs fabricated by unzipping of carbon

nanotubes and 3-stepped annealing

Low defects and 7-times larger energy band gaps

Non-lithographic

Nature Nanotech &

Latest Highlights

３．Antidot-lattice graphenes fabricated using nano-

porous alumina templates as etching masks

Anomalous magnetoresistance oscillations（10 layers）

PRL

Graphene

Antidots

edge

Antidot-lattice graphene

GNR

100nm

Antidot Lattice on Semiconductor 2DEG (1990)

M. Kato,S. Katsumoto, Y. Iye,

PRB 77, 155318 (2008).

D. Weiss, K. von Klitzing et al.,

PRL 70, 4118 (1993)

Rc = (nS)1/2 (h/2)/eBΔBABT = (h/e)/S

Commensurability peak

Aharonov-Bohm-type

Oscillation

Antidots

-

Antidot

Cyclotron orbit

High B

Low B

Under enough antidot spacing

Anomalous FQHEs200nm/Ls600nm = 1/3

Anomalous filling factor

Antidots

No antidots

Composite Fermion

Kang, Stormer, PRL71, 3850 (1993)

In Graphenes： How edge-localized electrons are

interacted with cyclotron-moton electrons?

Antidot Lattice as a scattering center for electrons

on 2DEG

Antidot Lattice Graphene

T. Shen et al., APL 93, 122102 (2008).

S.Russo et al., PRB

77, 085413 (2008).

J. Bai et al., Nature Nanotech. 5,

190 (2010).

Only a few publications No reports for

edges

Graphene

Antidots

Zigzag edge

Formation of low-defect antidot-lattice

graphene by porous alumina templates

GNR

Hydrogen annealing

50nm

Pore spacing 40nm

80nm

Pore spacing 20nm

15nm

Pore spacing 20nm

Porous alumina templates

FESEM images of ADLGs

AFM and STM images of

Hydrogen-terminated ADLGs

500nm

STM

100nm

AFM

T = 80K

Hiroshi Fukuyama

Tokyo University

100nm

M-H@4K

H[Oe]-1000 -500 0 500 1000

M(T

) [e

mu

]

-1.0e-4

-5.0e-5

0.0

5.0e-5

1.0e-4100

0

-100

50

-50

1000-1000 -500 5000

M-H@2K

H[Oe]-1000 -500 0 500 1000

M(T

) [e

mu

]

-6.0e-5

-4.0e-5

-2.0e-5

0.0

2.0e-5

4.0e-5

6.0e-560

20

40

-60

0

-40

-20

1000-500 5000-1000

M-H@2K

H[Oe]-1000 -500 0 500 1000

M(T

) [e

mu

]

-8.0e-4

-6.0e-4

-4.0e-4

-2.0e-4

0.0

2.0e-4

4.0e-4

6.0e-4

8.0e-4

0

-400

-800

400

800

1000-1000 -500 5000

Magne

tization (e

mu/1

00

m2)

Magnetic field (gauss)

(a) (b) (c)

T = 2K T = 2KT = 2K

Hydrogen Oxygen No antidots

All-carbon Ferromagnetism in ADLG

with Hydrogen-terminated edges

Mono-layer graphene

Evidence for zigzag at antidot edge

Correlation of localized electrons

with MR oscillations??

Sample A

Aharonov-Bohm-type Oscillations

in H2-terminated ADLGs

Commensurability peak = 80 nm

AD Space

80 nm

2Rc = (nS)1/2 (h/2)/eB

= a

nS 4 × 1011 cm-2

le = 2D/vF 800 nm >

2(a/2) = 540 nm

B = 200 mT

ΔBABT = (h/e)/(S)

(b)

52.5 7.51/B (T-1)

FF

T (

arb

. units)

(c)

0 < B < 2.5

2.5 < B < 5

Sample B

Fourier

Spectrum

AB-type oscillation

Low B

High B

Low B B200 mT

Electron trajectories on honey-comb ADL

and magnetoresistance oscillations

ΔBABT=(h/e)/S

S = 6(3-1/2/2)(a/2)2

2Rc = a

a

Runaway orbit

1st Unit cell

2nd Unit cell

SDHO orbit

(Commensurability MR peak orbit)

Graphene

Graphene

nanoribbons

Anti-dots

zigzag edges

Quantized electron orbitals around antidots

in an unit cell

a = 160 nm

En = h2/2mL2(n - Φ/φ0)

AB-type oscillation

2Rc = (nS)1/2 (h/2)/eB

= a

nS 4 × 1011 cm-2

le = 2D/vF 800 nm > 2(a/2) = 540 nm

En = h2/2mL2(n - Φ/φ0)

Aharonov-Bohm-type effect

ΔBABT=(h/e)/S

Sample A

Anomalous MR Oscillations in ADL- multi-layered

Graphenes

Commensurability peak = 80 nm

(b)

52.5 7.51/B (T-1)

FF

T (

arb

. units)

(c)

0 < B < 2.5

2.5 < B < 5

Sample B

Fourier

Spectrum2Rc = (nS)1/2 (h/2)/eB

= a

nS 4 × 1011 cm-2

le = 2D/vF 800 nm >

2(a/2) = 540 nmB260 mT

High B

High B

S: r for pore radius

B260 mT

Electron trajectories on honey-comb ADL

and magnetoresistance oscillations

ΔB=(h/e)/(r2) with r = 40 nm

2Rc = a

a

Runaway orbit

1st Unit cell

2nd Unit cell

SDHO orbit

(Commensurability MR peak orbit)

Graphene

Graphene

nanoribbons

Anti-dots

zigzag edges

Antidot radius

Absent AB effect

Bohr–Sommerfeld quantization

condition =Br2=m(h/e) m: integer

Like flux quanta in superconductor

Edge-

Localized

electrons

Quantization of magnetic flux

-

ΔBAB = (h/e)/(r2)

Aharonov-Bohm effect

2Rc = (nS)1/2 (h/2)/eB

= a

nS 4 × 1011 cm-2

le = 2D/vF 800 nm > 2(a/2) = 540 nm

En = h2/2mL2(n - Φ/φ0)

Aharonov-Bohm-type effect

Vector

potential

A

Ensemble average

Disappearance

ΔBABT=(h/e)/S

12.5 37.525

FF

T (a

rb.

un

its)

1/B (T-1)

(e)

0.6 < B < 1

Sample B

Fourier

Spectrum

△B2 = 70 mT ΔBABT =(h/e)/S =

50 mT

Contribution of larger unit cell (2nd unit cell)

Contents

1. Introduction

２．GNRs fabricated by unzipping of carbon

nanotubes and 3-stepped annealing

Low defects and 7-times larger energy band gaps

３．Antidot-lattice graphenes fabricated using nano-

porous alumina templates as etching masksAnomalous magnetoresistance oscillations

Non-lithographic

（10 layers）

Nature Nanotech &

Latest Highlights

PRL

Room-temperature Ferromagnetism （Monolyer）Submitted to Nature

All-carbon Ferromagnetism in ADLG

with Hydrogen-terminated edgesM-H@4K

H[Oe]-1000 -500 0 500 1000

M(T

) [e

mu

]-1.0e-4

-5.0e-5

0.0

5.0e-5

1.0e-4100

0

-100

50

-50

1000-1000 -500 5000

M-H@2K

H[Oe]-1000 -500 0 500 1000

M(T

) [e

mu

]

-6.0e-5

-4.0e-5

-2.0e-5

0.0

2.0e-5

4.0e-5

6.0e-560

20

40

-60

0

-40

-20

1000-500 5000-1000

M-H@2K

H[Oe]-1000 -500 0 500 1000

M(T

) [e

mu

]

-8.0e-4

-6.0e-4

-4.0e-4

-2.0e-4

0.0

2.0e-4

4.0e-4

6.0e-4

8.0e-4

0

-400

-800

400

800

1000-1000 -500 5000

Mag

neti

zati

on

(

em

u/1

00

m2)

(a) (b) (c)

T = 2K T = 2KT = 2K

M-H@300K

H[Oe]-1000 -500 0 500 1000

M(T) [emu]

-3.0e-5

-2.0e-5

-1.0e-5

0.0

1.0e-5

2.0e-5

3.0e-5

0

30

20

-10

-20

10

M-H@300K

H[Oe]-1000 -500 0 500 1000

M(T

) [e

mu

]

-3.0e-5

-2.0e-5

-1.0e-5

0.0

1.0e-5

2.0e-5

3.0e-5

-301000500-1000 -500 0

T = 300K

M-H@300K

H[Oe]-1000 -500 0 500 1000

M(T

) [e

mu

]

-6.0e-5

-4.0e-5

-2.0e-5

0.0

2.0e-5

4.0e-5

6.0e-5

10000-500

60

500-1000

40

20

0

-20

-60

-40

Magnetic Field (gauss)

T = 300K

M-H@40K

H[Oe]-1000 -500 0 500 1000

M(T

) [e

mu

]

-4.0e-5

-2.0e-5

0.0

2.0e-5

4.0e-530

0

15

-15

-30

-500-1000 10005000

T = 300KHydrogen

Hydrogen Oxygen

Oxygen

No antidots

No antidots

(d) (e) (f)

Hydrogen Oxygen No antidots

Estimation of magnetic moment at edge-carbon atoms

Only dangling-bonds at zigzag edges have magnetization

Saturation M/one carbon 100 B 100-times larger than

theory

All carbon atoms within 7nm region from the edges 1.2 B

Weak Ferromagnetism in ADL-Graphite

with Hydrogen-terminated edges

M-H@2K

H [Oe]-1000 -500 0 500 1000

M (

T)[

em

u]

-4.0e-5

-2.0e-5

0.0

2.0e-5

4.0e-5

Hydrogen

T = 2K

Mag

neti

zati

on

(

em

u/1

00

m2)

4

-2

0

2

-4

M-H@300K

H[Oe]-500 0 500

M(T

) [e

mu

]-1.0e-5

-5.0e-6

0.0

5.0e-6

1.0e-5

Hydrogen

T = 300K

-1

-0.5

0

0.5

1

Magnetic Field (gauss)

10005000500-1000 5000-500

2D defects array in Graphite and

Room-temperature Ferromagnetism

Cervenka et al., Nature

Physics 5, 840 (2009)

ZIGZAGArm chair

Ambiguous system and

poor reproducibility

T. Enoki et al., Sol. Stat.

Comm. 149, 1144 (2009)

Zigzag-edge related Ferromagnetism in

Activated carbon Fibers

Spin polarization and ferromagnetism at

zigzag edges with hydrogen termination

Kusakabe and Maruyama,

Phys. Rev. B 67, 092406

(2003)

Up spin

Down spin

Hydrogen

Group-theoretical

consideration

Spin polarization and magnetism of

zigzag-edge nanoribbon

On one edge On both edges

No termination

H. Lee et al.,. Phys. Rev. B 72, 174431 (2005)

first-principles density-

functional calculations

Correlation of Flat band and Spin polarization

with Hydrogen termination FerromagneticMajority Spin Minority Spin

H. Lee et al.,. Phys. Rev. B 72,

174431 (2005)

Antiferromagnetic

1 Hydrogen 2Hydrogen 2 & 1 Hydrogen

Up Spin Down Spin

Elimination of Magnetic moment at zigzag edges

with Oxygen termination

R.G.A. Veiga, et al., J. Chem. Phys.

128, 201101 (2008)

No oxygenOxygen

Edge

Elimination of Magnetic moment by Interlayer coupling in

Zigzag-edge graphite with Hydrogen termination

AB Stack with no termination

No termination

Lee, H. et al. Chem.Phys.Lett. 398 207 (2004)

Advantage of porous alumina template

for formation of low-defect ADLGs

zigzag

Non-lithographic

Hexagonal-shaped ADs placed like honeycomb array

Low damages

Alignment of the same edge structures to each

boundarySix ADs and GNRs/one AD

Large ensemble of GNRs

GNRs

If zigzag structure is the most

stiff, the advantages give a

large volume of zigzag-GNRs

and Ferromagnetism.

Contents

1. Introduction

２．GNRs fabricated by unzipping of carbon

nanotubes and 3-stepped annealing

Low defects and 7-times larger energy band gaps

３．Antidot-lattice graphenes fabricated using nano-

porous alumina templates as etching masks

Anomalous magnetoresistance oscillations

Room-temperature Ferromagnetism

Non-lithographic

（10 layers）

（Monolyer）

４．Future plans: (Quantum ) Spin-Hall effect

Controlling edge-spins by electric fields

Y-W. Son, S.Louie et al., Nature 444, 347–349 (2006)

0.0

Eext = 0.0 0.05 0.1 VA -1

Spin Current & Filter

Eext

0.05

0.1

Jsy = (h/2e)(J↑

y − J↓y )

Kane, C. L. and Mele, E. J.,.

Phys.Rev. Lett. 95, 226801 (2005)

(Quantum) Spin Hall Effect in Graphene

QSHE regime Insulating

regime

Over estimation of SOI??

M.Schmidt & D.Loss, Phys.

Rev. B 81, 165439 (2010)

Spin Hall Effect in graphen/graphen junction

with hydrogen termination

No SO Interaction

H-CH-C

sp3 SOI

M.Schmidt & D.Loss, Phys.

Rev. B 81, 165439 (2010)

SO Interaction

Spin Hall Effect in graphen/graphen junction

with hydrogen termination

Edge Bulk

Conclusions

1．GNRs fabricated by unzipping of carbon

nanotubes and 3-stepped annealing

Low defects and 7-times larger energy band gaps

2．Antidot-lattice graphenes fabricated using nano-

porous alumina templates as etching masks

Anomalous magnetoresistance oscillations

Room-temperature Ferromagnetism

Non-lithographic

3．Future plans: (Quantum) Spin-Hall effect

Controlling edge-spins by electric fields

MIT: Millie Dresselhaus

Colombia University: Philip Kim

Rice University: James Tour

Tokyo Institute of Technology: T.Ando, T.Enoki

Tokyo University: S.Tarucha, M.Yamamoto,

H.Fukuyama, T.Matsui, H. Aoki

Tokyo University, ISSP: Y.Iye, S.Katsumoto, T.Otsuka

AIST: K. Suenaga

My students and staff

Japan Science and Technology Agency:CREST

Hidetoshi Fukuyama

Jun Akimitsu

So many thanks to