1

1. Introduction2. Electronic properties of few-layer graphites

with AB stacking3. Electronic properties of few-layer graphites

with AA and ABC stackings4. Effects of electric field on optical properties

of few-layer graphites with AB stacking5. Conclusion

Low energy electronic properties of few-layer graphites

Low energy electronic properties of few-layer graphites

2

1. Introduction1. Introduction

Recent studies on the layered graphitesRecent studies on the layered graphites Theoretical : J.-C. Charlier, et al.• Phys. Rev. B 43, 4579 (1991) • Phys. Rev. B 44, 13237 (1991) • Phys. Rev. B 46, 4531 (1992) • Phys. Rev. B 46, 4540 (1992) • Carbon 32, 289 (1994) 1. the ab initio method.2. the tight-binding model.

Effects of Stacking sequences

3

1. Introduction1. Introduction

Experiments: K. S. Novoselov, et al. • Science 306, 666 (2004)

effects of electric field

• Nature 438, 197 (2005) Y. Zhang, et al.• Nature 438, 201 (2005)

effects of magnetic field

4

1. Introduction1. Introduction

few-layer graphitesfew-layer graphites spsp22(s-p(s-pxx-p-pyy) and ) and ππ(p(pzz) bondings) bondings

• AB stackingAB stacking

• ABC stackingABC stacking

• AA stackingAA stacking

5

1. Introduction1. Introduction

, ,, i ji j A j A Bk A

j

r a R r

1a

2a

b

A

B

,

0*

0

2

*0 ,,

0

0

2 cos 2y

y

k A

ik bik b x

A B A Bk B

fH

f

k af e e

R r H R r dr

K K : linear bands intersecting at EF=0.

ГГ : Maximum and minimum at ±3γ0.

M M : saddle points near ± γ0

γ0=2.598 eV

←←EEFF=0=0

6

2. Electronic properties of few-layer graphites with AB stacking2. Electronic properties of few-layer graphites with AB stacking

AB

A B A B

7

2. Electronic properties of few-layer graphites with AB stacking2. Electronic properties of few-layer graphites with AB stacking

, ,, i ji j A j A Bk A

j

r a R r

AB

E

0

†6 0 1 4

† †0 4 3

2 *1 4 6

†4 3 0

0n

f f

f f fH

f Ec f

f f f Ec

8

2. Electronic properties of few-layer graphites with AB stacking2. Electronic properties of few-layer graphites with AB stacking

ABAB

6.52γ0

K K : parabolic bands intersecting at 0

ГГ : Maximum and minimum at 3.05γ0 and -3.47 γ0

M M : saddle points

EF=-2.1X10-4γ0

γ0=2.598 eVDrastic change in

1. energy dispersion

2. very weak overlap

3. very low carrier density

4. band width

←←EEFF

9

2. Electronic properties of few-layer graphites with AB stacking2. Electronic properties of few-layer graphites with AB stacking

Drastic changes in

1. energy dispersions2. band-edge states3. band width

ABAB ABAB

6.73γ0 6.84γ0←←EEFF ←←EEFF

γ0=2.598 eV

10

2. Electronic properties of few-layer graphites with AB stacking2. Electronic properties of few-layer graphites with AB stacking

ABABABAB

0.073γ00.099γ0

Drastic change in

1. energy dispersions2. band-edge states3. Energy gap

γ0=2.598 eV

11

2. Electronic properties of few-layer graphites with AB stacking2. Electronic properties of few-layer graphites with AB stacking

Drastic change in

1. energy dispersions2. band-edge states3. energy gap

12

Strong modulation of energy gapStrong modulation of energy gap

semimetal-semiconductor transitionsemimetal-semiconductor transition

AB

2. Electronic properties of few-layer graphites with AB stacking2. Electronic properties of few-layer graphites with AB stacking

γ0=2.598 eV

13

AB

2D energy bands2D energy bands

logarithmic peaks logarithmic peaks ↔ ↔ saddle pointssaddle points

discontinuities ↔discontinuities ↔ local maximum and local minimumlocal maximum and local minimum

2. Electronic properties of few-layer graphites with AB stacking2. Electronic properties of few-layer graphites with AB stacking

γ0=2.598 eV

14

2. Electronic properties of few-layer graphites with AB stacking2. Electronic properties of few-layer graphites with AB stacking

AB

Effects of Electric Field:Effects of Electric Field:

induce logarithmic peaksinduce logarithmic peaks

discontinuitiesdiscontinuities

γ0=2.598 eV

15

Effects of Electric Field:Effects of Electric Field:

induce logarithmic peaksinduce logarithmic peaks

discontinuitiesdiscontinuities

2. Electronic properties of few-layer graphites with AB stacking2. Electronic properties of few-layer graphites with AB stacking

AB

AB

γ0=2.598 eV

16

A

C

B

B

3. Electronic properties of few-layer graphites with AA and ABC stackings3. Electronic properties of few-layer graphites with AA and ABC stackings

17

3. Electronic properties of few-layer graphites with AA and ABC stackings3. Electronic properties of few-layer graphites with AA and ABC stackings

changechange band widthband width

induce carrier densitiesinduce carrier densities

←←EEFF←←EEFF

γ0=2.598 eV

18

3. Electronic properties of few-layer graphites with AA and ABC stackings3. Electronic properties of few-layer graphites with AA and ABC stackings

induce band widthinduce band width

change low-energy dispersions change low-energy dispersions

band-edge statesband-edge states

←←EEFF←←EEFF

γ0=2.598 eV

19

3. Electronic properties of few-layer graphites with AA and ABC stackings3. Electronic properties of few-layer graphites with AA and ABC stackings

enhancementenhancement

• band overlapband overlap

• carrier densitycarrier density

20

3. Electronic properties of few-layer graphites with AA and ABC stackings3. Electronic properties of few-layer graphites with AA and ABC stackings

Drastic changes in

1. energy dispersion2. band edge states3. energy gap

21

3. Electronic properties of few-layer graphites with AA and ABC stackings3. Electronic properties of few-layer graphites with AA and ABC stackings

Strong modulation of energy gapStrong modulation of energy gap

semimetal-semiconductor transitionsemimetal-semiconductor transition

γ0=2.598 eV

22

3. Electronic properties of few-layer graphites with AA and ABC stackings3. Electronic properties of few-layer graphites with AA and ABC stackings

The differences between AA and ABCThe differences between AA and ABClow energy DOSlow energy DOSnumber ofnumber of logarithmic peaklogarithmic peak

γ0=2.598 eV

23

3. Electronic properties of few-layer graphites with AA and ABC stackings3. Electronic properties of few-layer graphites with AA and ABC stackings

Effects of E Effects of E

AA : carrier density enhancementAA : carrier density enhancement

ABC: special structures and energy gapABC: special structures and energy gap

γ0=2.598 eV

24

• shoulders

• peaks

2

'

, ' 1

'

' '

ˆ, ,

2 2

, ,Im

, ,

y h hxx y x y

h h estBZ

h hx y x y

h hx y x y

dkdk E PA k k k k

m

f E k k f E k k

E k k E k k i

4. Effects of electric field on optical properties of few-layer graphites with AB stacking

4. Effects of electric field on optical properties of few-layer graphites with AB stacking

←←EEFF=0=0

γ0=2.598 eV

25

4. Effects of electric field on optical properties of few-layer graphites with AB stacking

4. Effects of electric field on optical properties of few-layer graphites with AB stacking

Effects of E:

• frequency

• intensity

• peak number

γ0=2.598 eV

Ps

26

4. Effects of electric field on optical properties of few-layer graphites with AB stacking

4. Effects of electric field on optical properties of few-layer graphites with AB stacking

Effects of E:

• frequency

• intensity

• peak number

27 The strong dependence of absorption frequencies on electric field

4. Effects of electric field on optical properties of few-layer graphites with AB stacking

4. Effects of electric field on optical properties of few-layer graphites with AB stacking

γ0=2.598 eV

28

5. Conclusion5. Conclusion

1. The stacking sequences, the layer number, and the electric field strongly affect electronic properties of few-layer graphites, such as

▪ Energy dispersions

▪ Band-edge states

▪ Energy gap (semimetal-semiconductor transition)

▪ Band width

▪ Carrier densities

2. The effects of electric field on optical spectra include absorption frequencies, peak numbers, and spectra intensity.