1 1. Introduction 2. Electronic properties of few-layer graphites with AB stacking 3. Electronic properties of few-layer graphites with AA and ABC stackings 4. Effects of electric field on optica l properties of few-layer graphites with AB stacking 5. Conclusion Low energy electronic proper ties of few-layer graphites
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1 1.Introduction 2.Electronic properties of few-layer graphites with AB stacking 3.Electronic properties of few-layer graphites with AA and ABC stackings.
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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
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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
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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
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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
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2. Electronic properties of few-layer graphites with AB stacking2. Electronic properties of few-layer graphites with AB stacking
AB
A B A B
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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
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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
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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
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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
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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
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Strong modulation of energy gapStrong modulation of energy gap