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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
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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
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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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• 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
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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
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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
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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.