1. 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 optical properties of few-layer graphites with AB stacking 5.Conclusion Low energy electronic properties of few-layer graphites

2. 2 1. Introduction Recent studies on the layered graphites Recent 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. 3 1. 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. 4 1. Introduction few-layer graphites sp 2 (s-p x -p y ) and π(p z ) bondings sp 2 (s-p x -p y ) and π(p z ) bondings AB stacking AB stacking ABC stacking ABC stacking AA stacking AA stacking

5. 5 1. Introduction b A B K K : linear bands intersecting at E F =0. Г Г : Maximum and minimum at ±3γ 0. M M : saddle points near ± γ 0 γ 0 =2.598 eV ←E F =0

6. 6 2. Electronic properties of few-layer graphites with AB stacking AB ABA B

7. 7 2. Electronic properties of few- layer graphites with AB stacking AB E

8. 8 2. Electronic properties of few-layer graphites with AB stacking AB 6.52 γ 0 K K : parabolic bands intersecting at 0 Г Г : Maximum and minimum at 3.05γ0 and -3.47 γ 0 M M : saddle points E F =-2.1 X10 -4 γ 0 γ 0 =2.598 eV Drastic change in 1.energy dispersion 2.very weak overlap 3.very low carrier density 4.band width ←E F

9. 9 2. Electronic properties of few-layer graphites with AB stacking Drastic changes in 1.energy dispersions 2.band-edge states 3.band width AB AB 6.73 γ 0 6.84 γ 0 ←E F γ 0 =2.598 eV

10. 10 2. Electronic properties of few-layer graphites with AB stacking AB AB 0.073 γ 0 0.099 γ 0 Drastic change in 1.energy dispersions 2.band-edge states 3.Energy gap γ 0 =2.598 eV

11. 11 2. Electronic properties of few-layer graphites with AB stacking Drastic change in 1.energy dispersions 2.band-edge states 3.energy gap

12. 12 Strong modulation of energy gap Strong modulation of energy gap semimetal-semiconductor transition semimetal-semiconductor transition AB 2. Electronic properties of few-layer graphites with AB stacking γ 0 =2.598 eV

13. 13 AB 2D energy bands 2D energy bands logarithmic peaks ↔ saddle points logarithmic peaks ↔ saddle points discontinuities ↔local maximum and local minimum discontinuities ↔ local maximum and local minimum 2. Electronic properties of few-layer graphites with AB stacking γ 0 =2.598 eV

14. 14 2. Electronic properties of few-layer graphites with AB stacking AB Effects of Electric Field: induce logarithmic peaks discontinuities discontinuities γ 0 =2.598 eV

15. 15 Effects of Electric Field: induce logarithmic peaks discontinuities discontinuities 2. Electronic properties of few-layer graphites with AB stacking AB γ 0 =2.598 eV

16. 16 A C B B 3. Electronic properties of few-layer graphites with AA and ABC stackings

17. 17 3. Electronic properties of few-layer graphites with AA and ABC stackings changeband width change band width induce carrier densities ←E F γ 0 =2.598 eV

18. 18 3. Electronic properties of few-layer graphites with AA and ABC stackings induce band width change low-energy dispersions band-edge states band-edge states ←E F γ 0 =2.598 eV

19. 19 3. Electronic properties of few-layer graphites with AA and ABC stackings enhancement band overlap band overlap carrier density carrier density

20. 20 3. Electronic properties of few-layer graphites with AA and ABC stackings Drastic changes in 1.energy dispersion 2.band edge states 3.energy gap

21. 21 3. Electronic properties of few-layer graphites with AA and ABC stackings Strong modulation of energy gap Strong modulation of energy gap semimetal-semiconductor transition semimetal-semiconductor transition γ 0 =2.598 eV

22. 22 3. Electronic properties of few-layer graphites with AA and ABC stackings The differences between AA and ABC low energy DOS low energy DOS number oflogarithmic peak number of logarithmic peak γ 0 =2.598 eV

23. 23 3. Electronic properties of few-layer graphites with AA and ABC stackings Effects of E AA : carrier density enhancement AA : carrier density enhancement ABC: special structures and energy gap ABC: special structures and energy gap γ 0 =2.598 eV

24. 24 shoulders peaks 4. Effects of electric field on optical properties of few-layer graphites with AB stacking ←E F =0 γ 0 =2.598 eV

25. 25 4. Effects of electric field on optical properties of few-layer graphites with AB stacking Effects of E: frequency intensity peak number γ 0 =2.598 eV PsPs

26. 26 4. Effects of electric field on optical properties of few-layer graphites with AB stacking Effects of E: frequency intensity peak number

27. 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 γ 0 =2.598 eV

28. 28 5. 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.