Introduction Electronic properties of few-layer graphites with AB stacking

1. Low energy electronic properties of few-layer graphites • Introduction • Electronic properties of few-layer graphites with AB stacking • Electronic properties of few-layer graphites with AA and ABC stackings • Effects of electric field on optical properties of few-layer graphites with AB stacking • Conclusion

2. 1. Introduction 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) • Carbon32, 289 (1994) 1. the ab initio method. 2. the tight-binding model. Effects of Stacking sequences

3. 1. Introduction Experiments: • K. S. Novoselov, et al. • Science306, 666 (2004) effects of electric field • Nature438, 197 (2005) • Y. Zhang, et al. • Nature438, 201 (2005) effects of magnetic field

4. 1. Introduction few-layer graphites • sp2(s-px-py) and π(pz) bondings • AB stacking • ABC stacking • AA stacking

5. b A B 1. Introduction K : linear bands intersecting at EF=0. Г: Maximum and minimum at ±3γ0. M : saddle points near ± γ0 γ0=2.598 eV ←EF=0

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

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

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

9. AB AB 6.73γ0 ←EF ←EF 6.84γ0 γ0=2.598 eV 2. Electronic properties of few-layer graphites with AB stacking • Drastic changes in • energy dispersions • band-edge states • band width

10. AB AB 0.099γ0 0.073γ0 2. Electronic properties of few-layer graphites with AB stacking γ0=2.598 eV • Drastic change in • energy dispersions • band-edge states • Energy gap

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

12. AB 2. Electronic properties of few-layer graphites with AB stacking γ0=2.598 eV • Strong modulation of energy gap • semimetal-semiconductor transition

13. AB 2. Electronic properties of few-layer graphites with AB stacking γ0=2.598 eV 2D energy bands • logarithmic peaks ↔ saddle points • discontinuities ↔local maximum and local minimum

14. AB 2. Electronic properties of few-layer graphites with AB stacking γ0=2.598 eV Effects of Electric Field: induce logarithmic peaks discontinuities

15. AB AB 2. Electronic properties of few-layer graphites with AB stacking Effects of Electric Field: induce logarithmic peaks discontinuities γ0=2.598 eV

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

17. ←EF ←EF γ0=2.598 eV 3. Electronic properties of few-layer graphites with AA and ABC stackings changeband width induce carrier densities

18. ←EF ←EF γ0=2.598 eV 3. Electronic properties of few-layer graphites with AA and ABC stackings induce band width change low-energy dispersions band-edge states

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

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

21. γ0=2.598 eV 3. Electronic properties of few-layer graphites with AA and ABC stackings • Strong modulation of energy gap • semimetal-semiconductor transition

22. 3. Electronic properties of few-layer graphites with AA and ABC stackings γ0=2.598 eV • The differences between AA and ABC • low energy DOS • number oflogarithmic peak

23. 3. Electronic properties of few-layer graphites with AA and ABC stackings γ0=2.598 eV • Effects of E • AA : carrier density enhancement • ABC: special structures and energy gap

24. 4. Effects of electric field on optical properties of few-layer graphites with AB stacking ←EF=0 • shoulders • peaks γ0=2.598 eV

25. Ps 4. Effects of electric field on optical properties of few-layer graphites with AB stacking γ0=2.598 eV • Effects of E: • frequency • intensity • peak number

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

27. 4. Effects of electric field on optical properties of few-layer graphites with AB stacking γ0=2.598 eV The strong dependence of absorption frequencies on electric field

28. 5. Conclusion • 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 • The effects of electric field on optical spectra include absorption frequencies, peak numbers, and spectra intensity.