1. Optics on Graphene

2. Gate-Variable Optical Transitions in Graphene Feng Wang, Yuanbo Zhang, Chuanshan Tian, Caglar Girit, Alex Zettl, Michael Crommie, and Y. Ron Shen, Science 320, 206 (2008). Direct Observation of a Widely Tunable Bandgap in Bilayer Graphene Yuanbo Zhang, Tsung-Ta Tang, Caglar Girit1, Zhao Hao, Michael C. Martin, Alex Zettl1, Michael F. Crommie, Y. Ron Shen and Feng Wang (2009)

3. Graphene (A Monolayer of Graphite) 2D Hexagonal lattice

4. Electrically: High mobility at room temperature, Large current carrying capability Mechanically: Large Young’s modulus. Thermally: High thermal conductance. Properties of Graphene

5. Quantum Hall effect, Barry Phase Ballistic transport, Klein paradox Others Exotic Behaviors

6. Quantum Hall Effect Y. Zhang et al, Nature 438, 201(2005)

7. Optical Studies of Graphene Optical microscopy contrast; Raman spectroscopy; Landau level spectroscopy. Other Possibilites Spectroscopic probe of electronic structure. Interlayer coupling effect. Electrical gating effect on optical transitions. Others

8. Crystalline Structure of Graphite

9. Graphene 2D Hexagonal lattice

10. Band Structure of Graphene Monolayer P.R.Wallace, Phys.Rev.71,622-634(1947)

11. Band Structure of Monolayer Graphere

12.  Electron Bands of Graphene Monolayer

13. Band Structure in Extended BZ

14. Relativistic Dirac fermion. Band Structure near K Points  eV

15. Vertical optical transition Van Hove Singularity   Monolayer Bilayer Band Structures of Graphene Monolayer and Bilayer near K E F is adjustable x x

16. Exfoliated Graphene Monolayers and Bilayers Monolayer Bilayer Reflecting microscope images. K. S. Novoselov et al., Science 306, 666 (2004). 20  m

17. Raman Spectroscopy of Graphene A.S.Ferrari, et al, PRL 97, 187401 (2006) (Allowing ID of monolayer and bilayer)

18. Reflection Spectroscopy on Graphene

19. Experimental Arrangement Doped Si GrapheneGold 290-nm Silica OPA Det

20. Infrared Reflection Spectroscopy to Deduce Absorption Spectrum Differential reflection spectroscopy: Difference between bare substrate and graphene on substrate A B -  R/R  (R A -R B )/R A versus  R A : bare substrate reflectivity R B : substrate + graphene reflectivity 20  m dR/R = -Re[   from substrate  from graphene: interband transitons free carrier absorption Re  Absorption spectrum

21. Spectroscopy on Monolayer Graphene

22. Monolayer Spectrum x  R/R EFEF C: capacitance

23. Experimental Arrangement Doped Si GrapheneGold 290-nm Silica OPA Det VgVg

24. Gate Effect on Monolayer Graphene XXX Small density of states close to Dirac point E = 0 Carrier injection by applying gate voltage can lead to large Fermi energy shift. E F can be shifted by ~0.5 eV with V g ~ 50 v; Shifting threshold of transitions by ~1 eV  R/R EFEF If V g = V g0 + V mod, then should be a maximum at

25. Vary Optical Transitions by Gating Laser beam Vary gate voltage V g. Measure modulated reflectivity due to V mod at V ( Analogous to dI/dV measurement in transport)

26. Results in Graphene Monolayer = 350 meV The maximum determines V g for the given E F.

27. Mapping Band Structure near K For different , the gate voltage V g determined from maximum is different, following the relation,  R/R EFEF Slope of the line allows deduction of slope of the band structure (Dirac cone) 

28. 2D Plot of Monolayer Spectrum ExperimentTheory

29.  R/R)   60V   50V Vg  Strength of Gate Modulation

30. Bilayer Graphene (Gate-Tunable Bandgap)

31. Band Structure of Graphene Bilayer For symmetric layers,  = 0 For asymmetric layer,  E. McCann, V.I.Fal’ko, PRL 96, 086805 (2006);

32. Doubly Gated Bilayer Asymmetry:  D  (D b + D t )/2  0 Carrier injection to shift E F :  F   D =  (D b - D t )

33. Sample Preparation Effective initial bias due to impurity doping

34. Transport Measurement Maximum resistance appears at E F = 0 Lowest peak resistance corresponds to D b = D t = 0 .

35. Optical Transitions in Bilayer I: Direct gap transition (tunable, <250 meV) II, IV: Transition between conduction/valence bands (~400 meV, dominated by van Hove singularity) III, V: Transition between conduction and valence bands (~400 meV, relatively weak) If  E F =0, then II and IV do not contribute

36. Bandstructure Change Induced by Transitions II & IV inactive Transition I active x x IV II

37. Differential Bilayer Spectra (  D = 0) (Difference between spectra of D  0 and D=0) I I Larger bandgap  stronger transition I because ot higher density of states IV

39. Charge Injection without Change of Bandstructure (D fixed) x  D = 0  D  0 Transition IV becomes active Peak shifts to lower energy as D increases.. Transition III becomes weaker and shifts to higher energy as D increases. IV III

40. Difference Spectra for Different D between  D=0.15 v/nm and  D=0

41. Larger D

42. Bandgap versus D

43.  (dR/R)  (dR/R) 60V -(dR/R) -50V is comparable to  R/R in value Strength of Gate Modulation

44. Summary Grahpene exhibits interesting optical behaviors:. Gate bias can significantly modify optical transitions over a broad spectral range. Single gate bias shifts the Fermi level of monolayer graphene. Spectra provides information on bandstructure, allowing deduction of V F (slope of the Dirac cone in the bandstructure). Double gate bias tunes the bandgap and shifts the Fermi level of bilayer graphene. Widely gate-tunable bandgap of bilayer graphene could be useful in future device applications. Strong gating effects on optical properties of graphene could be useful in infrared optoelectronic devices.