台北市立阳明高级中学-OpticsonGraph.ppt

Optics on Graphene,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),Graphene (A Monolayer of Graphite),2D Hexagonal lattice,Electrically: High mobility at room temperature, Large current carrying capability Mechanically: Large Youngs modulus. Thermally: High thermal conductance.,Properties of Graphene,Quantum Hall effect, Barry Phase Ballistic transport, Klein paradox Others,Exotic Behaviors,Quantum Hall Effect,Y. Zhang et al, Nature 438, 201(2005),Optical Studies of Graphene,Optical microscopy contrast; Raman spectroscopy; Landau level spectroscopy.,Crystalline Structure of Graphite,Graphene,2D Hexagonal lattice,Band Structure of Graphene Monolayer,P.R.Wallace, Phys.Rev.71,622-634(1947),Band Structure of Monolayer Graphere,p-Electron Bands of Graphene Monolayer,Band Structure in Extended BZ,Band Structure near K Points,10 eV,Vertical optical transition,Van Hove Singularity,K,K,Monolayer,Bilayer,Band Structures of Graphene Monolayer and Bilayer near K,EF is adjustable,x,x,Exfoliated Graphene Monolayers and Bilayers,Monolayer,Bilayer,Reflecting microscope images.,K. S. Novoselov et al., Science 306, 666 (2004).,20 m,Raman Spectroscopy of Graphene,A.S.Ferrari, et al, PRL 97, 187401 (2006),(Allowing ID of monolayer and bilayer),Reflection Spectroscopy on Graphene,Experimental Arrangement,Doped Si,Graphene,Gold,290-nm Silica,OPA,Det,Infrared Reflection Spectroscopy to Deduce Absorption Spectrum,Differential reflection spectroscopy: Difference between bare substrate and graphene on substrate,A,B,-dR/R (RA-RB)/RA versus w,RA: bare substrate reflectivity RB: substrate + graphene reflectivity,20 m,dR/R = -Reh(w)s(w),h(w) from substrate s(w) from graphene: interband transitons free carrier absorption,Re s(w)/w: Absorption spectrum,Spectroscopy on Monolayer Graphene,Monolayer Spectrum,x,C: capacitance,Experimental Arrangement,Doped Si,Graphene,Gold,290-nm Silica,OPA,Det,Vg,Gate Effect on Monolayer Graphene,X,X,X,Small density of states close to Dirac point E = 0 Carrier injection by applying gate voltage can lead to large Fermi energy shift .,EF can be shifted by 0.5 eV with Vg 50 v; Shifting threshold of transitions by 1 eV,If Vg = Vg0 + Vmod, then should be a maximum at,Vary Optical Transitions by Gating,Laser beam,Vary gate voltage Vg.,Measure modulated reflectivity due to Vmod at V,( Analogous to dI/dV measurement in transport),Results in Graphene Monolayer,= 350 meV,The maximum determines Vg for the given EF.,Mapping Band Structure near K,For different w, the gate voltage Vg determined from maximum is different, following the relation ,Slope of the line allows deduction of slope of the band structure (Dirac cone) ,2D Plot of Monolayer Spectrum,Experiment,Theory,D(dR/R) (dR/R) 60V -(dR/R) -50V,Vg = 0,Strength of Gate Modulation,Bilayer Graphene (Gate-Tunable Bandgap),Band Structure of Graphene Bilayer,For symmetric layers, D = 0 For asymmetric layer, D 0,E. McCann, V.I.Falko, PRL 96, 086805 (2006);,Doubly Gated Bilayer,Asymmetry: D D (Db + Dt)/2 0 Carrier injection to shift EF: F dD = (Db - Dt),Sample Preparation,Effective initial bias due to impurity doping,Transport Measurement,Maximum resistance appears at EF = 0,Lowest peak resistance corresponds to Db = Dt = 0 .,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 dEF=0, then II and IV do not contribute,Bandstructure Change Induced by,Transitions II & IV inactive Transition I active,x,x,IV,II,Differential Bilayer Spectra (dD = 0) (Difference between spectra of D0 and D=0),I,I,Larger bandgap stronger transition I because ot higher density of states,IV,Charge Injection without Change of Bandstructure (D fixed),x,dD = 0,dD 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,Difference Spectra for Different D between dD=0.15 v/nm and dD=0,Larger D,Bandgap versus D,D(dR/R) (dR/R) 60V -(dR/R) -50V,is comparable to dR/R in value,Strength of Gate Modulation,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 VF (slope of the Dirac cone in the bandstructure). Double gate bias tunes the band