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Crystalline Structure of Graphite
Graphene
2D Hexagonal lattice
Band Structure of Graphene Mmodulated 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 ,
dR/R
2EF
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, ’ko, 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 shi