optics on graphene
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
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Optics on Graphene
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Gate-Variable Optical Transitions in GrapheneFeng 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 GrapheneYuanbo Zhang, Tsung-Ta Tang, Caglar Girit1, Zhao Hao, Michael C. Martin, Alex Zettl1, Michael F. Crommie, Y. Ron Shen and Feng Wang (2009)
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Graphene(A Monolayer of Graphite)
2D Hexagonal lattice
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Electrically: High mobility at room temperature, Large current carrying capability
Mechanically: Large Young’s modulus.
Thermally: High thermal conductance.
Properties of Graphene
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Quantum Hall effect,
Barry Phase
Ballistic transport,
Klein paradox
Others
Exotic Behaviors
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Quantum Hall Effect
Y. Zhang et al, Nature 438, 201(2005)
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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
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Crystalline Structure of Graphite
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Graphene2D Hexagonal lattice
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Band Structure of Graphene Monolayer
1 2
int
1 1
2 2
( )
Tight-binding calculation on bands:
, ( )
*( ),
( ) [1 ]
( ) | ( ) |
3
at
p
p
ik a ik a
p
p
H H H k
E f ku uH
u uf k E
f k e e
E k E f k
E
1 2 2 1
2
2cos 2cos 2cos ( )
1 4cos ( 3 / 2) 4cos( 3 / 2)cos(3 / 2)
' near K points
p x x y
p F
k a k a k a a
E k a k a k a
E v k
P.R.Wallace, Phys.Rev.71,622-634(1947)
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Band Structure of Monolayer Graphere
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Electron Bands of Graphene Monolayer
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Band Structure in Extended BZ
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Relativistic Dirac fermion.
Band Structure near K Points
eV
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Vertical optical transitionVan Hove Singularity
Monolayer Bilayer
Band Structures of Graphene Monolayer and Bilayer near K
EF is adjustable
x
x
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Exfoliated Graphene Monolayers and Bilayers
Monolayer Bilayer
Reflecting microscope images.
K. S. Novoselov et al., Science 306, 666 (2004).
20 m
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Raman Spectroscopy of Graphene
A.S.Ferrari, et al, PRL 97, 187401 (2006)
(Allowing ID of monolayer and bilayer)
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Reflection Spectroscopy on Graphene
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Experimental Arrangement
Doped Si
GrapheneGold
290-nm Silica
OPADet
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Infrared Reflection Spectroscopyto Deduce Absorption Spectrum
Differential reflection spectroscopy:Difference between bare substrate and graphene on substrate
A
B-R/R (RA-RB)/RA versus
RA: bare substrate reflectivity
RB: substrate + graphene reflectivity20 m
dR/R = -Re[
from substrate
from graphene: interband transitons
free carrier absorptionRe Absorption spectrum
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Spectroscopy on Monolayer Graphene
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Monolayer Spectrum
x
R/R
E EF
2 2
0
0 0
#electrons/holes
= ( ) / ( v )
v | |
( ) p-doped: 0
can be adjusted by carrier injection through .
FE
F F
F F
g
F g
n
E dE E
E n
n C V V V
E V
2( ) 2 / FE E v
C: capacitance
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Experimental Arrangement
Doped Si
GrapheneGold
290-nm Silica
OPADet
Vg
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Gate Effect on Monolayer Graphene
2( ) 2 / vFE E
X XX
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
R/R
EF
If Vg = Vg0 + Vmod, then should be a maximum at mod
( / )R R
V
2 FE
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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)
0
( / )
V
R R
V
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Results in Graphene Monolayer
= 350 meV
2 FE 0
2 20
v | |
( )
=( v ) | |
F F
g
F F g
E n
n C V V
E C V V
The maximum determines Vg for the given EF.
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Mapping Band Structure near KFor different , the gate voltage Vg determined from maximum is different, following the relation , mod
( / )R R
V
2 2
0( v ) | | F F gE C V V
R/R
EF
Slope of the line allows deduction of slope of the band structure (Dirac cone)
60.83 10 /Fv m s 0 70 vV
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2D Plot of Monolayer SpectrumExperiment Theory
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R/R) 60V50V
Vg
Strength of Gate Modulation
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Bilayer Graphene(Gate-Tunable Bandgap)
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Band Structure of Graphene Bilayer
For symmetric layers, = 0
For asymmetric layer,
E. McCann, V.I.Fal’ko, PRL 96, 086805 (2006);
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Doubly Gated Bilayer
Asymmetry: D (Db + Dt)/2 0
Carrier injection to shift EF: F D = (Db - Dt)
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Sample Preparation
0 ( - ) /b b b b bD V V d
0t ( - ) /t t t tD V V d
0,b tV Effective initial bias
due to impurity doping
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Transport Measurement
Maximum resistance appears at EF = 00 0( ) ( - ) / ( - ) / 0b t b b bb tt t tVD D V VD d V d
0D
Lowest peak resistance corresponds to Db = Dt = 0 .0 0, b tV V
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Optical Transitions in BilayerI: 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 EF=0, then II and IV do not contribute
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Bandstructure Change Induced by0 (from 0 with 0)D D D
Transitions II & IV inactive
Transition I active
x
x
IV
II
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Differential Bilayer Spectra (D = 0)(Difference between spectra of D0 and D=0)
I I
Larger bandgap stronger transition I because ot higher density of states
IV
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Charge Injection without Change of Bandstructure (D fixed)
xD = 0 D 0
Transition IV becomes activePeak shifts to lower energy as D increases..
Transition III becomes weaker and shifts to higher energy as D increases.
IV
III
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Difference Spectra for Different D between D=0.15 v/nm and D=0
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Larger D
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Bandgap versus D
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(dR/R) (dR/R) 60V -(dR/R) -50V
is comparable to R/R in value
Strength of Gate Modulation
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SummaryGrahpene 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 deducti
on of VF (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.
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