Optics on Graphene. Gate-Variable Optical Transitions in Graphene Feng Wang, Yuanbo Zhang, Chuanshan...
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Optics on Graphene
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)
Graphene(A Monolayer of Graphite)
2D Hexagonal lattice
Electrically: High mobility at room temperature, Large current carrying capability
Mechanically: Large Young’s 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.
Other Possibilites
• Spectroscopic probe of electronic structure.
• Interlayer coupling effect.• Electrical gating effect on optical transitions.
• Others
Crystalline Structure of Graphite
Graphene2D Hexagonal lattice
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)
Band Structure of Monolayer Graphere
Electron Bands of Graphene Monolayer
Band Structure in Extended BZ
Relativistic Dirac fermion.
Band Structure near K Points
eV
Vertical optical transitionVan Hove Singularity
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
GrapheneGold
290-nm Silica
OPADet
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
Spectroscopy on Monolayer Graphene
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
Experimental Arrangement
Doped Si
GrapheneGold
290-nm Silica
OPADet
Vg
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
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
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.
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
2D Plot of Monolayer SpectrumExperiment Theory
R/R) 60V50V
Vg
Strength of Gate Modulation
Bilayer Graphene(Gate-Tunable Bandgap)
Band Structure of Graphene Bilayer
For symmetric layers, = 0
For asymmetric layer,
E. McCann, V.I.Fal’ko, PRL 96, 086805 (2006);
Doubly Gated Bilayer
Asymmetry: D (Db + Dt)/2 0
Carrier injection to shift EF: F D = (Db - Dt)
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
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
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
Bandstructure Change Induced by0 (from 0 with 0)D D D
Transitions II & IV inactive
Transition I active
x
x
IV
II
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
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
Difference Spectra for Different D between D=0.15 v/nm and D=0
Larger D
Bandgap versus D
(dR/R) (dR/R) 60V -(dR/R) -50V
is comparable to R/R in value
Strength of Gate Modulation
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.