graphene.feng.08

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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
Properties of Graphene
Electrically:
High mobility at room temperature,
Large current carrying capability
Mechanically:
Large Young’s modulus.
Thermally:
High thermal conductance.
Exotic Behaviors
Quantum Hall effect,
Barry Phase
Ballistic transport,
Klein paradox
Others
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
Graphene
2D Hexagonal lattice
Band Structure of Graphene
Monolayer
H  H a t  H int ( k )
T ight-binding calculation on  bands:
f ( k )   u1 
 u1   E p ,
 
H  
 u 2   f *( k ), E p   u 2 
f ( k )   [1  e
ik  a1
e
ik  a 2
]
E ( k )  E p  | f ( k ) |
 Ep 
3  2 cos k  a1  2 cos k  a 2  2 cos k ( a 2  a1 )
 Ep 
1  4 cos ( 3 k x a / 2)  4 cos( 3 k x a / 2) co s(3 k y a / 2)
 E p  vF k '
2
near K points
P.R.Wallace, Phys.Rev.71,622-634(1947)
Band Structure of Monolayer Graphere
Electron Bands of Graphene
Monolayer
Band Structure in Extended BZ
Band Structure near K Points
~10 eV
Relativistic Dirac fermion.
Band Structures of Graphene
Monolayer and Bilayer near K
Bilayer
Monolayer
K
K
x
Vertical optical transition
x
Van Hove Singularity
EF is adjustable
Exfoliated Graphene
Monolayers and Bilayers
Reflecting microscope images.
20 m
Monolayer
Bilayer
K. S. Novoselov et al., Science 306, 666 (2004).
Raman Spectroscopy of Graphene
(Allowing ID of monolayer and bilayer)
A.S.Ferrari, et al, PRL 97, 187401 (2006)
Reflection Spectroscopy
on Graphene
Experimental Arrangement
Det
OPA
Gold
Graphene
290-nm
Silica
Doped Si
Infrared Reflection Spectroscopy
to Deduce Absorption Spectrum
Differential reflection spectroscopy:
Difference between bare substrate and graphene on substrate
20 m
A
B
RA: bare substrate reflectivity
RB: substrate + graphene reflectivity
-dR/R  (RA-RB)/RA versus w
dR/R = -Re[h(w)s(w)]
h(w) from substrate
s(w) from graphene: interband transitons
Re s(w)/w: Absorption spectrum
free carrier absorption
Spectroscopy
on Monolayer Graphene
dR/R
Monolayer Spectrum
x
2EF
w  E
n   # electro n s/h o les
=

EF
0
 ( E )dE   E F /  ( v F )
EF   vF
2
2
 ( E )  2 E /  vF
2
 | n |
n   C (V g  V 0 )
p -d o p ed : V 0  0
C: capacitance
E F can b e ad ju sted b y carrier in jectio n th ro u g h V g .
Experimental Arrangement
Det
OPA
Gold
Graphene
290-nm
Silica
Vg
Doped Si
dR/R
Gate Effect on Monolayer Graphene
X
XX
2EF
 (E )  2E /  vF
2
w
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
 (d R / R )
 V m od
should be a maximum at w  2 E F
Vary Optical Transitions by Gating
Laser beam
Vary gate voltage Vg.
Measure modulated reflectivity due
to Vmod at V
  (d R / R ) 


V

V0
( Analogous to dI/dV measurement in transport)
Results in Graphene Monolayer
w
= 350 meV
EF   vF
w  2EF
 | n |
n   C (V g  V 0 )
E F = ( v F )  C | V g  V0 |
2
2
The maximum determines Vg for the given EF.
Mapping Band Structure near K
For different w, the gate voltage Vg determined from
maximum  (d R / R ) is different, following the relation
V
E  ( v )  C |V  V |
,
2
F
2
F
g
0
dR/R
m od
2EF
w
Slope of the line allows deduction of slope of the band structure
6
(Dirac cone)  v F  0.83  10 m / s
V 0   70 v
2D Plot of Monolayer Spectrum
Experiment
w
Theory
Strength of Gate Modulation
Vg  0
D(dR/R)  (dR/R) 60V (dR/R) 50V
Bilayer Graphene
(Gate-Tunable Bandgap)
Band Structure of Graphene Bilayer
For symmetric layers, D = 0
For asymmetric layer, D  0
E. McCann, V.I.Fal’ko, PRL 96, 086805 (2006);
Doubly Gated Bilayer
Asymmetry:
D  D  (Db + Dt)/2  0
Carrier injection to shift EF: dF  dD = (Db - Dt)
Sample Preparation
D b    b (V b - V b ) / d b
0
D t    t (V t - V t ) / d t
0
Effective initial bias
V b , t  due to impurity doping
0
Transport Measurement
dD 0
Maximum resistance appears at EF = 0
d D  ( D b  D t )   b (V b - V b ) / d b   t (V t - V t ) / d t  0
0
0
0
0
Lowest peak resistance corresponds to Db = Dt = 0  V b , V t .
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
D  0 (from D  0 with d D  0)
IV
II
x
x
Transitions II & IV inactive
Transition I active
Differential Bilayer Spectra (dD = 0)
(Difference between spectra of D0 and D=0)
I
I
IV
Larger bandgap  stronger transition I
because ot higher density of states
Charge Injection without Change
of Bandstructure (D fixed)
dD 0
dD = 0
x
IV
III
Transition IV becomes active
Peak shifts to lower energy as D increases..
Transition III becomes weaker and shifts to higher
energy as D increases.
Difference Spectra for Different D
between dD=0.15 v/nm and dD=0
Larger D
Bandgap versus D
Strength of Gate Modulation
D(dR/R)  (dR/R) 60V -(dR/R) -50V
is comparable to dR/R in value
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 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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