Chemistry Reference
In-Depth Information
2.5
1.5
Symmetric
∆
/h
ω
0
=2.0
Ant
i
symmetric
∆
/h
ω
0
=2.0
2.0
1.0
δ
/h
ω
0
0.500
0.200
0.100
0.010
1.5
0.5
1.0
0.0
ω
0
0.500
0.200
0.100
0.010
δ
/h
0.5
-0.5
0.0
-1.0
Shift
Broadening
Shift
Broadening
-0.5
-1.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Fermi Energy (units of h
ω
0
)
Fermi Energy (units of h
ω
0
)
Fig. 7. Some examples of calculated frequency shift and broadening of the symmetric
(left) and antisymmetric mode (right) at the Γ point in a bilayer graphene. ∆
/
ω
0
=2.
The amount of the broadening due to disorder is denoted by
δ
.
1.5
∆
0.0
0.2
0.5
1.0
eFd/
1.0
0.5
Monolayer
0.0
Fig. 8. A schematic illustration of the
bilayer graphene with a top gate and a
bottom gate and the potential energy di-
agram. The distance between the layers
is given by
d
, the potential difference by
eF d
,and
F
ext
represents the field due to
the top gate.
-0.5
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Wave Vector (units of
∆
/
γ
)
Fig. 9. The energy dispersion for vary-
ing values of the potential difference
eF d
.
The dot-dot-dashed lines show that of a
monolayer graphene.
ε
+1
(
k
The band
) represents the lowest conduction band which touches the
highest valence band
ε
−
1
(
k
k
ε
±
2
(
k
)at
= 0. The bands
)aretheexcited
conduction and valence bands and
ε
+2
(
k
−ε
+1
(
k
δ
k
.
In bilayer graphene, optical phonons are classified into symmetric and
antisymmetric modes in which the displacement of the top and bottom
)
)=
independent of
