Chemistry Reference
In-Depth Information
Fig. 2. Energy band structure
E
(
k
) and density of states
D
(
E
) of (a) armchair nanorib-
bon and (b) zigzag nanoribbon. Here
N
= 30.
S
, the an amplitude of scattered waves
O
are related to an amplitude of
incident waves
I
,
O
L
O
R
=
I
L
I
R
=
rt
tr
I
L
I
R
S
.
(2)
r
r
are reflection matrices,
t
t
are transmission matrices,
L
Here,
and
and
and
denote the left and right lead lines. The Landauer-Buttiker formula
24
relates the scattering matrix to the conductance of sample. The electrical
conductance is calculated using the Landauer-Buttiker formula,
R
)=
e
2
π
tt
†
)=
e
2
G
(
E
Tr(
π
g
(
E
)
.
(3)
Here
) is the transmission matrix through the disordered region. For
simplicity, throughout this paper, we evaluate electronic conductance in
the unit of quantum conductance (
t
(
E
e
2
/π
), i.e. dimensionless conductance
g
(
E
).
3.1.
One-way excess channel system
In this subsection, we consider the conductance of zigzag nanoribbons in
the clean limit, which is simply given by the number of the conducting
channel. As can be seen in Fig. 3(a), there is always one excess left-going
channel in the right valley (
K
+
) within the energy window of
|E|≤
1.
Analogously, there is one excess right-going channel in the left valley (
K
−
)
within the same energy window. Although the number of right-going and
left-going channels are balanced as a whole system, if we focus on one of
two valleys, there is always one excess channel in one direction, i.e. a chiral
mode.
