Chemistry Reference
In-Depth Information
20). The energy is normalized by ∆
s,A
(∆
s,Z
),
denoting the end of single-channel energy regime of the left wider armchair
(zigzag) ribbon. These energy scales are related to the ribbon width by
∆
s,A
√
3
,
N
L
,N
R
)=(30
,
(32
20) and (
3
√
3
and ∆
s,Z
πγ
0
a/
2
W
πγ
0
a/
8
W
where
W
=(
M
L
+1)
a/
2
=
√
3(
and
2 for armchair and zigzag ribbons, respectively.
The maximum conductance is limited by the number of channel at the
right narrower ribbon (black dotted line in Figs. 6(c) and (d)).
The behaviour of conductance strongly depends on junction structure
in the single-channel energy regime (
W
N
L
+1)
a/
∆
s,
(
A,Z
)
|E| <
) while it does not in the
∆
s,
(
A,Z
)
multi-channel one (
). In the single-channel energy regime,
the conductance mostly remains unity in the AAA-junction while the zero
conductance dip appears in the AZA-junction at
|E| >
= 0. This zero con-
ductance dip is due to the anti-resonance induced by the coupling between
a continuous state at ribbon and a localized state at zigzag edge junction.
In addition, the junction region is mainly semiconducting and works as
a barrier for low-energy transport in the AZA-junction since the ribbon
width are narrowed as
E
. Hence, by the combination of
a resonance and a barrier effect, the width of zero conductance dip in the
AZA-junction is rather wide and the FWHM (full width at half maximum)
can be roughly estimated as ∆
s,A
. On the other hand, the junction region
is always metallic or semiconducting in the AAA-junction since the ribbon
width are narrowed as
M
L
−
1
,M
L
−
2
, ···
.
In the ZAZ-junction, the sharp zero conductance dips appear in the
vicinity of the end of single-channel energy regime (
M
L
−
3
,M
L
−
6
, ···
∆
s,Z
). In zigzag
ribbons, propagating electrons belong to one of two valleys in the single-
channel energy regime while the second channel will be opened in both
valleys as the energy of incident electrons increases. Since the group velocity
of a second channel is almost zero at the bottom of subband, the second
channel in the other valley works as a bound state similar to the zigzag
edge state at
E ±
E
= 0. The FWHM of dips can be roughly estimated as
∆
s,A
/
20 in our numerical simulation performed for several different values
of the ribbon width
N
N
L
− N
R
within
N
L
and the width difference ∆
=
the range
N
L
/
≤
N ≤
N
L
/
3.
In the ZZZ-junction, several zero conductance dips appear at non-zero
energies. This is due to the energy level splitting induced by the coupling
between the edge-localized state on A-sublattice at ribbon and the edge-
localized states on B-sublattice at junction. Moreover, the coupled states
have different nodes as the width difference ∆
3
∆
2
is getting larger.
20
N
