Chemistry Reference
In-Depth Information
g
g
K
+
+
g
K
−
(right-moving) and
g
=
g
K
+
+
g
K
−
the conductance
=
(left-moving) are equivalent.
3.2.
Perfectly conducting channel
tt
†
)(
The dimensionless electrical conductance,
)isthetrans-
mission matrix through the disordered region), is calculated by means of
the recursive Green function method.
25
As shown in Fig. 1, the impurities
are randomly distributed with a density
g
(
E
)=Tr(
t
(
E
n
imp
in the nanoribbons. In our
model we assume that the each impurity potential has a Gaussian form of
a range
d
exp
r
i
)=
r
0
(
random
)
−
|
r
i
−
r
0
|
2
d
2
V
(
u
(12)
where the strength
u
is uniformly distributed within the range
|u|≤u
M
.
Here
u
M
satisfies the normalization condition:
(
full space
)
(
√
3
exp
−
r
i
d
2
/
u
M
/
2) =
u
0
.
(13)
r
i
In this work, we set
n
imp
.
=0
.
1,
u
0
=1
.
0and
d/a
=1
.
5forLRIand
d/a
1 for SRI. Since the momentum difference between two valleys
is rather large, ∆
=0
.
, only short-range impurities (SRI)
with a range smaller than the lattice constant causes
inter-valley scattering
.
Long-range impurities (LRI), in contrast, restrict the scattering processes
to
intra-valley scattering
.
4
We focus first on the case of LRI using a potential with
k
=
k
+
− k
−
=4
π/
3
a
5which
is already sucient to avoid inter-valley scattering. Figure 4(a) shows the
averaged dimensionless conductance as a function of
d/a
=1
.
for different inci-
dent energies(Fermi energies), averaging over an ensemble of 40000 sam-
ples with different impurity configurations for ribbons of width
L
= 10.
The potential strength and impurity density are chosen to be
u
0
=1
N
.
0and
n
imp.
=0
.
1, respectively. As a typical localization effect we observe that
g
gradually decreases with growing length
L
(Fig. 4). However,
g
con-
verges to
= 1 for LRIs (Fig. 4(a)), indicating the presence of a single
perfectly conducting
channel. It can be seen that
g
g
(
L
) has an exponential
behavior as
g−
1
∼
exp(
−L/ξ
)
(14)
