Chemistry Reference
In-Depth Information
ξ
g→
with
1also
occur, if the incident energy lies at a value close to the change between
g
as the localization length. Deviations from the limit
+ 1 for the ribbon without disorder. This is for
example visible in above calculations for
E
=0
.
4 where the limiting value
g <
1 (Fig. 4(a)).
=2
n −
1and
g
=2
n
Fig. 4.
for zigzag nanorib-
bon with
N
= 10, (a)
d/a
=1
.
5 (no inter-valley scattering), (b)
d/a
=0
.
1 (inter-valley
scattering). Here
u
0
=1
.
0, and
n
imp.
=0
.
1. More than 9000 samples with different
impurity configuration are included in the ensemble average.
L
-dependence of the averaged dimensionless conductance,
g
In Fig. 4(b), the nanoribbon length dependence of the averaged con-
ductance for SRIs is shown. Since SRI causes the inter-valley scattering
for any incident energy, the electrons tend to be localized and the averaged
conductance decays exponentially,
g∼
exp(
−L/ξ
), without developing a
perfect conduction channel.
As the effect is connected with the subtle feature of an excess mode in
band structure, it is natural that the result can only be valid for suciently
weak potentials. For potential strengths comparable to the energy scale of
the band structure, e.g. the energy difference between the transverse modes,
the result should be qualitatively altered.
26
3.3.
Graphene nanoribbons with generic edge structures
As we have seen, zigzag ribbons with long-ranged impurity potentials retain
a single PCC. This PCC originates for the following two reasons: (i) The
spectrum contains two valleys (two Dirac
K
±
-points) which are well enough
separated in momentum space as to suppress intervalley scattering due to
the long-ranged impurities, (ii) the spectrum in each valley is chiral by
