Biomedical Engineering Reference
In-Depth Information
Tabl e 7. 4
Number of channels participating in transport, overlap
factor and resonance value of the degeneracy term in the para and
the meta configuration for the 6
↔
7 transition peak. It is
C
=
2
,where
|
are the spin and the quasi-angular
momentum quantum numbers, respectively. The values of
6
g
|
d
Lτ
|
7
g
l
τ
|
τ
and
Δ
max
are
given for
k
B
T
=
0
.
04
|
b
|
.From[
20
]
Number of channels
(
Overlap
factor
Degeneracy term
Δ
Configuration
S
N
S
N
+
1
)
Λ
max
[1/
k
B
T
]
Para
2
C
0,17
1
8
C
Meta
4
0,11
factor
. The overlap factor is basis independent, thus we can write the transition
probabilities for the 6
Λ
2
are the
spin and the quasi-angular momentum quantum number, respectively. The transition
probabilities have the same value, since all four 7-particle states are in this basis
equivalent (see Appendix C of [
20
] for a detailed proof). Under the
C
2
rotation
the symmetric 7-particle ground state does not acquire any phase factor. Under
the
C
3
rotation however, the two orbitally degenerate states acquire different phase
factors, namely
e
4
3
↔
7 transition as
|
6
g
|
d
Lτ
|
7
g
τ
|
=
C
,where
τ
and
4
3
i
and
e
−
i
, respectively. Thus the overlap factors
Λ
for the 6
↔
7
transition are:
1
2
Λ
para
=
8
C
·|
4
C
|
=
C
,
2
·
i
1
2
1
8
C
4
3
4
3
2
Ce
+
i
2
Ce
−
Λ
=
8
C
·
+
=
.
meta
4
·
The linear conductance is determined by the product between the number of
conducting channels, the overlap factor and the degeneracy term. Yet, it is the
destructive interference
between degenerate
E
-type orbitals, accounted for in the
overlap factor
, that gives the major contribution to the strong suppression of the
conductance in the meta configuration.
Λ
7.4.3.2
Negative Differential Conductance and Current Blocking
Interference effects between orbitally degenerate states are also affecting nonlinear
transport and producing in the
meta
configuration current blocking and thus NDC
at the border of the 6-particle state diamond (Fig.
7.4
). The upper panel of Fig.
7.6
shows the current through the benzene I-SET contacted in the meta configuration
as a function of the bias voltage. The current is given for parameters corresponding
to the white dashed line of Fig.
7.4
. In this region only the 6- and 7-particle ground
states are populated. At low bias the 6-particle state is mainly occupied. As the bias
is raised, transitions 6
7 occur and current flows. Above a certain bias threshold
a blocking state is populated and the current drops. For the understanding of this
↔
