Biomedical Engineering Reference
In-Depth Information
7 transition, one does
not
observe NDC at the border of
the 7-particle Coulomb diamond, but rather a strong suppression of the current. The
upper panel of Fig.
7.7
shows the current through the benzene I-SET contacted in
the meta configuration as a function of the bias voltage corresponding to the white
dotted line of Fig.
7.4
. The middle panels show the transition probabilities between
each of the 7-particle and the 6-particle ground state. The lower panel of Fig.
7.7
shows a sketch of the energetics at positive bias corresponding to the “expected”
resonance peak. Here electrons can enter the molecular dot at both leads, while the
exit is energetically forbidden at the left lead. Thus, if the system is in the 7-particle
state which is blocking the right lead, this state cannot be depopulated, becoming
the blocking state. On the other hand, transitions from the 6-particle ground state
to both 7-particle ground states are equally probable. Thus the blocking state will
surely be populated at some time. The upper plot of the
b
panel in Fig.
7.7
shows
the transition probability to the blocking state that accepts electrons from the source
lead but cannot release electrons to the drain. As just proved, in this case the current
blocking situation occurs already at the resonance bias voltage. For a higher positive
bias, the transition probability from the blocking state at the drain lead increases and
current can flow. This effect, though, can be captured only by taking into account
also the
H
eff
contribution to (
7.5
).
In the
para
configuration, the current as a function of the bias voltage is shown
in Fig.
7.8
. The current is given for parameters corresponding to the white dashed
line of Fig.
7.4
. In this case, no interference effects are visible. We see instead the
typical step-like behavior of the current in the regime of single electron tunnelling.
The panels on the right are the surface plots of
In contrast to the 6
→
L
/
2
1
2
L
→
∞
σ
†
σ
(
2
P
(
x
,
y
;
τ
)=
lim
L
d
z
|
7
g
τ
;
(
a
)
sym
|
ψ
r
)
|
6
g
|
.
(7.41)
−
L
/
2
The upper plot shows the transition probability to the symmetric 7-particle state,
the lower to the antisymmetric. Remember that in the para configuration only the
symmetric states contribute to transport. Evidently the symmetric state is in the para
configuration non-blocking. Additionally, since the coherences between orbitally
degenerate states and therefore the energy non-conserving terms do not play any
role in the transport, the physical basis states are not bias dependent. Thus in the
para configuration there are always non-blocking states populated and no NDC can
occur.
7.5
The Triple Dot I-SET
As a second example of I-SET we consider an artificial quantum dot molecule:
i.e. the triple dot I-SET. The triple dot SET has been recently in the focus of
intense theoretical [
31
,
32
,
52
-
56
] and experimental [
57
-
60
] investigation due to
