Biomedical Engineering Reference
In-Depth Information
The same region is plotted for different strengths of the external potential over the
molecule. In contrast to the contact perturbation, the amount of level splitting of the
former degenerate states is here bias dependent. This fact imposes a bias window
of interference visibility. The bias must be small enough, for the 7-particle states
to be quasi-degenerate and at the same time bigger than the thermal energy, so
that the occurring NDC is not obscured by the thermally broadened conductance
peak. A strong electrostatic potential perturbation closes the bias window and
no interference effect can be detected. Panel
a
of Fig.
7.19
represents the weak
perturbation regime with no qualitative differences with the unperturbed case. The
typical fingerprints of interference (NDC at the border of the 6-particle diamond
and current blocking for the 7
6 transition) are still visible for intermediate
perturbation strength (panel
b
) but this time only in a limited bias window. Due
to the perturbation strength, at some point in the bias, the level splitting is so
big that the quasi-degeneracy is lifted and the interference effects destroyed. In
panel
c
the quasi-degeneracy is lifted in the entire bias range. There is NDC at
the border of the 6-particle diamond, but is not accompanied by current blocking
as proved by the excitation line at the border of the 7-particle diamond (see arrow):
no interference occurs. The NDC is here associated with the sudden opening of a
slow current channel, the one involving the 6-particle ground state and the 7-particle
(non-degenerate) excited state (standard NDC).
Figure
7.20
refers to the setup under both the
bias and contact perturbations
.The
left panel shows the energy of the lowest 7-particle states as a function of the bias. In
the right panel we present the stability diagram around the 6
→
7 resonance. NDC
and current blocking are clearly visible only in the bias region where, due to the
combination of bias and contact perturbation, the two seven-particle states return
quasi-degenerate. Also the fine structure in the NDC region is understandable in
terms of interference if in the condition of quasi-degeneracy we take into account
the renormalization of the level splitting due to the energy non-conserving terms.
Interference effects predicted for the unperturbed benzene I-SET are robust
against various sources of symmetry breaking. Quasi-degeneracy,
↔
k
B
T
,
is the necessary condition required for the detection of the interference in the
stability diagram of the benzene I-SET.
δ
E
h
Γ
7.8
Conclusions
In this chapter we addressed the interference effects that characterize the electronic
transport through a symmetric single electron transistor based on quantum dot
molecules. Interestingly, in this class of devices interference effects survive even
in the weak tunnelling coupling regime when usually the decoherence introduced
by the leads dominates the picture and transport consists of a set of incoherent
tunnelling events.
After introducing the concept of interference single electron transistor (I-SET)
we formulate a simple interference condition (
7.24
) for I-SETs in terms of the
