Biomedical Engineering Reference
In-Depth Information
Tabl e 7. 6
Point groups to
which the molecule belongs
under the influence of the
contacts and the external bias
potential. From [
20
]
Type of
Symmetry
Symmetry
perturbation
(Para config.)
(Meta config.)
Contact perturbation
D
2
h
C
2
v
Bias perturbation
C
2
v
C
2
v
belongs in the perturbed setup. This point groups have only
A
-and
B
-type reducible
representations. Thus the corresponding molecular orbitals do not exhibit orbital
degeneracy.
No interference effects influence the transport in the para configuration. Thus we
do not expect its transport characteristics to be qualitatively modified by the new
setup with the corresponding loss of degeneracies. In the meta configuration, on
the other hand, interferences between orbitally degenerate states play a crucial role
in the explanation of the occurring transport features. Naively one would therefore
expect that neither conductance suppression nor NDC and current blocking occur in
a benzene I-SET with reduced symmetry.
Yet we find that, under certain conditions, the mentioned transport features are
robust under the lowered symmetry.
The perturbations due to the contacts and the bias lead to an expected level
splitting of the former orbitally degenerate states. Very different current-voltage
characteristics are obtained depending of the relation between the energy splitting
δ
E
and other two important energy scales of the system: the tunnelling rate
Γ
and the temperature
T
. In particular, when
δ
E
Γ
T
, interference phenomena
persist. In contrast when
T
interference phenomena disappear, despite
the fact that, due to temperature broadening, the two states still cannot be resolved.
In this regime, due to the asymmetry in the tunnelling rates introduced by the
perturbation, standard NDC phenomena, see Fig.
7.19
, occur.
Figure
7.18
shows from left to right closeup views of the stability diagram for
the setup under the influence of increasing
contact perturbation
around the 6
Γ
<
δ
E
7
resonance. The orbital degeneracy of the 7-particle states is lifted and the transport
behavior for the 6
↔
7 transition depends on the energy difference between the
formerly degenerate 7-particle ground states. In panel
a
the energy difference is
so small that the states are quasi-degenerate:
↔
k
B
T
. As expected, we
recover NDC at the border of the 6-particle diamond and current suppression at
the border of the 7-particle diamond, like in the unperturbed setup. Higher on-site
energy-shifts correspond to a larger level spacing. Panel
b
displays the situation
in which the latter is of the order of the level broadening, but still smaller than
the thermal energy (
δ
E
h
Γ
k
B
T
): no interference causing NDC and current
blocking can occur. Yet, due to thermal broadening, we cannot resolve the two 7-
particle states. Eventually, panel
c
presents the stability diagram for the case
δ
E
h
Γ
δ
E
>
k
B
T
: the level spacing between the 7-particle ground and first excited state is
now bigger than the thermal energy, thus the two transition lines corresponding to
these states are clearly visible at the border of the 6-particle stability diamond.
Figure
7.19
shows closeup views of the stability diagram for the setup under the
influence of the
bias perturbation
at the border of the 6- and 7-particle diamonds.
>
h
Γ
