Biomedical Engineering Reference
In-Depth Information
tunnelling transitions
amplitudes
of degenerate states with respect to the source and
drain lead. A generic model of I-SET is then introduced, together with our method
of choice to study the dynamics of the molecular I-SET: i.e., the density matrix
approach which starts from the Liouville equation for the total density operator
which enables the treatment of quasi-degenerate states, so crucial for the description
of the interference effects which are the focus of our investigation. As a further step,
we derive the most generic conditions for interference blockade and an algorithm
for the identification of the interference blocking states as linear combination of
degenerate many-body eigenstates of the system. The theory is sufficiently general
to be applied to any device consisting of a system with degenerate many-body
spectrum weakly coupled to metallic leads, e.g., molecular junctions, graphene
or carbon nanotube quantum dots, artificial molecules. In particular, the algebraic
formulation of the blocking condition in terms of kernels of the tunnelling matrices
T
±
,Eq.(
7.18
), allows a straightforward numerical implementation and makes the
algorithm directly applicable to complex junctions with highly degenerate spectrum.
For example, we have recently applied the same theory to study the transport
through STM junctions of single molecules on thin insulating films [
61
,
62
].
As an application of the theory we study the benzene and the triple dot I-SET.
For the first system, two different setups are considered, the para and the meta
configuration, depending on the position of the leads with respect to the molecule.
Within an effective
p
z
orbital model, we diagonalize exactly the Hamiltonian
for the molecule. We further apply a group theoretical method to classify the
many-body molecular eigenstates according to their symmetry and quasi-angular
momentum. With the help of this knowledge we detect the orbital degeneracy
and, in the para configuration, we select the states relevant for transport. The
application of the simple interference condition (
7.24
) enables us to predict the
existence of interference effects in the meta configuration. The stability diagrams
for the two configurations show striking differences. In the linear regime a selective
conductance suppression is visible when changing from the para to the meta
configuration. Only transitions between ground states with well-defined particle
number are affected by the change in the lead configuration. With the help of the
group theoretical classification of the states we recognize in this effect a fingerprint
of the
destructive interference
between orbitally degenerate states. We derive an
analytical formula for the conductance that reproduces exactly the numerical result
and supports their interpretation in terms of interference. Other interference effects
are also visible in the nonlinear regime where they give rise to NDC and current
blocking at the border of the 6-particle Coulomb diamond as well as to current
suppression for transitions between 7- and 6-particle states.
Despite its relative simplicity, the triple dot I-SET exhibits different types of
interference blocking and it represents an interesting playground of the general
theory. Specifically, we concentrated on the interference blockade that involves an
excited triplet state, a condition not accessible in the benzene I-SET.
In both cases we further analyze the blockade that involves orbitally and spin
degenerate states and we show how to realize all electrical preparation of specific
spin states. Thus we obtain an interference-mediated control of the electron spin in
