Biomedical Engineering Reference
In-Depth Information
electronic motion, has propitiated to name them as “artificial atoms”, because of
the similarity of their energy spectra with those from the elements of the periodic
table. By extension, quantum dot arrays are also termed “artificial molecules” or
QD molecules. Remarkably, the most noticeable difference is their typical energies.
While the excitation energies of natural atoms and molecules are of the order of eV,
those for quantum dots are three order of magnitude smaller. This allows one to take
advantage of effects hardly observable in natural molecules because of the required
energy scale.
As the dimensions of the region accessible to the electronic motions become
smaller, the quantum effects turn more notorious and a wave function description of
the electronic motion becomes mandatory. This wave character manifests itself in
intrinsically quantum effects, like coherence and interference. The control of such
effects is important to provide both a better understanding of the quantum realm and
new functionalities to the circuits [
1
,
2
]. Quantum interference allows to enhance or
to cancel, total or partially, the response of the system beyond the simple classical
additive behavior. Such an effect not only can pose a problem to be avoided but also
could provide new capabilities to the device with respect to its classical counterpart
[
3
,
4
]. Two remarkable effects arose from this quantum behavior, namely, the Fano
and the Aharonov-Bohm effects. In this chapter, we will show a way of including
these effects in a particular type of theoretical models and their consequences for
nanoscale structures. On the one hand, the ability of tuning the device configuration
and parameters allows one to control its response to externally applied fields or
voltages. On the other hand, the modification of the charge transport through the
nanostructure provides useful information on the material properties as well as to
design new applications with unprecedented functionalities [
5
].
Here, we present the non-equilibrium Green function (NEGF) formalism for
quantum transport and apply it to a system in a phase coherent non-interacting
regime. In experiments with nanostructures, various electrostatic gate voltages are
used to tune the device. The tunability of QD couplings allows one to change
the electronic transmission of the system. Under proper connection topologies, the
transmission can be completely suppressed at a given energy.
When a magnetic field perpendicular to a ring in the 2DEG is present, such as
the one shown in Fig.
8.1
, a periodic modulation of the phase of the wave function
arises. For this configuration, two or more spatial paths for transmission between
the source and drain terminals exist. In such a case, the phase varies with the
magnitude of the magnetic flux threading it. It has been experimentally shown that
connecting or disconnecting the arms of a ring of QDs by inducing the formation
of QD molecules between them produces an abrupt change in the conductance.
This result is usually interpreted in terms of the simplest fully-coherent single-
mode wave picture. We use the NEGF formalism together with a Hamiltonian for
nearest-neighbor interacting QDs placed at fixed discrete sites. This description
leads to the appealing interpretation of transmission pathways. They are formed
by the chain of sites (QDs) occupied by the electron when successively hopping
from one QD to its nearest neighbor. Throughout the chapter, we shall stress the
qualitatively modeling of the relevant effects and its interpretation, rather than their
