Biomedical Engineering Reference
In-Depth Information
by gate terminals which produce tunable potential bias. In theoretical models, those
potentials are included through variable parameters, like the energy of the electron
when it is localized in a given QD, referred to as the on-site energy.
There is still another way in which the electron wave function can change its
phase. In their seminal article, Aharonov and Bohm showed the now well-known
effect, named after them, that the magnetic vector potential
A
can influence the
motion of a quantum particle even in regions where the magnetic field
B
itself
vanishes [
7
]. In such a case, the phase shift of the wave function evaluated at two
different points in space changes by the integral of the
A
along a trajectory joining
those two points. The phase accumulated along a closed curve can be related to
the flux of the magnetic field enclosed by the curve, invoking the Stoke's theorem.
This local change of phase, entirely due to a non-vanishing vector potential, has no
classical analog [
8
].
8.2.2
Fano and Aharonov-Bohm Effects
In the following, we shall restrict ourselves to QDs under low biases, thus disregard-
ing processes leading to energy relaxation. In such a case, the linear conductance of
quantum dots is mostly due to elastic transport processes. In particular, we assume
a ballistic regime, as opposite to a diffusive one. A ring having QDs embedded into
their arms allows one to combine the two causes of interference aforementioned.
In order to be observable in the measured currents, the dimensions of the ring
must be of the order or smaller than the length after which the interaction of
electrons produces lost of coherence. The AB effect has been envisioned for the
feasible exploitation of the quantum phase in electronic devices [
4
,
9
-
14
]. Phase
coherent effects in AB rings have been treated theoretically in the literature [
15
-
31
]. Due to its origin, the presence of AB effect is used as an experimental probe
showing the signature of coherent behavior of the electronic transport in 2DEG
nanostructures [
32
-
35
], in graphene rings [
36
-
39
], or even at the leads [
40
]; to
study the lost of coherence of a system due to inelastic interactions [
14
,
41
], or
to determine the dependence of the coherence of the system on its parameters [
42
].
Interestingly, it has also been used as probe of coherence in experiments not directly
related to electronic transport, such as those measuring properties depending on the
entanglement between electrons [
43
].
Closely related to the concept of coherence is the quantum interference between
a discrete state with a continuum of states. This phenomenon was firstly studied
by Fano in the spectrum of photoionization of atoms and termed Fano effect after
him [
44
], although was found ubiquitous in a wide range of physical phenomena.
Interestingly, it has been observed in properly tailored nanoscale systems [
6
,
45
-
47
].
The first tunable experiment showing the characteristic asymmetric Fano profile in
the electron transmission was reported in an AB ring with a quantum dot embedded
in one of its arms [
45
]. Various parameters, such as the gate voltage and the magnetic
flux through the ring among others, allowed to tune the peak and dip of the profile.
