Biomedical Engineering Reference
In-Depth Information
C
12
(1
B
12
→
→
direct path through sites 1 and 2 (
t
12
), the path
Σ
4
2) and the path
Σ
t
12
e
i
ϕ
+
Vt
14
g
44
e
−
i
ϕ
+
→
→
→
(
ϕ
)=
(1
4
3
2), contributing to the self-energy
Σ
12
t
14
g
43
t
31
e
−
3
i
ϕ
. The absolute square of the self-energy is
t
12
+(
Σ
12
2
12
2
12
12
cos 2
12
cos 4
=
)
+(
Σ
)
+
(
+
Σ
)
Σ
ϕ
+
ϕ
,
Σ
2
t
12
2
t
12
Σ
(8.36)
12
where the phase of the big orbit (4
) characterizes the interference between the
pathways along the arms of the ring, whilst the phase of the small orbit (2
ϕ
ϕ
)
corresponds to the interference between them and the molecular bond.
8.4
Concluding Remarks
In this chapter, we have discussed two quantum interference-based phenomena,
namely, the Fano and AB effects. It has been argued that they have different origins.
The former originates in the external gate potentials used to produce and couple
the QDs, while the latter arises from an applied magnetic field perpendicular to the
heterostructure when a configuration of two or more alternative electron paths there
exists.
The Fano effect produces a typical asymmetric profile in the transmission
coefficient as a function of the electron energy. It is characterized by a peak
and an antiresonance in the conductance at two close energies. Using the Green
function formalism for the electron transport together with a discrete Hamiltonian
description, the conductance can be analyzed from the Green function of the
system disconnected from the source and drain terminals. The resonances in the
transmission occur at the poles of the Green functions between QD sites connected
to the source and drain, respectively. In particular, one type of antiresonance is due
to the cancellation of contributions to the self-energy along alternative transmission
paths. Including QDs in such paths, like in an AB interferometer, offers interesting
prospects for technological applications, e.g., by encoding those cancellations of
conductance as quantum bits.
The application of a magnetic field precludes the occurring of Fano antireso-
nances, because the magnetic phase induced by the AB effect, prevents the complete
cancellation of the electron transmission. This phase depends on the magnetic flux
enclosed by a given loop path and, therefore, on the closed trajectories available
to the electrons. Hence, this suppression of the conductance cancellation becomes
strongly sensitive to the formation of QDs molecular states due to their couplings.
Acknowledgments
This work was partly supported by SGCyT (Universidad Nacional del
Nordeste), National Agency ANPCYT and CONICET (Argentina) under grants PI F007/11,
PICTO-UNNE 204/07 and PIP 11220090100654/2010.
