Biomedical Engineering Reference
In-Depth Information
Fig. 8.4
The logarithm of the transmission function of a ring with coupling between its arms in
the configuration of connection (1,2), i.e., one of the dots of the molecule (QD2) is connected to
the contacting lead R. Electron energy
E
and on-site energy
2
are represented in the horizontal and
vertical axes. All interdot hopping parameters are the same,
t
12
ε
=
t
23
=
t
34
=
t
41
=
V
=
1. B
right
lines and dark regions
represent zones of high and low transmission, respectively
Application of gate potentials at dots 2 and 4 allows to tune their on-site energies
ε
2
and
ε
2
and the
electron energy
E
with and without magnetic flux for the connection (1,2). Bright
lines and dark regions represent zones of high and low transmission, respectively. In
absence of magnetic field (Fig.
8.4
a) three peaks of conductance are clearly visible
as depicted by the bright curves. The central peak has a marked linear dependence
on
ε
4
. Figure
8.4
shows the effect on the transmission
T
12
of varying
ε
2
while the external ones are weakly dependent on it, as seen from the slope of
the curves. Two antiresonances are also visible, namely, a faint vertical dark line at
E
V
. Figure
8.4
b-
d shows the effect of switching on and increasing the magnetic flux. As discussed
for the connection (1,3), the antiresonances are cancelled out. In particular, it should
be noted that the antiresonance at
E
=
0 independent on
ε
2
, and a vertical dark thicker line at
E
=
ε
4
−
=
0 turned into a peak of transmission. Also
the second antiresonance at
E
Φ
0
)
and the dark sharp straight line turns into a diffuse dark region of low transmission
(Fig.
8.4
b and c), then increasing at a larger magnetic flux (
=
ε
4
−
V
becomes weakened at low flux (
Φ
=
0
.
1
Φ
=
0
.
5
Φ
0
).
8.3.1
Tuning Fano Profiles with a Magnetic Field
Figure
8.5
shows in solid lines the transmission through an asymmetric ring where
the upper arm has hoppings much smaller than those of the lower arm (
t
12
=
t
23
t
34
=
t
41
in Fig.
8.1
b). The dotted blue and dashed red lines are the transmissions of
the upper and lower arms separately, calculated as three-site chains with a central
site having energy
ε
2
and
ε
4
, respectively, and lateral sites having on-site energies
ε
=
0.
Figure
8.5
a-c represents in solid line the transmission function of the four-QD
ring without coupling between the arms (
V
=
0) for
Φ
=
0,
Φ
0
/
4, and
Φ
0
/
2,
respectively. The dotted and dashed lines show
T
for the upper and lower arm,
respectively, as sketched in the inset schemes. They are the same for panels (a)-(c)
(
E
)
