Biomedical Engineering Reference
In-Depth Information
exp
i
L
M
h
π
=
−
σ
,
(7.56)
x
where
σ
x
is the first Pauli matrix. The relation is in fact an equation for
L
M
and the
solution reads:
11
11
h
2
L
M
=
.
(7.57)
Eventually we obtain
L
α
by rotation of
L
M
in the molecular plane, namely:
1
h
2
e
i
2
||
φ
χ
i
h
φ
χ
L
M
e
e
−
L
z
h
φ
χ
L
z
L
α
=
=
,
(7.58)
e
−
i
2
||
φ
χ
1
=
where
L
z
z
is the generator of the rotations along the principal rotational axis
for the 7-particle ground states of the benzene molecule.
2
h
σ
7.6.2
All-Electrical Spin Control
We come now to the phenomenology of the spin-dependent transport through a
benzene and a triple dot I-SET. The different panels of Figs.
7.14
and
7.15
show the
current through the benzene and triple dot I-SET, respectively, as a function of bias
and gate voltage. As in all SETs at low bias the so-called Coulomb diamonds, where
transport is energetically forbidden, occur. Within the diamonds the particle number
is fixed as indicated in the figures.
The characteristic fingerprint of I-SETs is represented by the
interference block-
ade
where the current decreases for increasing bias generating negative differential
conductance (NDC) and eventually vanishes (see green lines in the panels B and
CofFigs.
7.14
and
7.15
). Panels B in the same figures indicate moreover that,
for a given gate voltage and in absence of polarization in the leads, the current
is blocked only at one specific bias voltage. For parallel polarized leads, however,
at a given gate voltage, the current is blocked at
two specific
bias voltages, one
for each spin configuration (panels C). As demonstrated below, the blocking of
the minority electrons occurs for the smaller bias voltages. As such full control
of the spin configuration in the I-SET can be electrically achieved. The interference
blockade and its spin selectivity is also demonstrated in panels A and B of Fig.
7.16
.
Along the dotted (dashed) line a majority (minority) spin electron is trapped into the
molecule. The molecular spin state can thus be manipulated simply by adjusting the
bias across the I-SET. In the following we discuss the physics of the spin-selective
interference blocking and present the necessary ingredients for its occurrence.
From the analysis of the negative differential conductance and current blocking
associated with interference presented in Sects.
7.4
and
7.5
one would conclude
that the interference blocking is a threshold effect appearing when the bias opens
transitions to a specific set of degenerate states and surviving until transitions to
