Biomedical Engineering Reference
In-Depth Information
Fig. 7.17
Blocking
condition. Renormalization
frequencies
ω
L
σ
of a benzene
I-SET as function of the bias
and for different lead
polarizations. The current
blocking condition
0
is fulfilled at different biases
for the different spin states.
From [
21
]
ω
σ
=
L
In Fig.
7.17
the black curve depicts
ω
L
σ
as a function of the bias in absence of
polarization: the frequencies corresponding to the two spin species coincide and
thus vanish at the same bias. The same condition,
ω
L
σ
=
0
,
(7.59)
also determines the bias at which the current is completely blocked. In fact, at
that bias the effective Hamiltonian contains only the projection of the angular
momentum in the direction of the right lead (the drain) and the density matrix
corresponding to the full occupation of the 7-particle
R
-antisymmetric state (
ρ
=
|
ψ
R
,
a
ψ
R
,
a
|
) is the stationary solution of Eq. (
7.5
). As we leave the blocking bias
the effective Hamiltonian contains also the projection of the angular momentum in
the direction of the left lead and the
R
-antisymmetric state is no longer an eigenstate
of
H
eff
. The corresponding density matrix is not a stationary solution of (
7.5
)and
current flows through the system. The
L
↔
R
symmetry of the system implies, for
negative biases, the blocking condition
0.
All-electric-spin control is achieved, in an I-SET, only in presence of ferromag-
netic leads and with exchange interaction on the system as we prove by analyzing the
splitting of the renormalization frequencies
ω
R
σ
=
ω
χσ
.(seeEq.(
7.54
).) By introducing
0
α
2
, for simplicity equal in both leads, and using the
fact that benzene is paramagnetic we get:
0
α
↑
+
Γ
Γ
the average bare rate
Γ
=
1
2
¯
π
{
E
}
d
M
↑
|
0
α
ω
α
↑
−
ω
α
↓
=
Γ
P
α
7
g
↑|
d
M
↑
|
8
{
E
}
8
{
E
}|
7
g
m
↑
p
α
(
E
−
E
7
g
)
d
M
↑
|
+
7
g
↑|
6
{
E
}
6
{
E
}|
d
M
↑
|
7
g
m
↑
p
α
(
E
7
g
−
E
)
d
M
↓
|
−
↑|
d
M
↓
|
{
}
{
}|
↑
p
α
(
−
E
7
g
)
7
g
8
E
8
E
7
g
m
E
d
M
↓
|
−
7
g
↑|
6
{
E
}
6
{
E
}|
d
M
↓
|
7
g
m
↑
p
α
(
E
7
g
−
E
)
,
(7.60)
