Giant super-poissonian shot noise in spin-polarized SET structures
We study transport of spin-polarized electrons through a magnetic single-electron transistor (SET) in the presence of an external magnetic field. Assuming the SET to have a nanometer-sized central island with a single electron level, we find that the zero-frequency shot noise diverges as the on-do...
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| Zitieren: | Giant super-poissonian shot noise in spin-polarized SET structures / L.Y. Gorelik, S.I. Kulinich, R.I. Shekhter, M. Jonson, V.M. Vinokur // Физика низких температур. — 2007. — Т. 33, № 9. — С. 997–1001. — Бібліогр.: 12 назв. — англ. |
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irk-123456789-1209312017-06-14T03:07:09Z Giant super-poissonian shot noise in spin-polarized SET structures Gorelik, L.Y. Kulinich, S.I. Shekhter, R.I. Jonson, M. Vinokur, V.M. International Conference "Statistical Physics 2006. Condensed Matter: Theory and Application" We study transport of spin-polarized electrons through a magnetic single-electron transistor (SET) in the presence of an external magnetic field. Assuming the SET to have a nanometer-sized central island with a single electron level, we find that the zero-frequency shot noise diverges as the on-dot spin-flip rate goes to zero, provided the source and drain leads are completely polarized in the same direction. We present an analytical expression for the low-frequency super-poissonian shot noise that allows one to specify the necessary conditions for the experimental observation of the phenomenon. 2007 Article Giant super-poissonian shot noise in spin-polarized SET structures / L.Y. Gorelik, S.I. Kulinich, R.I. Shekhter, M. Jonson, V.M. Vinokur // Физика низких температур. — 2007. — Т. 33, № 9. — С. 997–1001. — Бібліогр.: 12 назв. — англ. 0132-6414 PACS: 73.23.–b, 73.40.Gk http://dspace.nbuv.gov.ua/handle/123456789/120931 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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International Conference "Statistical Physics 2006. Condensed Matter: Theory and Application" International Conference "Statistical Physics 2006. Condensed Matter: Theory and Application" |
| spellingShingle |
International Conference "Statistical Physics 2006. Condensed Matter: Theory and Application" International Conference "Statistical Physics 2006. Condensed Matter: Theory and Application" Gorelik, L.Y. Kulinich, S.I. Shekhter, R.I. Jonson, M. Vinokur, V.M. Giant super-poissonian shot noise in spin-polarized SET structures Физика низких температур |
| description |
We study transport of spin-polarized electrons through a magnetic single-electron transistor (SET) in the
presence of an external magnetic field. Assuming the SET to have a nanometer-sized central island with a
single electron level, we find that the zero-frequency shot noise diverges as the on-dot spin-flip rate goes to
zero, provided the source and drain leads are completely polarized in the same direction. We present an analytical
expression for the low-frequency super-poissonian shot noise that allows one to specify the necessary
conditions for the experimental observation of the phenomenon. |
| format |
Article |
| author |
Gorelik, L.Y. Kulinich, S.I. Shekhter, R.I. Jonson, M. Vinokur, V.M. |
| author_facet |
Gorelik, L.Y. Kulinich, S.I. Shekhter, R.I. Jonson, M. Vinokur, V.M. |
| author_sort |
Gorelik, L.Y. |
| title |
Giant super-poissonian shot noise in spin-polarized SET structures |
| title_short |
Giant super-poissonian shot noise in spin-polarized SET structures |
| title_full |
Giant super-poissonian shot noise in spin-polarized SET structures |
| title_fullStr |
Giant super-poissonian shot noise in spin-polarized SET structures |
| title_full_unstemmed |
Giant super-poissonian shot noise in spin-polarized SET structures |
| title_sort |
giant super-poissonian shot noise in spin-polarized set structures |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2007 |
| topic_facet |
International Conference "Statistical Physics 2006. Condensed Matter: Theory and Application" |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/120931 |
| citation_txt |
Giant super-poissonian shot noise in spin-polarized SET structures / L.Y. Gorelik, S.I. Kulinich, R.I. Shekhter, M. Jonson, V.M. Vinokur // Физика низких температур. — 2007. — Т. 33, № 9. — С. 997–1001. — Бібліогр.: 12 назв. — англ. |
| series |
Физика низких температур |
| work_keys_str_mv |
AT gorelikly giantsuperpoissonianshotnoiseinspinpolarizedsetstructures AT kulinichsi giantsuperpoissonianshotnoiseinspinpolarizedsetstructures AT shekhterri giantsuperpoissonianshotnoiseinspinpolarizedsetstructures AT jonsonm giantsuperpoissonianshotnoiseinspinpolarizedsetstructures AT vinokurvm giantsuperpoissonianshotnoiseinspinpolarizedsetstructures |
| first_indexed |
2025-07-08T18:53:13Z |
| last_indexed |
2025-07-08T18:53:13Z |
| _version_ |
1837105986347728896 |
| fulltext |
Fizika Nizkikh Temperatur, 2007, v. 33, No. 9, p. 997–1001
Giant super-poissonian shot noise in spin-polarized
SET structures
L.Y. Gorelik
1
, S.I. Kulinich
2,3
, R.I. Shekhter
2
, M. Jonson
2
, and V.M. Vinokur
4
1
Department of Applied Physics, Chalmers University of Technology, SE-412 96 G�teborg, Sweden
E-mail: gorelik@fy.chalmers.se
2
Department of Physics, G�teborg University, SE-412 96 G�teborg, Sweden
3
B.I. Verkin Institute for Low Temperature Physics and Engineering, 47 Lenin Ave., 61103 Kharkov, Ukraine
4
Materials Science Division, Argonne National Laboratory, 9700 South Cass Av, Argonne, Illinois 60439, USA
Received January 15, 2007
We study transport of spin-polarized electrons through a magnetic single-electron transistor (SET) in the
presence of an external magnetic field. Assuming the SET to have a nanometer-sized central island with a
single electron level, we find that the zero-frequency shot noise diverges as the on-dot spin-flip rate goes to
zero, provided the source and drain leads are completely polarized in the same direction. We present an ana-
lytical expression for the low-frequency super-poissonian shot noise that allows one to specify the necessary
conditions for the experimental observation of the phenomenon.
PACS: 73.23.–b Electronic transport in mesoscopic systems;
73.40.Gk Tunneling (for tunneling in quantum Hall effects).
Keywords: single-electron transistor, spin-flip time, shot-noise, Coulumb blockade, spin-polarized electrons.
Confinement of electrons to a quantum of dot nanometer
size crucially reduces the spin relaxation frequency [1] and
allows for the implementation of various schemes where
quantum information is carried by the spin of electrons [2–5].
Experimental evidence that the spin-flip time in quantum dots
can reach the millisecond range has recently been obtained*
[6,8]. Such long spin relaxation times is obviously an impor-
tant prerequisite for spintronics-based quantum information
processing. At the same time, the advantage coming from the
extremely weak spin relaxation might obviously be an obsta-
cle for its experimental study, demanding measurements of
extremely high accuracy and sensitivity [6]. This is why any
phenomenon that is exceedingly sensitive exclusively to spin
relaxation should be of considerable practical importance.
The Zeeman splitting of energy levels is the phenomenon tra-
ditionally invoked to discriminate between contributions
from different electronic spin-states to observable physical
properties. Today, a number of different methods are used to
create nonequilibrium spin populations and to study how they
relax towards equilibrium. Transport measurements, which
usually provide an excellent tool for such studies, are limited
when it comes to observing very weak spin relaxation by the
necessity to measure the extremely small electrical currents
that result from the electrons being trapped for long times on
the dot [6]. A large sensitivity to slow spin relaxation rates
therefore requires a careful choice of observable. Recently,
numerical simulations have revealed that shot noise in sin-
gle-electron transistor (SET) structures, which significantly
increases with the spin polarization of the tunneling electrons
[7,9], could be such an observable. In this paper we present
an analytical study of this phenomenon where we show that
spin-dependent tunneling in combination with the Coulomb
© L.Y. Gorelik, S.I. Kulinich, R.I. Shekhter, M. Jonson, and V.M. Vinokur, 2007
* The effect of intradot spin-flip scattering on shot noise was recently studied in Ref. 7. An increased shot-noise was reported
for tunneling of polarized electrons. However, this effect was analyzed only numerically, which does not allow the results to
be used as a tool for spectroscopy.
blockade phenomenon in SETs results in shot noise charac-
terized by a giant super-poissonian Fano factor at low fre-
quencies. Consequently low frequency noise measurements
provides a tool for detecting slow spin flip rates in a quantum
dot.
Below we will study the transport of spin polarized
electrons through a quantum using dot the SET geometry
represented in Fig. 1. Two magnetic leads, biased by a
voltage V serve as source and drain for the spin polarized
electrons, while two electronic states with different spin
orientation are available on the dot. An external magnetic
field oriented perpendicular to the magnetization of the
leads (which we assume are parallel) induces coherent
spin-flip processes on the dot.
To study the electronic transport through this system
we will use the Hamiltonian ��, where
� � � � � ,� � � � �� � � �l d T env (1)
and
� ,, ,
, ,
, ,
†
, ,�l a a� ��� � �
� � �
� � � � � �
� † † † † , '
, , '
'�d i i
i
a a
U
a a a a H a a� � �� �
� � �
�
� � �
� �
� �
�
2
,
�T T a a� �� �
� � �
� � � �
, ,
, ,
†( )H.c. . (2)
Here ��l describes noninteracting electrons in the leads
and a a� � � � � �, ,
†
, ,( ) is the creation (annihilation) operator
for electrons in lead � � ( , )L R with energy �� � �, , and spin
projection � �
( , ). The electron density of states
�
� in
each lead is assumed to be independent of energy but
strongly dependent on spin direction. The electrons in
each lead are held at a constant electrochemical potential
�L R FE eV/, � � 2, where e is the charge of an electron,
V � 0 is the bias voltage, and EF is the Fermi energy of the
ferromagnetic metal. The Hamiltonian ��d describes elec-
tronic states in the dot and their coupling to the external
magnetic field H � ( , , )H Hx z0 ; � is the Bohr magneton
and intra-dot electron correlations are characterized by
the Coulomb energy U ; the operator a a� �
† ( ) creates (de-
stroys) an electron with spin � and �� �
i
, ' are Pauli matrix
elements (i x y z� , , ). The third term in (1) represents
spin-conserving tunneling of electrons between dot and
leads while the last term describes the interaction between
dot-electrons and the magnetic environment.
In this paper we will study the case when the bias volt-
age V is much smaller than both the spacing between spa-
tially quantized levels on the dot and the Coulomb energy
U , but much larger than the Zeeman energy � ��H z (see
Fig. 1,a). This means that only one electron may be accu-
mulated on the dot. In addition, we will focus on the situa-
tion when the electrons on the leads are almost com-
pletely polarized in the same direction (for definiteness in
the «up» direction): �
� � �� �
/ � � �� � �
�
�� �/ 1 (
� �2 1 2�
�
�
�� T ).
The two phenomena of electron spin-polarization in the
leads and Coulomb blockade of double electron occupancy
on the dot determine the current that flows through the
system. To understand qualitatively the peculiarities of
electronic transport in this situation we consider the limi-
ting case when the electrons are completely polarized
(� �L R� � 0). In this case a transition of the spin of the dot
electron from «up» to «down» traps the electron on the dot,
and prevents a current to flow through the system (since
the Coulomb blockade prevents another, spin-up, electron
to enter the dot). This is why the temporal variation of the
current strictly follows the switching of electronic spin, al-
lowing for such events to be counted. A schematic picture
of the current fluctuations �I I I( ) ( )t t� – , where I is the av-
erage value of the current, is shown in Fig. 1,b. It is impor-
tant that the current-current correlation function S( )0 �
� � �� ��dt t� �� �I I( ) (0) , where �� ��� denotes a statistical aver-
age, serves as a measure of the time �
during which the
electron is trapped on the dot in the spin-down state — the
state that prevents a current to flow through the system.
Two possible channels for the escape of the electron from
this state should be identified: a) a stochastic spin-flip pro-
cess caused by the interaction with the environment and
characterized by the spin relaxation time � �rel � �
1
1 and b) a
magnetic-field induced coherent transition to the spin-up
998 Fizika Nizkikh Temperatur, 2007, v. 33, No. 9
L.Y. Gorelik, S.I. Kulinich, R.I. Shekhter, M. Jonson, and V.M. Vinokur
+
Hx
a
�L �R
�L �R
I(t)
t
b
I
��
0
�L
�R
Fig. 1. a — Sketch of the nano-magnetic SET device discussed
in the text: a quantum dot, modelled as a single spin-degenerate
electron level, is coupled to two leads with parallel magnetiza-
tion. The tunneling rates �
L R( )
( )
describe the coupling between
and dot electrodes, while the external magnetic field Hx induces
flips between the spin-up and the spin-down state on the dot. The
difference � �L R eV� � in electrochemical potential of the leads
is due to a bias voltage V . b — Schematic picture of the current
fluctuations in the case when the leads are completely polarized
in the same direction (I is the average current).
s t a t e . T h e l a t t e r i s c h a r a c t e r i z e d b y t h e r a t e
�H xH / /� ( ) ( )2 2� � �, w h e r e � ( ) ( )� �� �2 /
� � � �Im ( )2 1� � �i R is the density of spin-up states on the
dot. Therefore � �
� � �( )1
1
H and S( )0 may be estimated as
S H( ) ( )0 1
1� � ��
.
If H x = 0 we have
H � 0 and one can see from the above
expression that the zero-frequency shot noise is a diver-
gent function of the spin relaxation rate reaching giant
values for slow enough relaxation. Below we will show
that the average current, on the other hand, does not at all
depend on the external magnetic field and the internal
spin relaxation rate if � �
� � 0. Hence a simultaneous
measurement of both the current and the noise for oppo-
site polarities of the bias voltage allows one to deduce the
value of the spin-flip rate.
In order to quantitatively investigate the current and
shot noise in the SET structure described above one can
use the quantum master equation for the reduced density
matrix � ( ) �( )� �r lt t� Tr that describes the state of the dot ( ��
is the total density matrix and Trl denotes a trace over all
electronic states in the leads).
The operator � ( )�r t acts on the Fock space of the quantum
dot, which in the Coulomb blockade regime is spanned by
the three basis vectors | ,0� | | , | |
† † � � �
� � �
a a0 0 . In this ba-
sis � ( )�r t is a 3 3� matrix. The diagonal element � �0 0| � ( )|�r t
represents the probability for the dot to be unoccupied, the
singly occupied dot is described by the 2 2� matrix block
� ( � ) | � | ', '� � � � �� �� � � �r r , while nondiagonal elements
� �� �| � |r 0 equal zero.
The time evolution of the probability � and the density
matrix �� is determined by a system of equations that de-
scribe the coupled processes of stochastic charge transfer
and coherent spin dynamics [10] (below we will take
e � �� 1),
�
�
� � �
�
� } � �}
�
� �
t
L RTr{ Tr{� � ,
�
�
� �
�
��
!"
� � �
� �
� , � � � , � {�
� �
� � � � �# ��
t
i Hz
x x L R
�
� $�
2
1
2
� }, (3)
where � ( ) � ( )� � � � �� � � � � �� � � �
I/ /z2 2. The linear
operator �� �{�} describes the spin relaxation in a singly
occupied dot caused by interaction with the environment.
In the general case it can be written in the form
�� � � � � � % � � � � �{�} � [ � � ) �] � � )�� � � �
&
�1 2z z i
i z
iTr ( Tr Tr ( . (4)
Here �1 and � 2 are, respectively, the spin relaxation rate
and the spin dephasing rate, while the coefficient % �
� tanh( ) (' '�/2 is the inverse temperature) characterizes
the difference in the populations of spin-up and spin-
down states if the system is in equilibrium with the envi-
ronment. Here we will consider the case when the thermal
energy is much higher than the Zeeman splitting (but
lower than the bias voltage) and take % � 0. The spin relax-
ation rate �1 defines the rate of direct spin-flip transitions
induced by the environment and as a result has a
first-hand influence on the low-frequency shot noise. In
contrast, the dephasing rate � 2, which controls the decay
of nondiagonal elements of the reduced density matrix,
affects spin-flip processes only indirectly. As we will see
below, it only renormalizes the effect of the external mag-
netic field.
Within our approach the average current, I I� �� �� ��
� i H N R[ � , � ], where �N R is the electron number operator in
the right lead, can be calculated from the formula [10]
I R� Tr { � � },� �0 (5)
where ( , � )� �0 0 represent the stationary solution of
Eq. (3). In our further considerations we will use the for-
malism developed in Ref. 11. Following this approach it
is convenient to rewrite Eqs. (5) in the form
� �
�
� �
|
|
(
(
t
L , (6)
w h e r e t h e c o l u m n v e c t o r |(� i s g i v e n b y |(� �
� � �
( , , , , ) |� � � � � (T T , while the matrix L is
determined by Eqs. (3). In this notation the formula for
the average current, Eq. (5), takes the form
I T� � �( (0 0| |J , (7)
were |( 0� obeys equation
L| .( 0 0� � . (8)
By this means the elements of the steady-state density ma-
trix, the vector | ( , , , , )( 0 1 1 1 0 0T T� � , satisfy the equation
L
T T|( 0 0� � , and J is a «current» matrix that has only two
nonzero elements � , �J JR R12 13� �
� � . We solved Eq. (8)
and found the following expression for the average cur-
rent when �� �� 1:
I I
h
h
OR
R L R
�
� �
� � � �
�
)
*
+
+
,
-
.
.0
2
1
2
1
� �
� / � � �
��
~
( ) ~
( ) . (9)
Here ~ ,� � /1 1 0� � / IR R� � and
I h
H
H
H
/
L R
L R
x x
R
0
2
0
2 2
22 2
�
�
�
)
*
++
,
-
.. �
�
� �
� � � �
,
( )
(
�
� 2 2
2� )
.
Analyzing the above expression one finds that in the ab-
sence of spin-flip processes ( , )H x � �0 01� the current
vanishes if �R 0 0 . Indeed, under such conditions the
electron can not leave the spin-down state and the current
is blocked forever. Then, from (9) it follows that with
identical leads ( )� � �L R� � the current is equal to
I O0 � ( )� and does not depend (to leading order in � on the
Giant super-poissonian shot noise in spin-polarized SET structures
Fizika Nizkikh Temperatur, 2007, v. 33, No. 9 999
magnetic field, relaxation rates or Zeeman splitting. Be-
low we will study the shot noise for this very case.
The noise power spectrum is defined as twice the Fou-
rier transform of the current-current correlation function
(see Ref. 12 for a review):
S dt i t( )1 1� �2 e [ �( ) � ]�� �� �I t I I(0) 2 . (10)
Within our formalism the correlation function �� ��� �I I(t) (0)
can be expressed in the form [11]
�� �� � � � � ��( ) �( ) ( ) ( ) | |I t I t t tT0 0 0I ( )� 2 ( (JP J
� � � �2 ( (( ) | (– ) |t tT
0 0JP J , (11)
where P L( )t t� exp is an evolution operator. The first
term on the right hand side of Eq. (11) is the self-correla-
tion term.
Using Eqs. (10) and (11) one can rewrite the formula
for the shot noise in terms of the eigenvalues 3 i of the
matrices L L, T and their associated eigenvectors | ,3 i �
|3 i
T �. Taking into account that the eigenvalue, 3 0 say, that
corresponds to the steady-state solution of Eq. (8), is zero
(accordingly | | , | | )3 ( 3 (0 0 0 0� � � � � �T T , we get
S I Ti
ii
i( ) ( , )1
3
1 3
3 3� �
�&
�2
4
2 2
0
0 ,
T i
i i
i i
( , )
| | | |
|
3 3
3 3 3 3
3 30
0 0�
� � � �
� �
J J
.
(12)
The eigenvalues 3 i are given by zeros of the characteris-
tic polynomial P P( ) | | ( )3 3 3 3� �Det | L – I | 0 . We have
found that in the general case (with arbitrary values of the
parameters � �, ,i xH and � ) the polynomial P0( )3 has the
form
P R0 2
2 22( ) [( ) ]3 3 �� � � � �� �
� � � � � �[ ( ) ]3 3 �2
12 � �L R D
� � � � �4 2 22
1( ) ( ) ( )� 3 � 3H x R L R� � � , (13)
where
D L R R� � � � ( ) ( )2 1 1� � �� � �� and �� � �� � �( )1 2/ .
From the above expression it follows that one of the
roots of the characteristic polynomial 31 vanishes like
3 � �1
2
1�� � � A hR� ( ~ ) (14)
if � �, 1 and H x go to zero;
A /L R L R� � � 4 ( ) ( ) ( , )2 12� � � �
is a dimensionless coefficient of order one.
As a consequence, the correlation function S( )0 may
according to Eq. (12) diverge and exhibit a giant super-
poissonian behavior for small values of these parameters.
By calculating the «transition» coefficient T ( , )3 30 1 , in the
case of strongly polarized leads ( )� �� 1 and small spin-flip
frequency
�sf R Rh� � �� � �2
1 (15)
we get (to leading order) the following expression for the
low-frequency Fano factor F S / I( ) ( )1 1� 2 *
F A
A
R
sf R
sf R
( )
( )
1 /
�
1
�
� 2 2 2
2 2 2
�
�
�
�
� �
. (16)
Equation (16), together with (9) and (15), is the main
result of our considerations. First, from these equations it
follows that the spin dephasing rate � 2, in contrast to the
spin relaxation rate �1, only influences the contribution of
the transverse magnetic field to the spin-flip process, and
that its effect, according to Eq. (9), is strongly restricted
by the condition 4 1� 5 �R . Then from (16) one can see
that the zero-frequency shot noise diverges as 1/ sf
dem-
onstrating a high sensitivity to the intensity of spin-flip
processes, if the leads are completely polarized ( )� � 0 . If
the polarization of the leads is not complete, the spin-flip
processes significantly affect the shot noise only if the
spin-flip frequency
sf is not much smaller than the «mi-
nority» tunneling rate �R
:
� �R x RH /H � �( )0
2
1� � .
This brings an important restriction on the use of shot
noise measurements as a tool for probing spin-flip pro-
cesses. Indeed, from the above inequality it follows that
in order to increase the sensitivity of shot noise to spin
flips (in particular to the spin relaxation rate �1) one has to
diminish either � (by increasing the polarization in the
leads) or the «majority» tunneling rate �R
. However, the
latter alternative is not preferable, since it decreases the
value of the current.
If there is no transverse magnetic field the spin-flip
frequency coincides with the spin-relaxation rate �1. For
this case we have obtained the following expression for
F( )1 :
F
D
( )1
� 1 �
1 � 1
� �
�
� �
1 1
2
2
4
3
2 2
, (17)
1000 Fizika Nizkikh Temperatur, 2007, v. 33, No. 9
L.Y. Gorelik, S.I. Kulinich, R.I. Shekhter, M. Jonson, and V.M. Vinokur
* Equation (9) shows that the average current does not depend (in leading order) on the spin-flip rate
sf if the leads are strongly
polarized. Hence the low-frequency Fano factor completely characterizes the behavior of the low-frequency shot noise.
where
�1 2� �
( )� � � �L R L R ,
� � � �2 1 18 2� � � � �
� � � � � �L L R R R R D( ) ( ) ,
� �3 1
24 2� � � �( )� �L R D ,
which is valid for any values of 1 �
�, � , and �1. One can
easily check that this expression is in agreement with Eq.
(16). From Eq. (17), as well from Eq. (16), it follows that
the zero-frequency Fano factor diverges as 1 1/ � when the
relaxation rate goes to zero if �, H x � 0, i.e., if the leads
are completely polarized and the transverse magnetic
field is zero. On the other hand, if the leads are fully po-
larized and spin-flip processes are absent ( )�1 0� , the
Fano factor F( )0 should coincide with the one that has
been calculated for spinless electrons [11]. The correct
value of the shot noise at zero frequency may be obtained
from Eq. (17) if one takes the appropriate limits in the
correct order, so that
F F( , ) lim lim ( , )1 � 1 �
1 �
� � �
0 0
0 01
0 0
1
1
.
To understand this ordering one has to take into account
that an infinite time is needed to measure zero-frequency
noise, while in a real experimental situation the frequency
under consideration can not be smaller than the inverse
observation time.
We have also calculated the zero-frequency shot noise
in the limit of a strong transverse magnetic field,
(H x
2 1�� . It turns out that only one term in the sum (12)
gives a nonvanishing contribution to the shot-noise in this
limit; the corresponding root of the characteristic poly-
nomial (13) has the asymptotic value
3 h � � � �( ) ( )2 1 2� �L R xO / H( .
Calculating the «transition» coefficient T h( , )3 30 we ob-
tained the following expression for the zero-frequency
Fano factor:
F L R
L R
( )
( )
0 1
4
2 2
� �
�
� �
� �
. (18)
From this expression one can see that in the limit of a
strong magnetic field the zero-frequency shot noise, like
the average current, does not depend on the spin-flip rate,
in particular not the rate due to the magnetic field.
In conclusion, we have studied transport of spin-polar-
ized electrons through a magnetic SET in the presence of
an external magnetic field. Assuming the SET to have a
nanometer-sized central island with a single-electron
level we found that the zero-frequency shot noise di-
verges as the rate for spin-flips on the goes dot to zero if
leads are completely polarized in the same direction. We
presented an analytical expression for the low-frequency
super-poissonian shot noise and discussed the conditions
required for the experimental observation of such an en-
hancement of the low-frequency noise.
This work was supported in part by the European
Commission through project FP6-003673 CANEL of the
IST Priority. The views expressed in this publication are
those of the authors and do not necessarily reflect the offi-
cial European Commission’s view on the subject. Finan-
cial support from the Swedish SSF, the Swedish VR, and
from the U.S. DOE Office of Science through contract
No. W-31-109-ENG-38 is also gratefully acknowledged.
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