Table Of ContentManipulation of a single magnetic atom using polarized single electron transport in a
double quantum dot
Wenxi Lai and Wen Yang
Beijing Computational Science Research Center, Beijing 100094, China
Weconsidertheoreticallyamagneticimpurityspindrivenbypolarizedelectronstunnelingthrough
a double quantum dot system. Spin blockade effect and spin conservation in the system make the
5 magneticimpuritysufficientlyinteractwitheachtransferringelectron. Asaresults,asinglecollected
1 electron carries information about spin change of the magnetic impurity. The scheme may develop
0 all electrical manipulation of magnetic atoms by means of single electrons, which is significant for
2 theimplementation of scalable logical gates in information processing systems.
p
PACSnumbers: 76.30.Da,72.25.Pn,42.50.Dv,73.23.Hk
e
S
2 I. Introduction electrons are very weak. In contrast, the QD spin filter
2 inducesspindependenttunneling,whichmakessureeach
Magnetic atoms are critical spin systems which have
electron would be completely flipped by the magnetic
] potential applications in data storage and quantum in-
l atom before it passes through the filter. Therefore, each
l formationprocessing.1–3 In particular,using electrons to
a collected electron can be correlated with the change of
h manipulatemagneticatomsisanaturalsteptowardsthe spin state in the magnetic atom. There are several facts
- implementationofscalablememoryunits forfuture inte-
thatareverybeneficialforthe realizationofour scheme.
s
grated circuits. In dilute II-VI semiconductor quantum
e First,coupledtwoQDscanbefabricated,dopingasingle
m dots (QD), interaction between a manganese (Mn) atom magnetic ion in one of them.10 Second, spin life time of
anda carriercanbe effectively describedwith the sp−d
. an electronin II-VI semiconductor quantum dots can be
t exchange interaction.4–6 Based on the impurity-carrier
a longenough. Electronrelaxationtimeinasimilarsystem
m coupling, electrical control of the single magnetic atom was reported to be 50 ns in a previous work.11 In a QD
is feasible by injecting different charges in the magnetic
- imbedded a magnetic atom, a longer life time of around
d atom doped QD.6 1 µs was predicted.12 Third, Magnetic atom such as Mn
n As shown both in experiment2 and theory,7 electrons
impurity with relaxation time from 1 µs to 0.4 ms was
o candirectlytunnelthroughaMnatombytakingitsspin observedinexperiment.10,13Thetimeislongerthandriv-
c
states. The ground state and excited states of the Mn
[ ingtimeofthemagneticatom,whichwillbeshownlater
atom can be identified with the current, since they sup-
in the present work. Forth, the technique for real time
5 port different conductance. However, in the tunneling
detection of single electron tunneling has been well de-
v from a STM tip to Cu2N surface through an individual veloped recently.14–17 Fifth, polarizedelectron currentis
9
Mn atom, the Mn spin spontaneous relaxation is more
8 availablefromseveralsources,forinstance,QDspinsplit-
1 frequent than excitation by tunneling electrons.2 Com- ter under the premise of local magnetic field,18,19 ferro-
7 pared with the case in high dimensional bulk material, magnetic leads,20,21 graphene or carbon atom wires.22,23
0 the life time of the Mn spin is much longer in a QD.8 Recently, nuclear spins of donor atoms such as phospho-
1. Therefore, coherent electrical manipulation of the Mn rus and 29Si have been coherently controlled and read
spin is possible in low dimensional nanostructure. In a
0 using bounded electrons in these donors and the spin to
5 QD doped with a single Mn atom, charge and conduc- charge conversion. Electromagnetic field was applied to
1 tance of the single electron tunneling can be related to initialize these nuclear spins.24–26 Comparing with these
: the spin state of the Mn atom.9 Whereas, it is hard to
v early works, the main advance in our present protocol is
exactlyconnectaquantumstateofthemagneticatomto
i that the magnetic atom would be manipulated all elec-
X a single electron in the above QD system, which should
trically. In other words, a magnetic atom can be con-
r be a problem required to be solved for future quantum
trolledonlyusingasingleelectrontransistorwithoutthe
a
information processing.
applicationofanyelectromagneticfield. Eventheinitial-
In this paper, we propose a scheme for all electrical
ization of the impurity spin can be progressed using the
manipulation of the magnetic impurity spin, scaling the
single electron tunneling in principle.
numberofdrivingelectronsdowntoone. Tothisend,we
consider two inter-coupled semiconductor QDs, in which II. MODEL AND THEORY
one QD contains a single magnetic impurity and couples
to a spin polarized electron source. The other QD is lo- Our model is illustrated in Fig. 1. The two QDs are
calized in a homogeneous magnetic field and connected denoted by dot 1 and dot 2 with ground orbital levels
to a normal conductance, playing a role of a spin filter. ε1 andε2, respectively. Bothelectronpolarizationinthe
In previous study,2,6,7,9 electrons transport through the left lead and the external magnetic field B~ that applied
magnetic atom without any qualification to their spins, onthedot2areassumedtobeparalleltotheQDgrowth
as a result, interaction between the magnetic atom and directionz. Electronsinjectedfromthe leftleadintothe
2
ofthe magneticatom. Inthis case,due tospinconserva-
tion, if spin of the magnetic atom is changed from hMˆ i
z
to hMˆ i+n ~, then the number of electrons detected in
z ↓
therightleadshouldequalton andtheirspinsaredown
↓
polarized.
Themagneticatomcanalsobedrivenreversely,which
is presented in Figs. 1(e)-(h). Since the magnetic field is
turnedtobeinzdirectionhere,thespinfilteronlyallows
spin up electrons tunnel through the dot 2. The input
electrons are required to be in spin down state and out-
put electrons are expected to be in spin up state. Each
transported electron contributes to the spin of the mag-
netic atom with the value −~. It yields the impurity
magnetization orient in the reversal way, which means
spin of the magnetic atom would be changed from hMˆ i
FIG.1: (Coloronline)Schematicillustrationoftheprinciple z
to hMˆ i−n ~ with collection of n spin up electrons.
in our model. In (a) - (d) the applied magnetic field is in z ↑ ↑
downdirectionanduppolarizedelectronsareinjectedintothe Togiveaquantitativedescriptiontothemodel,weuse
doubleQD.In(e)-(h),theexternalmagneticfield ischanged the following Hamiltonian5,27
to beupdirection and down polarized electrons are injected.
Hˆ =Hˆ +Hˆ +Hˆ +Hˆ +Hˆ , (1)
d1 d2 d12 lead tun
dot 1 are coupled to the magnetic atom by the ferro-
magneticHeisenbergtypespinexchangeinteraction. We where the Hamiltonian for dot 1 is
describe spin of the magnetic atom with mean value of
the spin along z direction hMˆzi, where Mˆ is the mag- Hˆd1 =ε1nˆ1+U1nˆ1↑nˆ1↓−jeM~ˆ ·S~ˆ1, (2)
netic atom spin operator and the bracket indicates aver-
ageoverquantumstates of the system. Bias voltageand and the Hamiltonian for dot 2 is
the magnetic field is tuned that just the lowest levels of
the two QDs fall within the bias window µL >ε1, ε↓ (or Hˆd2 =ε2nˆ2+U2nˆ2↑nˆ2↓+g∗µBB~ ·S~ˆ2. (3)
ε )> µ , where the indexes ↓, ↑ indicate electron states
↑ R
with spin up and down, respectively. In addition, the The inter-dot tunneling Hamiltonian reads
intra-dot Coulomb blockade energies U , U correspond-
1 2
ing to the dot 1 and the dot 2 are assumed to be much Hˆd12 =~Ω(nˆ12+nˆ†12)+Unˆ1nˆ2. (4)
larger than other energy scales, which yields only single
electron occupation is involved in either of the QDs. It Here, nˆ = nˆ +nˆ , nˆ = cˆ† cˆ , nˆ = cˆ† cˆ , nˆ =
i i↑ i↓ i↑ i↑ i↑ i↓ i↓ i↓ 12
remarkably simplifies our model and calculation. nˆ +nˆ , nˆ = cˆ† cˆ , nˆ = cˆ† cˆ . cˆ (cˆ ) is
12↑ 12↓ 12↑ 1↑ 2↑ 12↓ 1↓ 2↓ i↑ i↓
In Figs. 1(a)-(d), the magnetic field in this config-
the annihilation operator of spin up (down) electron in
uration is applied along the −z direction with value
dot i (i = 1,2). S and S represent electron spin in
B~ = (0,0,−B). It means, in dot 2, the ground state the dot 1 and the d1ot 2, re2spectively. U is the inter-
level is ε↓ = ε2−g∗µBB/2 and the first excited level is dot Coulomb potential. The exchange coupling strength
ε↑ = ε2 +g∗µBB/2, where g∗ is the Lande g-factor of between the electron in dot 1 and the magnetic atom
electron in the QD, µB is the Bohr magneton. The sys- is given by je = J|ψ0(rM)|2 with exchange integral J
temrequiresspinupelectronsthatinjectedfromthe left and the electron ground state wave function ψ at the
0
lead into the dot 1. We take energy levels that satisfy magnetic impurity position r .
M
ε↑ > µL and ε↑ −ε1 ≫ ~Ω, where ~Ω is inter-dot cou- Theleftandrightelectronicleadsaredescribedbythe
plingstrength. Thisenergystructureformsaspincondi- free electron baths with the Hamiltonian
tionedrepulsivepotentialwhichensuresthatthespinup
electron is forbidden to enter the dot 2 until its spin is Hˆ = ǫ cˆ† cˆ . (5)
lead αk αkσ αkσ
flippedtobeupsidedownduetoitscouplingtothemag- X
k,σ;α=L,R
netic atom. As soon as the electron spin changes to be
down,it wouldbe allowedto passthroughthe dot 2 and The dot 1 is coupled to the left leads and the dot 2 is
collected in the right lead. At the same time, the spin coupled to the right lead by
of magnetic atom would change from hMˆ i to hMˆ i+~.
z z
If a spin down electron is injected from the left lead, it Hˆ = V cˆ† cˆ + V cˆ† cˆ +H.c., (6)
tun L Lkσ 1σ R Rkσ 2σ
directly transports through the double dots without any X X
k,σ k,σ
change in the spin of the magnetic atom. However, if
the left lead is a fully up polarized electron source, each with the left and right tunneling amplitudes V and V ,
L R
passed electron would be connected to the spin change respectively.
3
Time evolutionof electrontransportthrough the dou-
ble QD system is described by a quantum master equa-
tion which is derived based on the Hamiltonian (1) and ∂ 1
ρˆ = [Hˆ +Hˆ +Hˆ ,ρˆ]+Lˆ ρˆ+Lˆ ρˆ. (7)
theLiouville-vonNeumannequationintheBorn-Markov ∂t i~ d1 d2 d12 L R
approximation. Since the transport in our system is a
process of single electron sequential tunneling through
QDs and works in the weak tunneling regime, the mas- The Liouville super-operators, Lˆ and Lˆ , acting on
L R
ter equation is an effective approach to describe our the density matrix ρˆ describe tunneling on the left and
model.28–30 Equation of motion is given in terms of the rightsideofthedoubledots,respectively. Theyarewrit-
reduced density matrix ρˆof the system, ten as
1
Lˆ ρˆ= Γσ(fˆ (cˆ† ρˆcˆ −cˆ cˆ† ρˆ)+(1−fˆ )(cˆ ρˆcˆ† −c† c ρˆ)+H.c.), (8)
L 2 L L,σ 1σ 1σ 1σ 1σ L,σ 1σ 1σ 1σ 1σ
X
σ
and
1
Lˆ ρˆ= Γσ(fˆ (cˆ† ρˆcˆ −cˆ cˆ† ρˆ)+(1−fˆ )(cˆ ρˆcˆ† −cˆ† cˆ ρˆ)+H.c.), (9)
R 2 R R,σ 2σ 2σ 2σ 2σ R,σ 2σ 2σ 2σ 2σ
X
σ
where the Fermi distribution function in the left lead is
fˆL,σ = (exp[(ε1 +U1nˆ1σ¯ −µL)/kBT]+1)−1 and in the
right lead is fˆR,σ, = (exp[(εσ + U2nˆ2σ¯ − µR)/kBT] + (a)2.5 (b)2.5 1.0
1b)y−t1h,edeopcecnudpiantgionon, nthiσ¯e=chacr†1gσ¯icn1gσ¯,enofereglyecUtrioncownditihtiosnpeind 12..50 12..50 000...468 PPPP---1531/2///222
σ¯. Here, the spin index σ¯ is defined that if σ =↑ (↓), 1.0 1.0 0.2 P3/2
P5/2
tghiveennσ¯by=↓Γ↑α(↑)=. TΓαh(e1t+unPnαel)i/n2garantdesΓa↓αre=spΓinα(d1e−pePnαd)e/n2t 00..05 1.0 00..05 0.00 10 20t / 30 40 50
Hwietrhe,tIhασe icsutrhreenctuprroelanrtizwaittihonpuPrαe=spi(nIα↑σ−onIα↓t)h/e(Isα↑id+e oIfα↓)α. --10..05 00..68 PPP---531///222 --10..05
(aαs Γ=αL=,R2π).~|Ttαh|e2Nbaαr(eǫ)tuwnitnheltinhge draetnessitcyaonfbsteaetexsprNesαs(eǫd) --21..05 000...024 PPP135///222 --21..05
0 10 20 30 40 50 60 70
of electrons at energy ǫ. -2.5 t / -2.5
0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 70 80
t / t /
III. MANIPULATION OF A MAGNETIC
ATOM WITH SPIN M=5/2
FIG.2: (Color online) Timeevolutionofthesingleimpurity
The Hilbert space of the double QD system is gen- magnetizationasafunctionoftime. (a)Theappliedexternal
erated by the basic vectors |ii1|mi1|ji2, where |ii1 and magnetic field is B~ = (0,0,−B). (b) The applied external
|ji2 represent electronic state in dot 1 and dot 2, re- field is B~ = (0,0,B). The Parameters are µL = 75Γ, µR =
spectively. Here, i,j = 0 denote the empty state, −75Γ, ε1 = 0, ε2 = 62.5Γ, g∗µBB = 135Γ, je = 3Γ, kBT =
i,j =↓,↑ indicate occupation states of single electron 12.5Γ, ΓL =ΓR =Γ,PR =0, ~Ω=5Γ, U =10Γ.
with spin down and spin up, respectively. |mi is eigen-
1
state of the impurity spin operator Mˆ with eigenvalues
z
m=−M,−m+1,...,M. |ii |mi |ji . Whentheimpurityspinchangesto|5/2i,it
1 1 2
First, we consider a typical single magnetic atom becomes parallel to the injected electron spin and there
which displays a spin of M = 5/2 in the QD, such will be no spin flip in the later time. Then the electron
as Fe or Mn. These magnetic atoms have six quan- tunnelingshouldbeswitchedoffandthespindownpolar-
tized spin states |mi, with corresponding eigenvalues izedcurrentdecreasesto be zeroas plotted inFig.3 (b).
m = −5/2,−3/2,−1/2,1/2,3/2,5/2.4 In Fig.2(a), initial The figures also show that orientation time of the Mn
state |ψM(0)i of the magnetic atom is set to be any of spinis a few tens of ns when one takes a tunneling char-
thesixquantizedstates. Inallcasesthemagneticatomis acteristictimeofΓ−1 ∼1ns. Itiscomparabletothetime
driventothefinalstate|5/2i. InaveragevalueoftheMn scaleofapreviouslyreportedopticalcontrol.13Sinceeach
spinhM i=Tr[Mˆ ρˆ]traceistakenoverthebasicvectors electron contributes to the spin change of the magnetic
z z
4
(a) (b) (a) (b)
5 0.25 I 1.0 1.0
I P-1/2 n
0.20
4 0.8 P1/2 0.8 n
0.12
n3 0.15 0.6 0.6 0.10 I/e
0.08 I/e
2 0.10 0.4 0.4 00..0046
1 0.05 0.2 0.02
0.2 0.00
0 10 20 30 40 50 60
0 0.00 t /
0.0
0.0
0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60
t / t / 0 10 20 30 40 50 60 0 10 20 30 40 50 60
t / t /
FIG.3: (Coloronline)(a)Thenumberofspindownelectrons FIG.4: (Coloronline)(a)Probabilitiesofthemagneticatom
collected intherightsideof thesystem. (b)Currentforspin in its spin states |−1/2i and |1/2i. The magnetic atom is
upanddownelectronsasafunctionoftime. Theparameters initially in the state |−1/2i. (b) The number of collected
are thesame as that in Fig. 2 electrons with spin up and spin down corresponding to the
case (a). The parameters are µL =70Γ, µR =−70Γ, ε1 =0,
ε2=57.5Γ, g∗µBB=125Γ,je =2Γ,kBT =10Γ,ΓL =ΓR =
atom with momentum ~, the magnetic atom initialized Γ, PL=1, PR =0, ~Ω=3Γ, U =10Γ.
in the states |ψ (0)i=|−5/2i, |−3/2i, |−1/2i, |1/2i,
M
|3/2i, |5/2ileads to finite electronscollectedin the right
lead with definite numbers hn i = 5,4,3,2,1,0, respec- itis a verygoodsystemfor date storage,where only sin-
↓
tively. ItcanbeseeninFig.3(a)forcorrespondinginitial gleelectronofcurrentandthetwostatesofthemagnetic
spin states. The collected electron number is calculated atom is correlated.
using the formula Thesmallfluctuationinthecurrentisoccurreddueto
the back action from the system. Since charge transfer
through the double dots requires electron spin flip, the
1 ∞ amplitude of current is proportional to rate of electron
hn i= I (t)dt, (10)
σ e Z σ spin change. The rate of spin change is determined by
0
thestrengthofspincouplingbetweenthemagneticatom
where Iσ(t) is current on the right side of dot 2. The andelectrons. Therefore,we candeduce thatthe oscilla-
current is derived from the charge fluctuating in the two tions observed in Fig.4 is contributed from the coherent
dots d(hn1i + hn2i)/dt = σ=↑,↓(ILσ − IRσ)/e with the coupling between the magnetic atom and an individual
replacement I (t) = Iσ. TPhe reversal time evolution of electron. Indeed, character of the small oscillation can
σ R
the magnetization is shown in Fig. 2 (b). be tuned by changing the spin coupling strength je. Ac-
tually, the back action effect can also be seen in the for-
IV. MANIPULATION OF A MAGNETIC mer situation for M = 5/2. However, considering six
ATOM WITH SPIN M=1/2 spin states of the magnetic atom are involved in the ex-
change interactionand the largercouplings j and Ω are
e
Now, we consider a magnetic ion with spin M = 1/2, taken, the small oscillation during the evolution of the
suchasCu2+. Thiskindofimpurityhasparticularmean- spin states and current is too smooth to be observed.
ingthatitsmaximummagnetizationdifferenceis~,from The above results are described in a relatively ideal
−~/2 to ~/2 or by inverse. In this case, only a sin- situation. At the end of this section, let us talk about
gle electron is involved in the tunneling. As shown in somemorepracticalcases. Fig.5(a)revealsthatincrease
Fig.4(a), when we set initial state of the magnetic atom oftheinter-dottunneling strengthexcitesaspinupelec-
to be |−1/2i, it is transformed into |1/2i. At the same tronfromthe dot1 intothe excitedlevel ε↑ ofthe dot 2.
time,the uppolarizedcurrentischangedtobedownpo- It leads to the unexpected spin up electron leakage from
larizedcurrentafterinteractingwiththe magneticatom. thedoubledotsystemintotherightlead. Torestrainthe
The down polarized current is expected to be collected electron leakage through the excited level ε↑, we suggest
in the right side, which is characterized by a singe elec- thatonecantakearelativelysmallinter-dotcoupling~Ω
tron with spin down as shown in Fig.4(b). To show the whichisrequiredtobemuchsmallerthanthedecoupling
collected charge is really limited, average current as a ε↑−ε1.
function of time is plotted in the inset of Fig.4(b). The Thesystemisalsosensitivetopolarizationoftheright
downpolarizedcurrentsharplyincreasesandthendisap- lead. In Fig. 5(b), it is illustrated that when the polar-
pears slowly with a small fluctuation. The up polarized ization is not pure, the number of electrons collected in
currentisnegligibleweak. Fromthepointofapplication, the right lead is larger than the expected value. Since
5
the right lead. Therefore, some local magnetic fields are
5 (a) = = necessary in the nanostructure. To this end, a proper
4 = = quantity of external magnetic field can be exerted on
= =
n 3 the left lead for the generationof spin polarizedelectron
2
1 source. As the QD is a zero dimensional nanoscale sys-
0 tem,oursuggestionisusingamagneticgrain,suchasCo
0 50 100 15 0 200 250 300
5 (b) PL=1.0 PL=0.8 PL=0.6 grain,33,34 to create magnetic field on the right QD. To
4 PL=0.4 PL=0.2 PL=0.0 exploreitseffectivenessweestimatethefieldstrengthofa
n
3 typicalCograinwhichconsistsofhundredsofatoms. We
2
assume the Co grain is a uniformly magnetized sphere.
1
Then, the field of the grain can be obtain from the for-
0
0 50 100 150 200 250 300 mulaB = 2µ M,µ ispermeabilityoffreespaceandMis
1.0 (c) 3 0 0
0.8 magnetizationofthe grain.35 We takethataveragemag-
n0.6
0.4 kBT=10 kBT=20 neticmomentperCoatomis1.5µB. Inrealmaterialsthe
0.2 kBT=30 kBT=40 localmagneticmomentisalwayslargerthanthisvalue.33
0.0
-0.2 kBT=50 kBT=60 We take diameter of a Co atom is about 0.15nm. Then,
0 10 20 30 40 50 60 70 80 90 magnetic field of the Co grainis estimatedto be not less
t /
than B =6.6T. By increasingsize of the Co grain,more
FIG. 5: (Color on line) (a) Number of spin up electrons col- strong field can be obtained. In a CdTe semiconductor
lected intherightsideofthedoubleQDwith differentinter- QD, the corresponding Zeeman splitting of an electron
dot coupling strength, kBT = 10Γ, PL = 1. (b) Number of reaches |g∗µBB|=0.64meV, where the g-factor is given
spin down electrons for different spin polarization in the left by g∗ = −1.67 in this material.36 To guarantee the left
lead, kBT = 10Γ, ~Ω = 3Γ. (c) Number of collected spin QDandtherightleadisnoteffectivelyinfluencedbythe
down electrons at different temperature, ~Ω = 3Γ, PL = 1. surrounding magnetic field, magnetic shielding may be
The rest parameters are thesame as that in Fig. 4. applied here to protect the spreading field. One kind of
the magneticshielding materialsis superconductingchip
which expels magnetic field via the Meissner effect. An-
non-purely polarized currentcontains electrons with dif-
otherkindshieldingmaterialiscertainhighpermeability
ferentspinorientations,therebysomeelectronscouldnot
metalalloywhich,incontrastthesuperconductor,draws
be blocked by dot 2.
the field into themselves. Taking an example with the
The negative number of electrons in Fig. 5(c) implies
high permeability shielding with permeability µ, field in
that electrons in the right lead have certain probability the shielded volume is 9b3µ0 times smaller than the
toflowintotheQDsatthebeginningoftunnelingdueto 2(b3−a3)µ
the thermal excitation, since the QDs is empty initially. outside field.37 For the convenience of quantitative esti-
Afterthesystemreachessteadystate,thehigherthetem- mation, the shielding material here is assumed to be a
perature,thelargerelectrondistributionwouldbe inthe spherical shell with inner radius a and outer radius b.
QDs. The electron staying in the QDs comes from the When the permeability µ is large enough, good shield-
leads. Therefore,netnumberofelectronscollectedinthe ing of the field in the shielded area can be achieved. In
right lead decreases when temperature increases. practice,astheQDcouplestoanelectronicreservoirand
anotherdot,theshieldingmaterialmaybenotabsolutely
V. DISCUSSIONS closed with a lower efficiency.
In the Hamiltonian of our model, spin exchange inter-
In experiment, to realize electron transport through a action between the two QDs is not considered. In fact,
magnetic atom doped II-VI semiconductor QD is still a when each quantum dot contains one electron, the ex-
challenge. There are some well developed experimental change interaction does not play important role for the
backgrounds, for instance, the spin dependent electron whole system. The reason is that the electron in dot 2
transportthrougha quantumwellthatcontainingdilute has definite spin direction. It has to gain large energy
magnetic material,31 and resonant tunneling through a to change spin. However, it is hard for the electron in
CdSe self-assembledQD with Mn ions.32 In addition, an dot 1 to provide the large energy. Besides, the system is
attempt to orienta Mn spinusing the chargethattrans- robustagainstthe double occupancyindot1. Since cur-
ported from a neighboring QD has been successfully re- rentinjectedfromtheleftleadisassumedtobepurespin
alized.10 polarized, two electrons with different spin states in dot
Tocreatealocalmagneticfieldisakeytechnicalprob- 1 does not break the spin conservation as soon as dot 2
lemfortheexperimentalimplementationofourproposal. guaranteesto output electronswith pure spin. Whereas,
The left lead is a polarized electron source, so an exter- double occupancy in dot 2 induces spin leakage and, as
nal magnetic field may be required on it. In addition, a result, the correlation between electrons and the mag-
the right QD needs a magnetic field to create a Zeeman netic atom becomes weak. Even though, considering the
splitting for an electron. At the same time, these mag- highCoulombblockadeeffectineitheroftheQDs,double
neticfieldsmusthavenegligibleaffecttotheleftQDand occupancy in any dot is negligible small in our model.
6
Asaninformationprocessingsystem,itscharacteristic VI. CONCLUSIONS
times areverysignificant. Therearetwokinds ofcritical
times,oneofthemismanipulationtimeτ ofthesystem, Inthesystem,changeofmagneticimpurityspiniscor-
s
another is lowest life-time bound τ of these information related to spin state and number of single electrons that
i
carriers, such as the magnetic atom and electrons. The tunneling throughthe twoQDs. Basedonthis principle,
manipulation time of the system indicates a time range we give the following predictions: (i) Our model works
duringwhichanelectronisemittedfromtheleftleadand as an electron source in which number of emitted elec-
then collectedin the rightlead,at the same time control trons canbe determined beforehandby setting an initial
of the magnetic atom is accomplished. It is clear that stateofthemagneticatomorusingamagneticatomwith
spin life times of the informationcarriersare required to certain spin M. In particular, a single electron emitter
be, at least, longer than the manipulation time of the is available using a magnetic atom with spin 1/2. (ii)
system, i.e. τ > τ . As mentioned in the introduction, The number of polarized transferring electrons can be
i s
a single Mn spin relaxation time from 1 µs to 0.4 ms recorded in the spin state of the magnetic atoms. (iii)
in CdTe QD10,13, and electron life time from 50 ns to 1 The change in spin state of the magnetic atom should
µs in II-VI semiconductor systems are reported. Even be detected by counting the number of electrons that
in a QD including certain charges, the Mn atom relaxes emitted from the double QDs. (iv) Spin state of the
in a time scale of about 100 ns.38 As shown in section magnetic impurity can be controlled, in principle, by in-
III and IV, manipulation time of the system is about jecting suitable number of spin polarized electrons, and
50 ns for a characteristic time of the electron tunneling, this controlling is reversal.
Γ−1 ∼ 1ns. Furthermore, there is still a space for re-
ducing the manipulation time of the system. Actually,
properly increasing the dot-reservoir coupling (electron Acknowledgments
tunneling rate) or inter-dot coupling would improve the
rate of controlprocess. In this case, a more lower bound We appreciate the valuable discussion with Shuhui
of the spin life time is allowed. Zhang about the numerical calculation.
1 L. Thomas, F. Lionti, R. Ballou, D. Gatteschi, R. Sessoli, 16 S. Gustavsson, R. Leturcq, M. Studer, I. Shorubalko, T.
and B. Barbara, Nature383, 145 (1996). Ihn, K. Ensslin, D.C. Driscoll, and A.C. Gossard, Surface
2 S. Loth, K. von Bergmann, M. Ternes, A. F. Otte, C. P. Science Reports 64, 191 (2009).
Lutzand A.J. Heinrich,Nature Phys.6, 340 (2010). 17 J. P. Pekola, O.-P. Saira, V. F. Maisi, A. Kemppinen, M.
3 R. Hanson and D. D. Awschalom, Nature 453, 1043 M¨ott¨onen, Y. A. Pashkin, D. V. Averin, Rev.Mod. Phys.
(2008). 85, 1421 (2013).
4 L. Besombes, Y. L´eger, L. Maingault, D. Ferrand, H.Ma- 18 P.Recher,E.V.Sukhorukov,andD.Loss,Phys.Rev.Lett.
riette, J. Cibert, Phys.Rev.Lett. 93, 207403 (2004). 85, 1962 (2000).
5 D. E. Reiter, T. Kuhn, and V. M. Axt, Phys. Rev. B 85, 19 R.Hanson,L.M.K.Vandersypen,L.H.W.vanBeveren,
045308 (2012). J.M.Elzerman,I.T.Vink,andL.P.Kouwenhoven,Phys.
6 Y. L´eger, L. Besombes, J. Ferna´ndez-Rossier, L. Main- Rev.B 70, 241304 (2004).
gault,andH.Mariette,Phys.Rev.Lett.97,107401(2006). 20 P. Hyde, L. Bai, D. M. J. Kumar, B. W. Southern, C.-M.
7 F.Delgado,J.J.Palacios,andJ.Ferna´ndez-Rossier,Phys. Hu,S.Y.Huang,B.F.Miao,andC.L.Chien,Phys.Rev.
Rev.Lett. 104, 026601 (2010). B 89, 180404 (2014).
8 M. Scheibner, T. A. Kennedy, L. Worschech, A. Forchel, 21 A. Dirnaichner, M. Grifoni, A. Pru¨fling, D. Steininger, A.
G. Bacher, T. Slobodskyy, G. Schmidt, and L. W. K.Hu¨ttel,andC.Strunk,Phys.Rev.B91,195402(2015).
Molenkamp, Phys. Rev.B 73, 081308 (2006). 22 Z. Y. Li, W. Sheng, Z. Y.Ning, Z. H. Zhang, Z. Q. Yang,
9 J.Ferna´ndez-RossierandR.Aguado,Phys.Rev.Lett.98, and H. Guo, Phys. Rev.B 80, 115429 (2009).
106805 (2007). 23 V. M. Karpan, G. Giovannetti, P. A. Khomyakov,M. Ta-
10 M. Goryca, T. Kazimierczuk, M. Nawrocki, A. Golnik, J. lanana, A. A. Starikov, M. Zwierzycki, J. van den Brink,
A.Gaj,P.Kossacki,P.Wojnar,G.Karczewski,Phys.Rev. G. Brocks, and P. J. Kelly, Phys. Rev. Lett. 99, 176602
Lett. 103, 087401 (2009). (2007).
11 D.H.Feng,I.A.Akimov,andF.Henneberger,Phys.Rev. 24 J. J. Pla, K Y. Tan, J. P. Dehollain, W. H. Lim, J. J. L.
Lett. 99, 036604(2007). Morton, D. N. Jamieson, A. S. Dzurak and A. Morello,
12 M. D. Petrovi´c and N. Vukmirovi´c, Phys. Rev. B 85, Nature489, 541 (2012).
195311(2012). 25 J. J. Pla, K. Y. Tan, J. P. Dehollain, W. H. Lim, J. J. L.
13 C. Le Gall, L. Besombes, H.Boukari, R. Kolodka, J. Cib- Morton,F.A.Zwanenburg,D.N.Jamieson,A.S.Dzurak,
ert,and H.Mariette, Phys.Rev.Lett.102,127402(2009). A. Morello, Nature496, 334 (2013).
14 J. Bylander, T. Duty, and P. Delsing, Nature 434, 361 26 J.J.Pla,F.A.Mohiyaddin,K.Y.Tan,J.P.Dehollain,R.
(2005). Rahman, G. Klimeck, D. N. Jamieson, A. S. Dzurak, and
15 W. Lu, Z. Ji, L. Pfeiffer, K. W. West, and A.J. Rimberg, A. Morello, Phys.Rev.Lett. 113, 246801 (2014).
Nature 423, 422 (2003). 27 D. Becker, S. Weiss, M. Thorwart, and D. Pfannkuche,
7
New J. Phys. 14, 073049 (2012). (2000).
28 S. A. Gurvitz and Y. S. Prager, Phys. Rev. B 53, 15932 34 L. V.Dzemiantsova, M. Hortamani, C. Hanneken,A.Ku-
(1996). betzka, K. von Bergmann, and R. Wiesendanger, Phys.
29 T. Novotny´, A. Donarini, and A.-P. Jauho, Phys. Rev. Rev.B 86, 094427 (2012).
Lett. 90, 256801 (2003). 35 D. J. Griffiths, Introduction to electrodynamics, 3rd ed,
30 S. Braig and P. W. Brouwer, Phys. Rev. B 71, 195324 Prentice Hall (1999).
(2005). 36 F. Qu and P. Hawrylak, Phys. Rev. Lett. 95, 217206
31 A. Slobodskyy, C. Gould, T. Slobodskyy, C. R. Becker, (2005).
G. Schmidt, and L.W. Molenkamp, Phys. Rev. Lett. 90, 37 J.D.Jackson,Classicalelectrodynamics,3rded,JohnWi-
246601 (2003). ley and Sons (1999).
32 C. Gould, A. Slobodskyy, D. Supp, T. Slobodskyy, P. 38 C. Le Gall, R. S. Kolodka, C. L. Cao, H. Boukari, H. Ma-
Grabs, P. Hawrylak, F. Qu, G. Schmidt, and L.W. riette,J. Ferna´ndez-Rossier,andL.Besombes, Phys.Rev.
Molenkamp, Phys. Rev.Lett. 97, 017202 (2006). B 81, 245315 (2010).
33 R.N.NogueiraandH.M.Petrilli,Phys.Rev.B63,012405
