Spin manipulation in a double quantum-dot–quantum-wire coupled system
S. Sasakia兲
NTT Basic Research Laboratories, NTT Corporation, Atsugi, Kanagawa 243-0198, JapanS. Kang
Institute of Physics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japanand CREST-JST, Honmachi, Kawaguchi, Saitama 331-0012, JapanK. Kitagawa
Faculty of Science, Tokyo University of Science, Kagurazaka, Tokyo 162-8601, Japanand CREST-JST, Honmachi, Kawaguchi, Saitama 331-0012, JapanM. Yamaguchi
NTT Basic Research Laboratories, NTT Corporation, Atsugi, Kanagawa 243-0198, Japanand CREST-JST, Honmachi, Kawaguchi, Saitama 331-0012, Japan

S. Miyashita and T. Maruyama
NTT Advanced Technology Corporation, Atsugi, Kanagawa 243-0198, Japan

H. Tamura and T. Akazaki
NTT Basic Research Laboratories, NTT Corporation, Atsugi, Kanagawa 243-0198, Japanand CREST-JST, Honmachi, Kawaguchi, Saitama 331-0012, Japan

Y. Hirayama
NTT Basic Research Laboratories, NTT Corporation, Atsugi, Kanagawa 243-0198, Japanand SORST-JST, Honmachi, Kawaguchi, Saitama 331-0012, Japan

H. Takayanagi
NTT Basic Research Laboratories, NTT Corporation, Atsugi, Kanagawa 243-0198, Japan,
Faculty of Science, Tokyo University of Science, Kagurazaka, Tokyo 162-8601, Japan,
and CREST-JST, Honmachi, Kawaguchi, Saitama 331-0012, Japan

共Received 17 January 2006; accepted 16 May 2006; published 25 July 2006兲
We have studied spin correlation in a double quantum-dot–quantum-wire coupled device revealed in
low-temperature transport characteristics. We demonstrate nonlocal control of the Kondo effect in
one dot by manipulating the spin states of the other. The modulation of the local density of statesin the wire region due to the Fano-Kondo antiresonance and the Ruderman-Kittel-Kasuya-Yoshidaexchange interaction are the two possible mechanisms underlying the observed features. When the
dot states are indirectly probed in the side-coupled geometry, double suppression of the wire
conductance is observed due to the Fano-Kondo antiresonance involving both dots. © 2006
American Vacuum Society. 关DOI: 10.1116/1.2218866兴

I. INTRODUCTION
Recent advances in the fabrication of semiconductor
nanostructures have opened up possibilities to investigate
various quantum correlation effects. A quantum dot 共QD兲 isan important building block for constructing functional devices since its electronic states are tunable by external parameters such as gate voltages and magnetic field. The QD
behaves as a single magnetic impurity with spin S = 1 / 2
when it holds an odd number N of electrons. This magnetic
aspect is clearly revealed in the Kondo effect, where the spinin the QD antiferromagnetically couples with another spin in
the lead electrodes at low temperatures.1–6 The Kondo effectmanifests itself as an increase of the conductance at Coulomb blockade regions, and as a zero-bias peak in the differential conductance versus source-drain bias characteristics,
which results from the coherent higher order tunneling. Thisis the case for the conventional geometry where the sourcea兲Electronic mail: satoshi@nttbrl.jp

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J. Vac. Sci. Technol. B 24„4…, Jul/Aug 2006

and drain electrodes are attached to both ends of the dot; i.e.,the only current path is through the “magnetic impurity.”
When a QD is attached to the side of another quantum
wire 共QW兲, on the other hand, the Fano resonance is observed in the conductance of the QW due to an interference
between a localized state of the QD and a continuum of theQW.7–9 Moreover, in the odd electron number regions between two Fano resonances, the electrons in the QW experience enhanced scattering by the localized spin in the QD, or
the Kondo “cloud” suppresses the QW conductance, which isreferred to as the Fano-Kondo antiresonance.10–14 By adding
a second QD to this dot-wire coupled system, one can study
the indirect correlation between two localized spins mediatedby conduction electrons in the interceding QW, which
is known as Ruderman-Kittle-Kasuya-Yoshida 共RKKY兲
interaction.15–20
In this article, we present a transport measurement on two
QDs coupled to the opposing sides of a quasi-onedimensional QW.16 This system offers the minimum interdot
distance realizable in lateral mesoscopic devices, and is ad-

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Sasaki et al.: Spin manipulation in a double quantum-dot–quantum-wire coupled system

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III. RESULTS AND DISCUSSION

FIG. 1. 共a兲 Current through the right QD, IR in response to excitation sourcedrain voltage Vac = 3 ␮V 共Vdc = 0 V兲 as a function of VpR. A solid triangle
denotes a Kondo valley with an odd NR. The left QD is not formed yet. The
inset shows a scanning electron micrograph of the double QD-QW coupleddevice together with a schematic of the measurement setup. Dotted lines
indicate the positions of the QDs and QW. 共b兲 Gray-scale plot of the conductance through the right QD as a function of Vdc and VpR. Black corresponds to 15 ␮S and white to 65 ␮S. Dotted lines denote edges of the
Coulomb diamonds and a solid triangle denotes a Kondo ridge found in the
odd NR Coulomb blockade region. 共c兲 Gray-scale plot of the conductancethrough the right QD as a function of magnetic field and VpR 共VpR = 0 V兲.
Black corresponds to 0 S and white to 70 ␮S. A solid triangle denotes the
Kondo valley.

vantageous for studying the RKKY interaction, which decays
on the length scale of the Fermi wavelength. We demonstratenonlocal control of the Kondo effect in one dot by tuning thespin states of the other, which suggests the RKKY interaction
as an underlying mechanism. We also discuss the FanoKondo antiresonance effect in the side-coupled geometry
where the QD states are indirectly probed via the QW
conductance.
II. EXPERIMENTThe inset to Fig. 1共a兲 shows the double QD-QW coupleddevice fabricated by depositing Ti/ Au Schottky gates on thesurface of a GaAs/ AlxGa1−xAs heterostructure. The twodimensional electron gas 共2DEG兲 is located 90 nm below thesurface. Two QDs and a QW between them are formed
共shown by dotted lines兲 by biasing the eight gates. To avoid
the formation of another QD in the central QW region, VsR
and VsL are biased more negatively than VmR and VmL. Transport measurement is performed with a standard lock-in technique at temperature of about 100 mK in a dilution refrigerator. The source-drain bias Vsd = Vdc + Vac, where Vdc is a dc
offset, and ac excitation 共about 13 Hz兲 Vac = 3 ␮V. Magnetic
field perpendicular to the 2DEG plane is applied mainly to
reduce the tunnel coupling without electrostatic energy shift.
JVST B - Microelectronics and Nanometer Structures

We begin by confirming the conventional Kondo effect ina single QD. We form only the right QD with VsR= −1.35 V, VdR = −0.39 V, and VmR = −0.45 V, such that thetunnel coupling between the QD and the source lead and thatbetween the QD and the drain lead are almost equal. Figure
1共a兲 shows the current through the right QD, IR, as a functionof VpR 共Coulomb oscillation characteristics兲 when the left
QD is not formed yet. Pairs of Coulomb oscillation peaks areobserved suggesting that the electron number in the right
QD, NR, is odd in the Coulomb blockade regions between
paired peaks 共at VpR = −0.81, −0.75, and −0.69 V兲. The dotlead tunnel coupling increases as VpR increases because of
the capacitive coupling between different gates. Then, theKondo temperature increases, leading to the increased conductance in the odd NR Coulomb blockade valleys for morepositive VpR. For instance, the conductance at the valley
marked with a solid triangle is significantly enhanced due tothe Kondo effect. Figure 1共b兲 shows Coulomb diamond characteristics where the conductance is plotted as a function of
the source-drain voltage, Vdc, and the plunger gate voltage
VpR. The conductance is enhanced along Vdc = 0 only within
the odd NR diamond forming a ridge structure 共solid triangle兲, which corroborates the Kondo effect.
Figure 1共c兲 shows magnetic field dependence of the Coulomb oscillation characteristics. The Kondo effect is suppressed owing to the Zeeman splitting and the reduced
dot-lead tunnel coupling as magnetic field increases. Consequently, the conductance at the Kondo valley marked with asolid triangle gradually decreases. At the same time, the alternating high and low conductance regions are observed atmore positive VpR forming a pattern like a chessboard.21 As
magnetic field increases, rearrangement of electrons occurs
between the outer orbital 共the ground Landau level兲 and theinner orbital 共the higher Landau level兲 within the fixed total
NR region. Since the outer orbital is coupled with the leads
more strongly than the inner orbital, the Kondo effect occurs
when the electron number in the outer orbital, rather than the
total electron number, is odd, resulting in the observed chessboard pattern.
Next, we form another QD 共the left QD兲 by biasing theother gates. The exit tunnel barrier of the left QD is completely pinched off such that the only current path is throughthe right QD. This is done to avoid a spurious mirror effect,
which occurs in the presence of multiple current paths.22
Figure 2共a兲 shows the gray-scale plot of the conductancethrough the right QD as a function of VpL and VpR. The gate
voltage that controls the coupling of the left QD with the restof the system, VsL = −1.04 V, is adjusted in the weakcoupling regime. The two dotted lines designate Coulomb
oscillation peaks for the right QD, and the region between
them is the same Kondo valley as the one marked with atriangle in Fig. 1. The position of the Coulomb oscillation
peaks are shifted from that in Fig. 1 due to slightly different
gate voltage conditions. A series of almost vertical ridges areobserved as VpL is swept. When the conductance through the
QW is independently measured as a function of VpL with the2026

Sasaki et al.: Spin manipulation in a double quantum-dot–quantum-wire coupled system

FIG. 2. 共a兲 Gray-scale plot of the conductance through the right QD as afunction of VpL and VpR in the weak-coupling regime with VsL = −1.04 V.
Black corresponds to 10 ␮S and white to 42 ␮S. Dotted lines denote Coulomb oscillation peaks for the right QD and the region between the dottedlines correspond to odd NR. Arrows on the upper horizontal axis mark two
sets of spin-pair resonances. 共b兲 Conductance profiles taken along the midKondo valley of the right QD with the coupling gate voltage VsL changed
between −0.9 and −1.04 V in 20 mV steps. VpR is simultaneously swept totrace the midvalley. For clarity, curves are offset vertically. The scales on theaxes apply to the lowermost VsL = −0.9 V trace. The two dash-dotted lines
denote spin-pair peaks. Odd NL regions are marked with solid triangles, andone even NL region on the VsL = −0.9 V trace is marked with an open triangle. A gray solid line connects the same NL regions in VsL = −0.9 V andVsL = −1.04 V traces.

same gate voltage conditions, the Fano resonances associatedwith the left QD are observed as slightly asymmetric peaks.23
Since these Fano resonances are almost in phase with theabove ridges found in the right QD conductance, we assign
the ridges to the resonances of the left QD states with thechemical potential of the lead. The ridges are not observed
when VsL is smaller than about −1.2 V because the left QD is
decoupled from the rest of the system. Please note that thefour ridges marked with arrows form two sets of pairs, suggesting that up-spin and down-spin electrons consecutively
occupy the same orbital state within the pair. Based on thisspin-pair behavior, we deduce that narrow gaps within thepair correspond to the Coulomb blockade regions where thenumber of electrons in the left QD, NL, is odd. Although the
Kondo valley conductance is somewhat reduced from theoriginal value at VpL = 0, the Kondo effect still remains between the ridges. For the present weak-coupling condition,
there is no noticeable difference in the conductance between
even and odd NL regions. Although no more ridges are observed at VpL ⬍ −0.5 V, this does not guarantee that NL = 0
there. In the case of the charge detection scheme, where theelectrostatic energy shift caused by a change in N is measured by a nearby point contact, zero electron regime is commonly reached.24–26 In our present measurement, on the
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other hand, the resonance signal disappears if the tunnel coupling of the left QD is lost due to more negative VpL evenwhen NL ⫽ 0.
Next, we increase the coupling of the left QD by increasing VsL. Figure 2共b兲 shows the evolution of the conductanceprofiles taken along the mid-Kondo valley of the right QD
when VsL is changed from −1.04 V 共weak-coupling regime兲
to −0.9 V 共strong-coupling regime兲. The resonances associated with the left QD states appear as peaks in the weakcoupling regime. The spin-pair peaks and the odd NL regions
are marked with dash-dotted lines and solid triangles, respectively. We estimated the shift in VpL of the resonance peaksin the weak-coupling regime in response to a slight shift in
VsL that does not affect the Fano line shape, and found thatthe electrostatic energy shift caused by VsL is almost identical to that caused by VpL in our device. Based on this, wefound that the resonances appearing as conductance maxima
in the weak-coupling regime change into minima in thestrong-coupling regime, just as in the previous report by Satoet al.14 The same odd NL regions in the uppermost trace andlowermost one are connected with a gray solid line.
Figure 3共a兲 shows a plot similar to Fig. 2共a兲, but with
VsL = −0.9 V, in the strong-coupling regime. Here, in contrast
to Fig. 2共a兲, the resonances of the left QD states produce
conductance minima. The intensity of the several conductance maxima corresponding to fixed NL seems to alternate
between VpL = −130 and −70 mV. Here, the maxima at VpL= −90 mV correspond to the even NL peak marked with anopen triangle in Fig. 2共b兲, although the position is slightly
shifted because of the different measurement time. As shownin Fig. 3共c兲, the zero-bias Kondo peak still remains in thedIR / dVdc vs Vdc characteristics. On the other hand, the conductance is smaller at two adjacent maxima with odd NL 共at
VpL = −102 and −73 mV兲, and no Kondo peak is found, as
shown in Fig. 3共c兲. Thus, a nonlocal control of the Kondo
effect in the right QD is realized by changing the number ofelectrons in the left QD.
When the Fano resonance involving the left QD modulates the conductance of the QW, it also indirectly modulates
the dot current IR since the QW acts as one lead for the right
QD. As coupling of the left QD increases, the Fano-Kondo
antiresonance suppresses the conductance at the odd NL
regions.14 It is expected that the Fano resonance modulates
the local density of states of the QW, as the enhanced zerobias conductance shown in Fig. 3 in Ref. 8 suggests. Because
TK ⬀ exp共−1 / ␳J兲, where ␳ is the density of states and J is thecoupling constant,27 TK decreases when ␳ decreases. Thismay be one mechanism for the suppressed Kondo effect forthe odd NL cases because ␳ is reduced by the Fano-Kondo
effect compared to even NL.
Another mechanism that could be responsible for the observed even-odd effect is the RKKY interaction. When both
NR and NL are odd, the RKKY interaction couples two spinsin the two QDs via interceding conduction electrons either
ferromagnetically or antiferromagnetically depending on the
distance between them. The effective interdot distance in our
device is considered to be close to zero since they couple to2027

Sasaki et al.: Spin manipulation in a double quantum-dot–quantum-wire coupled system

FIG. 3. 共a兲 Gray-scale plot of the conductance through the right QD as afunction of VsL and VpR with VsL = −0.9 V in the strong-coupling regime.
Black corresponds to 5 ␮S and white to 35 ␮S. Dotted lines denote Coulomb oscillation peaks for the right QD and the region between the dottedlines correspond to odd NR Kondo valley. The open and solid triangles
denote even and odd NL regions, respectively. 共b兲 The same plot as 共a兲
except B = 0.15 T. 共c兲 dIR / dVdc vs Vdc for odd NL 关VpL = −102 and −73 mV,
the solid triangles in 共a兲兴 and for even NL 关VpL = −90 mV, the open triangle
in 共a兲兴. VpR is fixed at −775 mV in the middle of the odd NR Coulomb
blockade valley. The open triangle for VpL = −90 mV data denotes a zerobias Kondo peak.

the opposing sides of the quasi-one-dimensional QW 共having
two to three conduction channels for the gate voltage conditions explored兲 with a small relative distance along the wire
direction.15,16 Hence, the ferromagnetic coupling may be realized, and a relatively large interaction strength is expected.
If this is the case, the localized spin in one QD is ferromagnetically locked by the remote spin in the other QD, and the
Kondo effect is suppressed. However, this RKKY mechanism is inseparable from the Fano-Kondo-modulated densityof states scenario described above, and presumably bothmechanisms are in action.
By applying magnetic field perpendicular to the 2DEG
plane, one can reduce the tunnel coupling without the electrostatic energy shift. Figure 3共b兲 shows the same data as inFig. 3共a兲 except that B = 0.15 T. In this case, conductancemodulation by VpL is absent and the overall conductance isenhanced compared to Fig. 3共a兲. This is because the left QD
is decoupled by magnetic field and the Fano 共-Kondo兲 effectdisappears. In fact, the Kondo effect is recovered within thewhole Kondo valley irrespective of NL. When much stronger
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FIG. 4. 共a兲 Gray-scale of plot of the conductance through the QW as afunction of VpL and VpR with VsL = −1.15 V, VsR = −1.25 V, VdL = VdR= −0.5 V, and VmL = VmR = −0.4 V. Black corresponds to 2e2 / h 共77 ␮S兲 andwhite to 3e2 / h 共116 ␮S兲. Black dotted lines and solid triangles on the axes
denote Fano resonances and odd electron number regions, respectively. 共b兲
Magnetic field dependence of the QW conductance profile taken along thewhite dotted line in 共a兲 with constant NL 共VpL and VpR are simultaneously
swept兲. ⌬R and ⌬L denote the conductance suppression due to the FanoKondo effect involving the right QD and the left QD, respectively.

magnetic field is applied 共Ⰷ1 T兲, the Kondo effect is eventually suppressed because of the Zeeman splitting and the
reduced dot-lead tunnel coupling, as Fig. 1共c兲 suggests.
These two different magnetic field scales indicate that the
dot-lead coupling is more robust than the dot-wire side
coupling.
Finally, we change the experimental setup and measure
the current through the QW. Figure 4共a兲 shows gray-scale
plot of the QW conductance as a function of VpL and VpR.
The exit of both QDs are pinched off. Four 共two兲 clear Fano
resonances are observed for the right 共left兲 QD indicated byblack dotted lines on the axes. Surprisingly, the period ofthese Fano resonances 共⬃100 mV兲 is much larger than the
typical resonance period 共⬍30 mV兲 discussed so far. Actually, such small period resonances are also found in Fig. 4共a兲at VpR ⬎ −0.9 V. Therefore, we ascribe the large period resonances to smaller QDs 共having larger charging energy兲which are formed after the original QDs are pinched off. Thismay be related to our specific gate electrode geometry where,
unlike conventional design, the plunger gate electrodes are
not recessed with respect to the exit gate electrodes to which
VdL and VdR are applied. The electrostatic coupling between

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Sasaki et al.: Spin manipulation in a double quantum-dot–quantum-wire coupled system

the original QD and the smaller QD on the right side isobserved as a honeycomblike pattern at VpR ⯝ −0.8 V, as iscommonly observed in the stability diagram of a normal
double dot.28 The different slopes of the resonance lines between the smaller QDs and the original ones reflect the factthat the smaller QDs are located closer to the center than theoriginal ones and have a larger capacitive coupling to theplunger gate on the opposite side.
Let us now focus on the features originating from thesmaller QDs. Each resonance line is almost straight and does
not show the honeycomb distortion, indicating that thechange in NL 共NR兲 by one has negligible influence on theelectrostatic energy of the right 共left兲 QD because of theinterceding QW. The conductance at the odd N regions
marked with solid triangles are suppressed due to the FanoKondo effect. In particular, the conductance is minimum
when both NL and NR are odd because of the double FanoKondo suppression.16,29
Figure 4共b兲 shows the magnetic field dependence of the
conductance profile taken along the white dotted line in Fig.
4共a兲 with constant odd NL. In the B = 0 T trace, there are twodips at VpR = −1.05 V and at VpR = −1.2 V due to the Fano
resonance between the right QD and the QW. The conductance between the dips 共odd NR兲 are suppressed comparedwith the outer regions 共even NR兲 due to the Fano-Kondo
effect. As magnetic field increases, tunnel coupling between
the QD and the QW is reduced. Then, the Fano resonances
and the Fano-Kondo effect are suppressed and the overall
conductance gradually increases. By comparing the trace at
B = 0.3 T, where all the features are lost, and that at B = 0 T,
the suppressed conductance due to the Fano-Kondo effectinvolving the right 共left兲 dot, ⌬R 共⌬L兲, is estimated to be
5 ␮S 共10 ␮S兲 at the center of the double-suppression region,
as shown in Fig. 4共b兲.

IV. SUMMARY
We have performed transport measurement on the double
QD-QW coupled system and demonstrated nonlocal controlof the Kondo effect in one QD by manipulating the spinstates of the other. The Kondo temperature in one QD may
be modulated via the local density of states modulation in the
QW due to the Fano-Kondo antiresonance involving theother QD. As another mechanism, the RKKY interaction between the two QDs is considered. We have also observed the
double Fano-Kondo antiresonance in the conductance of the
QW when both QDs have odd electrons. We have found that
all the features measured in two different setups are dimin-

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ished by the application of a magnetic field perpendicular to
the 2DEG, which reduces the tunnel couplings between QDs
and QW.
ACKNOWLEDGMENT
This work is financially supported by Grant-in-Aid for
Scientific Research from the Japan Society for the Promotionof Science.
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