We present transport measurements on a system of two lateral quantum dots in a perpendicular magnetic field. Due to edge channel formation in an open conducting region, the quantum dots are chirally coupled. When both quantum dots are tuned into the Kondo regime simultaneously, we observe a change in the temperature dependence of the differential conductance. This is explained by the RKKY exchange interaction between the two dots. As a function of bias the differential conductance shows a splitting of the Kondo resonance which changes in the presence of RKKY interaction.DFG/EXC/QUESTNTH School for Contacts in Nanosystem

Haug, Rolf J.

Heine, Alexander W.

Schuh, Dieter

Tutuc, Daniel

Wegscheider, Werner

Journal of Physics : Conference Series

Institutionelles Repositorium der Leibniz Universität Hannover

This content has been downloaded from IOPscience. Please scroll down to see the full text.Download details:IP Address: 194.95.157.141This content was downloaded on 08/08/2016 at 12:30Please note that terms and conditions apply.Exchange interaction in chirally coupled quantum dotsView the table of contents for this issue, or go to the journal homepage for more2013 J. Phys.: Conf. Ser. 456 012014(http://iopscience.iop.org/1742-6596/456/1/012014)Home Search Collections Journals About Contact us My IOPscienceExchange interaction in chirally coupled quantum dotsDaniel Tutuc1, Alexander W. Heine1, Dieter Schuh2, WernerWegscheider2,3, and Rolf J. Haug11Institut für Festkörperphysik, Leibniz Universität Hannover, Appelstraße 2, D-30167Hannover, Germany2Institut für Experimentelle und Angewandte Physik, Universtät Regensburg,Universitätsstraße 31, D-93053 Regensburg, Germany3Laboratorium für Festkörperphysik, ETH Zürich, Schafmattstraße 16, CH-8093 Zürich,SwitzerlandE-mail: heine@nano.uni-hannover.deAbstract. We present transport measurements on a system of two lateral quantum dots ina perpendicular magnetic ﬁeld. Due to edge channel formation in an open conducting region,the quantum dots are chirally coupled. When both quantum dots are tuned into the Kondoregime simultaneously, we observe a change in the temperature dependence of the diﬀerentialconductance. This is explained by the RKKY exchange interaction between the two dots. Asa function of bias the diﬀerential conductance shows a splitting of the Kondo resonance whichchanges in the presence of RKKY interaction.1. IntroductionSemiconductor quantum dots (QDs) are highly tunable devices and therefore have attractedmuch interest in the scientiﬁc community. Using the spin of the QD as a qubit in quantuminformation processes is one of the proposed applications [1]. For this application it is necessaryto provide non-local manipulation and readout of the spin information of a QD. One possiblemechanism to entangle the spins of diﬀerent QDs beyond the nearest neighbour approach is theRuderman-Kittel-Kasuya-Yosida (RKKY) interaction between magnetic moments. This indirectnon-local exchange interaction is mediated by charge carriers and locks the magnetic momentsin a new ground state. The latter is either ferromagnetic or antiferromagnetic depending on thedistance between the magnetic moments and the Fermi wave vector of the charge carriers [2].Another entanglement mechanism of a single QD spin to a many-body electron system is theKondo eﬀect [3, 4, 5]. At very low temperatures the spin of a QD is screened by the electronsin the leads and forms a new singlet ground state with the binding energy Tk. In an otherwiseCoulomb-blocked situation this singlet ground state allows the electron of the highest occupiedenergy level to leave the dot and to be replaced by an electron from the leads with opposite spin.Therefore the dot becomes transparent at zero bias (the so-called zero bias anomaly) because itsspin is constantly ﬂipped.In a system where the Kondo eﬀect as well as the RKKY exchange interaction are present,one expects a competition between these two mechanisms which can be observed in transportproperties [6, 7].HMF-20 IOP PublishingJournal of Physics: Conference Series 456 (2013) 012014 doi:10.1088/1742-6596/456/1/012014Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distributionof this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.Published under licence by IOP Publishing Ltd 12. Experimental SetupOur sample is prepared on a GaAs/AlGaAs heterostructure containing a two dimensional electronsystem 37 nm below the surface with an electron density of 3.95 × 1015 m−2. Two lateral QDs(QD1 and QD2) are deﬁned by local anodic oxidation using an AFM [8, 9]. Figure 1 (a) showsan AFM picture of the structure. The QDs are tunnel coupled to individual drains (D1 and D2)and to an open conducting region with a length of ∼ 600 nm. This region connects the QDsand is used as source contact (S). The tunnel barriers and the energy levels of the QDs can betuned by six in-plane gates and an individual bias can be applied to each QD. The measurementswere performed in a 3He/4He dilution refrigerator with an electron temperature of about 80 mK.Standard lock-in technique was used and the diﬀerential conductance Gi = dIi/dV (i = 1, 2) ofeach dot was measured individually. A magnetic ﬁeld was applied perpendicular to the sample.More detailed information concerning the experimental setup can be found in Ref. [10].3. Kondo chessboard and RKKY interactionThe measurement of the diﬀerential conductance G1 of QD1 at zero bias as a function of gatevoltage VG6 and perpendicular magnetic ﬁeld leads to a pattern of alternating tiles of low andhigh diﬀerential conductance (Fig. 1 (c)). This pattern originates from the formation of Landaulevels (LLs) in the QD in perpendicular magnetic ﬁeld when two LLs are observable. In thepresented situation the ﬁlling factor is 2 < ν < 4. Kondo transport then only involves energystates of the lowest LL. The number of electrons in this LL0 can be controlled by varying thenumber of ﬂux quanta on the dot which redistributes the electrons between the LLs. This isachieved by a change in the magnetic ﬁeld. A modulation of the total number of electrons onthe dot by sweeping the gate voltage also changes the occupation of LL0. These two mechanismslead to the so-called Kondo chessboard [11, 12, 13, 14], seen in Fig. 1 (c).-5.5 -5.0 -4.5B (T)-40-30-20-100V G6 (mV)-5.5 -5.0 -4.5B (T)-40-30-20-100VG6  (mV)0.10.30.5 G2 (e²/h)G6211 2G6 SD1 D2G2 G3500nmG5G1 G4(a) (b)(c) (d)1.01.31.6 G1 (e²/h)Figure 1. (a) AFM picture of the sample. The oxide lines in bright colour deﬁne the structure.(b) Schematic of the edge channels for perpendicular magnetic ﬁeld with negative polarity.(c)+(d) Diﬀerential conductance of QD1 (c) and QD2 (d) as function of magnetic ﬁeld andgate voltage.HMF-20 IOP PublishingJournal of Physics: Conference Series 456 (2013) 012014 doi:10.1088/1742-6596/456/1/0120142The diﬀerential conductance G2 of QD2 in Fig. 1 (d) shows a more complicated pattern: anegative of the Kondo chessboard in QD1 is visible that is superimposed by a stripe pattern.The reason for that is the formation of edge channels in the open central region. For the givenmagnetic ﬁeld polarity a schematic of transport through the edge channels is shown in Fig. 1 (b).QD2 lies "downstream" and the changes of the electrostatic potential at the site of QD1, e.g. byonset of the Kondo eﬀect, can be seen in the transport properties of QD2. Thus the couplingbetween the QDs is chiral and the chirality can be changed by reversing the magnetic ﬁeldpolarity [10].The intervals where both QDs are tuned into the Kondo region simultaneously can be easilyidentiﬁed in the superimposed pattern exhibited by QD2. In QD1, Kondo transport can beobserved between -4.97 T and -4.77 T, while QD2 exhibits the Kondo eﬀect between -5.05 T and-4.92 T. Therefore between -4.97 T and -4.92 T transport through both QDs is Kondo enhanced(marked in red). A detailed temperature analysis in this region yields a strong change in thebehaviour of the Kondo temperatures compared to the case when only one QD is tuned intothe Kondo regime (see [10]). This change indicates a modulation in the ground state of thesystem. Since this eﬀect can be observed in both QDs for both magnetic ﬁeld polarities, it is notcaused by any electrostatic eﬀect. Instead it is attributed to the quantum mechanical interactionmediated by the electrons in the edge states, the RKKY exchange interaction.4. Bias dependenceTo probe the inﬂuence of the RKKY interaction on the zero bias anomaly, a bias Vsd1 was appliedat drain 1 and the diﬀerential conductance G1 was measured along the dashed line in Fig. 1 (c).The result is shown in Fig. 2 (a). The region of Kondo transport can be seen clearly and between-4.9 T and -4.8 T a splitting can be observed in Fig. 2 (b). In traces taken along the colouredlines in Fig. 2 (a) the detailed evolution of this splitting is revealed. For the trace of -4.83 T twopeaks at about ±0.24 mV are clearly visible. When QD2 enters the Kondo regime at -4.92 T,this splitting decreases to ±0.12 mV and the peaks are considerably smaller. In the centre of theoverlap region at -4.96 T the peaks vanish completely.1.641.601.561.52-0.4 -0.2 0.0 0.2 0.4 B = -4.83 T B = -4.92 T B = -4.96 T-5.3-5.2-5.1-5.0-4.9-4.8-4.7-0.4 -0.2 0.0 0.2 0.4B (T)Vsd1 (mV)1.31.8 G1 (e²/h) G1 (e²/h)Vsd1 (mV)(a) (b)Figure 2. (a) Diﬀerential conductance G1 as function of magnetic ﬁeld and bias voltage forﬁxed gate voltage VG6 = −20mV (dashed line in Fig. 1 (c)). (b) Traces measured along thecoloured lines in (a).This clear change in the zero bias anomaly splitting when both QDs are tuned into the Kondoregime is another hint for the presence of the RKKY exchange interaction between the two QDs.HMF-20 IOP PublishingJournal of Physics: Conference Series 456 (2013) 012014 doi:10.1088/1742-6596/456/1/0120143When the polarity of magnetic ﬁeld is changed and QD2 is "upstream", a similar eﬀect can beseen as function of the bias on drain 2.Note that the observed splitting at -4.83 T is a factor of 2 larger than the expected Zeemansplitting for bulk GaAs (|g∗| = 0.44) of about 130 µeV at 5 T.5. ConclusionWe have shown the chiral coupling of two QDs in a perpendicular magnetic ﬁeld. The RKKYexchange interaction between the magnetic moments of the QD can be probed by using theKondo eﬀect as a spectroscopic tool. By analysing the Kondo temperature a change in theground state of the system can be conﬁrmed which is present regardless of chirality. In biasdependent measurements a splitting of the zero bias anomaly of QD1 can be observed, whenonly one QD shows the Kondo eﬀect. It is strongly suppressed, when both QDs exhibit Kondotransport and the RKKY interaction is present.AcknoledgmentsWe acknowledge ﬁnancial support by the German Cluster of Excellence QUEST and the NTHSchool for Contacts in Nanosystems.References[1] Loss D and DiVincenzo D P 1998 Phys. Rev. A 57(1) 120126[2] Ruderman M A and Kittel C 1954 Phys. Rev. 96(1) 99102[3] Goldhaber-Gordon D, Göres J, Kastner M A, Shtrikman H, Mahalu D and Meirav U 1998 Phys. Rev. Lett.81 52255228[4] Goldhaber-Gordon D, Shtrikman H, Mahalu D, Abusch-Magder D, Meirav U and Kastner M A 1998 Nature391 156159[5] Cronenwett S M, Oosterkamp T H and Kouwenhoven L P 1998 Science 281 540544[6] Craig N J, Taylor J M, Lester E A, Marcus C M, Hanson M P and Gossard A C 2004 Science 304 565567[7] Simon P, López R and Oreg Y 2005 Phys. Rev. Lett. 94 086602[8] Held R, Vancura T, Heinzel T, Ensslin K, Holland M and Wegscheider W 1998 Applied Physics Letters 73262264[9] Keyser U F, Schumacher H W, Zeitler U, Haug R J and Eberl K 2000 Applied Physics Letters 76 457459[10] Tutuc D, Popescu B, Schuh D, Wegscheider W and Haug R J 2011 Phys. Rev. B 83(24) 241308[11] Keller M, Wilhelm U, Schmid J, Weis J, v Klitzing K and Eberl K 2001 Phys. Rev. B 64 033302[12] Fuehner C, Keyser U F, Haug R J, Reuter D and Wieck A D 2002 Phys. Rev. B 66 161305[13] Stopa M, van der Wiel W G, Franceschi S D, Tarucha S and Kouwenhoven L P 2003 Phys. Rev. Lett. 91046601[14] Rogge M C, Fühner C and Haug R J 2006 Phys. Rev. Lett. 97 176801HMF-20 IOP PublishingJournal of Physics: Conference Series 456 (2013) 012014 doi:10.1088/1742-6596/456/1/0120144

Exchange interaction in chirally coupled quantum dots

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