We investigate Kondo effect and spin blockade observed on a many-electron
quantum dot and study the magnetic field dependence. At lower fields a
pronounced Kondo effect is found which is replaced by spin blockade at higher
fields. In an intermediate regime both effects are visible. We make use of this
combined effect to gain information about the internal spin configuration of
our quantum dot. We find that the data cannot be explained assuming regular
filling of electronic orbitals. Instead spin polarized filling seems to be
probable.Comment: 4 pages, 5 figure

Haug, R. J.

Kupidura, D.

Reinwald, M.

Rogge, M. C.

Wegscheider, W.

English

arXiv

We investigate the Kondo effect and spin blockade observed in a many-electron quantum dot and study the magnetic field dependence. At lower fields, a pronounced Kondo effect is found, which is replaced by the spin blockade at higher fields. In an intermediate regime, both effects are visible. We make use of this combined effect to gain information about the internal spin configuration of our quantum dot. We find that the data cannot be explained assuming regular filling of electronic orbitals. Instead, spin polarized filling seems to be probable

Rogge, M.

Reinwald, Matthias

Wegscheider, Werner

Haug, R.

University of Regensburg Publication Server

Probing a Kondo-Correlated Quantum Dot with Spin Spectroscopy

We investigate the Kondo effect and spin blockade observed in a many-electron quantum dot and study the magnetic field dependence. At lower fields, a pronounced Kondo effect is found, which is replaced by the spin blockade at higher fields. In an intermediate regime, both effects are visible. We make use of this combined effect to gain information about the internal spin configuration of our quantum dot. We find that the data cannot be explained assuming regular filling of electronic orbitals. Instead, spin polarized filling seems to be probable. © 2006 The American Physical Society

Rogge, M.C.

Haug, Rolf J.

Institutional Repository of Leibniz Universität Hannover

PRL 96, 046802 (2006) P H Y S I C A L R E V I E W L E T T E R Sweek ending3 FEBRUARY 2006Probing a Kondo-Correlated Quantum Dot with Spin SpectroscopyD. Kupidura,1 M. C. Rogge,1,* M. Reinwald,2 W. Wegscheider,2 and R. J. Haug11Institut für Festkörperphysik, Universität Hannover, Appelstraße 2, D-30167 Hannover, Germany2Angewandte und Experimentelle Physik, Universität Regensburg, D-93040 Regensburg, Germany(Received 14 September 2005; published 1 February 2006)0031-9007=We investigate the Kondo effect and spin blockade observed in a many-electron quantum dot and studythe magnetic field dependence. At lower fields, a pronounced Kondo effect is found, which is replaced bythe spin blockade at higher fields. In an intermediate regime, both effects are visible. We make use of thiscombined effect to gain information about the internal spin configuration of our quantum dot. We find thatthe data cannot be explained assuming regular filling of electronic orbitals. Instead, spin polarized fillingseems to be probable.DOI: 10.1103/PhysRevLett.96.046802 PACS numbers: 73.63.Kv, 72.15.Qm, 73.21.La, 73.23.HkFIG. 1. (a) AFM picture of our device with source (S) anddrain (D) leads and gates (G1 to G4). (b) Schematic picture:Under the influence of a magnetic field, the dot can be repre-sented as edge and core areas for the two lowest Landau levels.The dot is coupled to source and drain represented here by spinpolarized edge states.Quantum dot systems containing confined electronshave been studied intensively both theoretically [1] andexperimentally [2] during the past decades. They haveproven to be excellent systems to explore the physics ofconfined charge carriers. Beyond the Coulomb blockade[1,3], many effects have been found to reveal quantummechanical and spin properties of confined electrons,among them the Kondo effect and spin blockade. TheKondo effect is caused by correlated cotunneling events[4,5] resulting in enhanced conductance when sequentialtunneling is Coulomb blocked. The underlying mechanismis due to the formation of a spin singlet between conduc-tion electrons and the localized spin in the quantum dot.Spin blockade as introduced by Ciorga et al. [6] appears inlateral dot systems when applying a magnetic field perpen-dicular to the sample surface. Spin dependent transportsuppression is found as a consequence of electron injectionfrom spin polarized edge states.In this Letter, we investigate the interplay between thesetwo effects, as they appear in the same sample in slightlydifferent magnetic field regions. We study the magneto-conductance for the Kondo effect and spin blockade indi-vidually and the transition between them. Results fromboth effects are then combined to gain information aboutthe internal spin configuration of the quantum dot.Our device is defined by terms of local anodic oxidation[7] on a GaAs=AlGaAs heterostructure containing a 2-dimensional electron system (2DES) 37 nm below thesurface. The 2DES has an electron density of ne  3:941015 m2 and mobility of e  52:7 m2 V1 s1 at 4.2 K.Figure 1(a) shows an atomic force microscope (AFM)picture of our dot with leads source (S) and drain (D) beingthe electron reservoirs and in plane gates (G1–G4), respec-tively. Gates G1 and G4 are designed to control the cou-pling to the leads, while gates G2 and G3 control theelectrostatic potential of the dot. The measurements areperformed in a He3=He4 dilution refrigerator at 50 mKwith a magnetic field B applied perpendicular to the 2DES.Standard lock-in technique is used to record the differential06=96(4)=046802(4)$23.00 04680conductance G as a function of gate voltages and magneticfield.Figure 1(b) shows a simplified model of our system inthe relevant field regime. The properties of the dot arebasically characterized by the two lowest Landau levelsformed at the edge and the core of the dot (filling factordot > 2). The 2-dimensional leads are subject to the quan-tum Hall effect and, thus, develop spin polarized edgechannels that get separated in space with increasing B.The visibility of the Kondo effect and spin blockade de-pends on this separation and, thus, on the strength of themagnetic field.For relatively low fields up to approximately 3.5 T, theleads can still be considered as unpolarized. Here we findKondo physics. The Kondo effect is induced by a commonstate of electrons on the dot and electrons in the leads. If—high tunnel coupling presumed—the total spin of the dot isS  1=2, a singlet state can be formed with the leadsallowing cotunneling events even if sequential tunnelingis Coulomb blocked. As a consequence, finite transport isobserved between individual Coulomb peaks. Since trans-port via this Kondo state involves spin flips, both spinsmust be present in the leads.2-1 © 2006 The American Physical SocietyPRL 96, 046802 (2006) P H Y S I C A L R E V I E W L E T T E R Sweek ending3 FEBRUARY 2006Figure 2(a) shows a measurement in the relevant Kondoregime. The differential conductance G is measured as afunction of the voltage applied to gate 3 and the magneticfield. Several Coulomb peaks are visible. Their peak posi-tions, e.g., the ground state energies, exhibit a zigzagbehavior as the field increases. Negative gradients corre-spond to transport through the edge of the dot, whiletransport through the center leads to a positive gradient.In between, we find a regular pattern of enhanced conduc-tance caused by a Kondo effect involving the edge of thedot. The center of the dot is not involved in this Kondoeffect, since the tunnel coupling to the leads is not highenough. Thus, transport via a Kondo singlet state corre-sponds to a total spin S  1=2 at the edge of the dot. Thisspin depends on the number of electrons at the edge, whichcan be changed in two different ways. An electron canenter the edge either coming from the leads or coming fromthe dot center. The first mechanism is induced by increas-ing the gate voltage increasing the total number of elec-trons. Therefore, a regular modulation of the Kondo effectis found as a function of VG3. This is demonstrated inFig. 2(b), where G is plotted as a function of VG3 alongthe dashed line in Fig. 2(a). The alternating Kondo effect isvisible as an alternating height of successive Coulombvalleys. The second mechanism is used when increasingthe magnetic field. With increasing B, electrons are redis-FIG. 2. (a) Differential conductance G as a function of mag-netic field B and gate voltage VG3. A chessboard pattern isobserved caused by Kondo conductance in the Coulomb valleysbetween individual Coulomb peaks. The Kondo effect is modu-lated by electron number and magnetic field. (b) A trace alongthe dashed line in (a) demonstrates the alternating height ofsuccessive Coulomb valleys (exemplarily marked with a squareand a circle).04680tributed from the second Landau level in the center to thefirst Landau level at the edge. This leads to a Kondomodulation as a function of B and overall to a chessboardpattern as reported in Refs. [8–11].Above 3.5 T, the spatial separation of the edge channelsbecomes prominent, and the leads are more and more spinpolarized leading to a pronounced spin blockade. This isvisible in Fig. 3(a). Again, several Coulomb peaks arevisible as a function of VG3 and B but this time for a higherfield range. The zigzag pattern of the peak position stillreflects the energy of the ground states located at the centerof the dot (positive slope) or at the edge (negative slope). Inaddition, a bimodal behavior of the peak amplitude isfound when transport occurs through the edge. This isshown in Fig. 3(b). The peak amplitude for the peakmarked as Ib in Fig. 3(a) is plotted as a function of B.Since the edge states in the leads are spatially separated,the overlap of the wave functions between the lead and thedot for the energetically higher spin state (spin up in thefollowing) is reduced as the more distant edge state isinvolved and transport is blocked. In contrast, electronswith the lower spin state (spin down) coming from thecloser edge state cause an unsuppressed transport. Thiseffect allows one to detect the spin of an electron addedto the dot. Crossing a Coulomb peak in the gate voltagedirection with an unsuppressed amplitude leads to theFIG. 3. (a) At higher fields, spin polarized edge states in theleads give rise to the spin blockade. Transport with spin upelectrons is suppressed compared to spin down transport. Thearrows denote charging with the assigned spin detectable withthe amplitude of the corresponding Coulomb peak. (b) Peakamplitude for peak Ib. The bimodal behavior due to spin block-ade is clearly visible.2-2PRL 96, 046802 (2006) P H Y S I C A L R E V I E W L E T T E R Sweek ending3 FEBRUARY 2006addition of an electron with spin down, while the additionvia a low amplitude corresponds to a spin up electron [seearrows in Fig. 3(a)].So far, both regimes were investigated separately. In thefollowing, we will concentrate on the interplay between theKondo effect and spin blockade. The peak amplitudes ofthe peaks marked as Ia and Ib in Figs. 2 and 3 are plotted ingray as a function of magnetic field in Fig. 4. The strengthof the bimodal behavior reflects the strength of the spinblockade. At 3.2 T, almost no oscillation is visible. Theleads are still unpolarized, and, thus, no spin blockade isobserved. With increasing B, the edge states start to splitand the spin blockade becomes visible. Above 4 T, itreaches its maximum. The black curve represents the con-ductance in the Coulomb valley (IIa and IIb in Figs. 2 and3) above the depicted peak. At 3.2 T, a strong oscillation isobserved due to a pronounced Kondo effect. Increasing thefield separates the edge states. This leads to a suppressionof the Kondo effect, since the transport over the Kondostate involves spin flips requiring both spin orientations inthe leads. At 4.5 T, the Kondo effect is strongly suppressed.In an intermediate regime around 4 T, both effects arevisible simultaneously. Thus, the results from both effectscan be combined. We find that a high peak amplitudecorresponding to spin down transport is accompanied bya suppressed Kondo effect in the Coulomb valley above.Therefore, the addition of an electron to the energeticallylower spin down state does not lead to a total spin S  1=2required for Kondo conductance. Instead, the Kondo effectreflecting a total spin of S  1=2 appears above a low peakamplitude when an electron with the energetically higherspin up state is added. This discrepancy shows that theelectronic state structure within our dot cannot be de-scribed in terms of noninteracting electrons. A simple3.2 4.50.130.10.5B (T)-0.1IIaIaIbIIbG(e/h)2peakG      (e/h)2valley0FIG. 4. Peak amplitude along Coulomb peak Ia/Ib (gray curve)and conductance in the Coulomb valley IIa/IIb above (blackcurve). While the bimodal behavior along the peak increaseswith magnetic field due to spin blockade, the oscillations due tothe Kondo effect in the valley vanish. Around 4 T, both effectsare visible and comparable. A high amplitude at the peak goesalong with a suppressed conductance in the valley (see dottedlines).04680model with regular filling of dot orbitals featuring a spinsinglet phase is not applicable. Instead, the addition ofelectrons is realized favoring spin polarized configurations,i.e., a sort of Hund’s rule.We propose an explanation based on theoretical resultsinspired by an experiment given by Ciorga et al. [12]. Theyinvestigated the dot  2 transition in a lateral quantum dotfeaturing spin blockade as well but no Kondo effect. Aphase transition from a spin singlet phase towards a spinpolarized phase was found depending on the number ofelectrons. For electron numbers below approximately 30,the spin singlet phase was observed with a regular filling ofdot orbitals. Above this critical number, spin polarizedconfigurations were observed.We find that the model developed by Ciorga et al. for theinternal spin configuration above the critical electron num-ber can be applied to our results which fits the assumptionof having a high electron number N  160. The model isshown in Fig. 5. Four ‘‘Kondo fields’’ are shown withKondo conductance in the lower left and the upper right[Fig. 5(a) shows the measurement and Fig. 5(b) the model].Thus, in these fields we assume the total spin of the edge tobe S  1=2. This is explained with the highest orbital inthe edge to be half filled with a spin down electron. Goingfrom the lower left to the upper left, a Coulomb peak iscrossed with a high amplitude. Thus, the half filled orbitalis not filled with a spin up electron. Instead, the next orbitalis entered with a spin down electron. The total spin of theedge is S  1, and the Kondo effect disappears. If now themagnetic field is increased, an electron is redistributedfrom the center to the edge and the first half filled orbitalat the edge is filled, leaving one half filled orbital with thetotal spin S  1=2. The Kondo effect is restored.We want to mention that the results obtained here mayhave a universal character. Very similar results were ob-tained by Keller et al. [9]. A Kondo induced chessboardpattern was observed. The peak amplitude which behavesFIG. 5. (a) Increased region of Fig. 3(a) showing both theKondo effect and spin blockade (same color scale as in Figs. 2and 3). (b) Model of the spin configuration of the dot gainedfrom the combination of results from the Kondo effect and spinblockade. The coincidence of low conductance along a peak andhigh conductance in the valley above is explained with spinpolarized filling of electrons.2-3PRL 96, 046802 (2006) P H Y S I C A L R E V I E W L E T T E R Sweek ending3 FEBRUARY 2006the same way as in our sample was plotted, but no attentionwas paid to this effect. The chessboard was explained withregular filling featuring a spin singlet phase. This is, in ouropinion, not valid. Instead, an electron number of approxi-mately 50 supports our assumption of spin polarized fill-ing. Measurements done by Fühner et al. [8] for an electronnumber of approximately 180 showing the magnetic fluxdependence of the chessboard pattern also confirm ourresults. Other chessboard measurements combined withcalculations were performed by Stopa et al. [10]. With anelectron number below 30, they assumed a regular filling.Their calculations might, therefore, not be applicable forchessboard patterns at higher electron numbers. Regularfilling was also obtained in Refs. [11,13]. The electronnumber in Ref. [13] is slightly above 50 but seems stillto be low enough for the spin singlet phase probably due todifferent dot parameters.In conclusion, we investigate the Kondo effect and spinblockade in a lateral quantum dot depending on thestrength of a magnetic field applied perpendicular to thesample surface. At lower fields, we observe a Kondoinduced chessboard pattern modulated by the number ofelectrons and the magnetic field. At higher fields, the leadsbecome spin polarized and spin blockade sets in, makingthe electronic spin detectable. The Kondo conductancevanishes here, since both spin orientations in the leadsare needed for the Kondo effect. In intermediate fields,both effects are observed. A combined analysis reveals theinternal spin configuration of the dot. We find that themeasurements cannot be described by a regular filling ofelectronic orbitals within a model of noninteracting elec-trons. Instead, for this high electron number a differentapproach featuring spin polarized filling with a sort ofHund’s rule must be assumed. The comparison with otherresults challenges former interpretations of chessboard04680patterns and yields a consistent picture with the dot phasedepending on the electron number.This work has been supported by BMBF.2-4*Electronic address: rogge@nano.uni-hannover.de[1] C. W. J. Beenakker, Phys. Rev. B 44, 1646 (1991).[2] L. P. Kouwenhoven, D. G. Austing, and S. Tarucha, Rep.Prog. Phys. 64, 701 (2001).[3] M. A. Kastner, Phys. Today 46, No. 1, 24 (1993).[4] S. Sasaki, S. De Franceschi, J. M. Elzerman, W. G. van derWiel, M. Eto, S. Tarucha, and L. P. Kouwenhoven, Nature(London) 405, 764 (2000).[5] D. Goldhaber-Gordon, Hadas Shtrikman, D. Mahalu,David Abusch-Magder, U. Meirav, and M. A. Kastner,Nature (London) 391, 156 (1998).[6] M. Ciorga, A. S. Sachrajda, P. Hawrylak, C. Gould,P. Zawadzki, S. Jullian, Y. Feng, and Z. Wasilewski,Phys. Rev. B 61, R16 315 (2000).[7] M. Ishii, and K. Matsumoto, Jpn. J. Appl. Phys. 34, 1329(1995).[8] C. Fühner, U. F. Keyser, R. J. Haug, D. Reuter, and A. D.Wieck, Phys. Rev. B 66, 161305(R) (2002).[9] M. Keller, U. Wilhelm, J. Schmid, J. Weis, K. vonKlitzing, and K. Eberl, Phys. Rev. B 64, 033302(2001).[10] M. Stopa, W. G. van der Wiel, S. De Franceschi,S. Tarucha, and L. P. Kouwenhoven, Phys. Rev. Lett. 91,046601 (2003).[11] J. Schmid, J. Weis, K. Eberl, and K. v. Klitzing, Physica(Amsterdam) 9E, 54 (2001).[12] M. Ciorga, A. Wensauer, M. Pioro-Ladriere, M. Korkusin-ski, J. Kyriakidis, A. S. Sachrajda, and P. Hawrylak, Phys.Rev. Lett. 88, 256804 (2002).[13] M. C. Rogge, F. Cavaliere, M. Sassetti, R. J. Haug, andB. Kramer, cond-mat/0507036.

Probing a Kondo-correlated quantum dot with spin spectroscopy

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Probing a Kondo correlated quantum dot with spin spectroscopy

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