Single electron tunneling is studied in a many electron quantum dot in high
magnetic fields. For such a system multiple transitions of the spin
configuration are theoretically predicted. With a combination of spin blockade
and Kondo effect we are able to detect five regions with different spin
configurations. Transitions are induced with changing electron numbers.Comment: 4 pages, 5 figure

Fuhner, C.

Haug, R. J.

Rogge, M. C.

English

arXiv

Single electron tunneling is studied in a many electron quantum dot in high magnetic fields. For such a system multiple transitions of the spin configuration are theoretically predicted. With a combination of spin blockade and Kondo effect we are able to detect five regions with different spin configurations. Transitions are induced with changing electron numbers. © 2006 The American Physical Society

Rogge, M.C.

Fühner, C.

Haug, Rolf J.

Institutional Repository of Leibniz Universität Hannover

Multiple Transitions of the Spin Configuration in Quantum DotsM. C. Rogge,* C. Fühner, and R. J. HaugInstitut für Festkörperphysik, Universität Hannover, Appelstraße 2, D-30167 Hannover, Germany(Received 15 June 2006; published 24 October 2006)Single electron tunneling is studied in a many electron quantum dot in high magnetic fields. For such asystem multiple transitions of the spin configuration are theoretically predicted. With a combination ofspin blockade and Kondo effect we are able to detect five regions with different spin configurations.Transitions are induced with changing electron numbers.DOI: 10.1103/PhysRevLett.97.176801 PACS numbers: 73.63.Kv, 72.15.Qm, 73.21.La, 73.23.HkSpin physics in semiconductor quantum dots [1] haspushed the research on nanostructures since quantumdots were suggested as essential elements in quantumcomputing devices [2]. The spin of a single electron on aquantum dot can act as a qubit and thus great efforts weremade to prepare, manipulate, and read the spin on fewelectron quantum dots. But, in addition, the research onmany electron dots has come up with exciting results andnew effects dealing with spin. While it is possible to detectthe spin orientation on very few electron dots just byidentifying energy levels, conclusions about the spin con-figuration in many electron dots must be drawn indirectlyfrom additional spin dependent effects. A few years ago itwas demonstrated that so called spin blockade can be usedto read the spin of the tunneling electron in lateral quantumdots in a perpendicular magnetic field [3]. More informa-tion about the spin configuration can be obtained when aKondo effect [4] is observed depending on the spin con-figuration in Coulomb blocked regions [5,6].In a perpendicular magnetic field with two Landau levelsin the quantum dot (filling factor 4> dot > 2), a shellstructure is assumed for the dot with Landau level 0 inthe edge and level 1 in the core (see Fig. 1) [7]. Anunpolarized spin configuration is expected at the edge ofthe dot for low electron numbers in high magnetic fields[8]. That means the total spin at the edge of the dot is 0whenever the electron number is even, and 12 when theelectron number is odd: Seven; Sodd  0;12 with Sevenand Sodd the total spin at the edge of the dot for even andodd electron numbers (see Fig. 1). A few years ago mul-tiple transitions of the spin configuration were theoreticallypredicted and calculated at the dot  2 boundary [9]. Thespin polarization should increase with increasing electronnumber, 0; 12 ! 1;12 ! 1;32 . . . . These transitions of thespin configuration are related to spin flips in the dot < 2regime when the spin configuration approaches the maxi-mum density droplet. The first two spin configurations (0,12 ) and (1,12 ) can be identified with the combination of spinblockade and Kondo effect [10]. While the first transitionbetween these two configurations was observed in a fewelectron quantum dot [11], experimental evidence for mul-tiple transitions was never found.We close this gap and present measurements of multipletransitions in the magnetoconductance of a many electronquantum dot. We make use of the combination of both spinblockade and Kondo effect at 4> dot > 2 to identify fiveregions with different spin configurations. Transitions be-tween these regions are induced with changing electronnumber as predicted. Nevertheless some observations im-ply slight deviations from the theoretical picture. Evidenceis found for a change of spin configuration back and forth[e.g., 0; 12 ! 1;12 ! 0;12] instead of a continuously in-creasing spin polarization. These results, as well as resultsabout the position of the transitions as a function of mag-netic field, should affect eventually forthcoming calcula-tions for dot > 2.Our sample [12] is fabricated in split-gate technology ona GaAs=AlGaAs heterostructure with a two-dimensionalelectron system (2DES) 57 nm below the surface (see insetof Fig. 2). The electron density is n  3:7 1015 m2, themobility is   130 m2=V s. An electronic dot diameterof 250 nm yields an electron number of 180.Differential conductance measurements were carried outcoreedgeeven oddFIG. 1 (color online). Schematic diagram for a lateral quantumdot in a high perpendicular magnetic field. A shell structure withtwo Landau levels is established in the dot; level 0 at the edge(with total spin Seven, Sodd) and level 1 in the core. The leadsshown are spin polarized due to the spatial separation of edgechannels.PRL 97, 176801 (2006) P H Y S I C A L R E V I E W L E T T E R Sweek ending27 OCTOBER 20060031-9007=06=97(17)=176801(4) 176801-1 © 2006 The American Physical Societyin a 3He-4He dilution refrigerator at a base temperature of20 mK using standard lock-in technique. With the gatevoltage VG the dot was tuned in a Kondo regime wheresignatures of finite Kondo conductance were studied indetail as a function of a magnetic field B applied perpen-dicular to the sample surface.Such a measurement is shown in Fig. 2. The differentialconductance G is measured as a function of B and VG.Many Coulomb peaks are visible, reflecting changes of theelectron number by one for each peak (nearly horizontallines). The depicted range of the gate voltage shows75 peaks corresponding to a change of the electron numberby 75 electrons. In the Coulomb blockade regions betweenthe peaks we find a finite conductance due to the Kondoeffect which appears because of second order cotunnelingprocesses. This leads to a chessboard like pattern [8,13] ofhigh and low differential conductance. We concentrate ouranalysis on the right side of the dashed line were the patternis most regular. Here in the 4> dot > 2 regime (the fillingfactor of the 2DES 2DES is well above 6 in the magneticfield studied here) only the first Landau level situated at theedge of the dot is involved in the Kondo conductance. Thusthe Kondo effect depends on the spin configuration at theedge, which is different for even and for odd electronnumbers (Seven  Sodd). Therefore the Kondo effect de-pends on the parity of the electron number at the edge ofthe dot (just parity in the following), which is changedeither by electron exchange with the leads induced by gatevoltage or by electron exchange with the center of the dotinduced by the magnetic field.Apart from the alternating Kondo conductance there isalso an alternating peak amplitude of the Coulomb peakswith the same periodicity as the Kondo pattern. This is dueto spin blockade [3]. The magnetic field separates the spinpolarized edge channels in the leads (see Fig. 1) and thusthe tunneling probability and as a consequence the differ-ential conductance becomes spin dependent. Spin-up trans-port is suppressed compared to spin-down transport. Spinblockade and the Kondo effect can be observed simulta-neously in an intermediate field regime [10]. Since theperiodicity of both effects is identical, the combinationestablishes a stable pattern which should not change ifthe spin configurations for even and odd electron numbersat the edge of the dot do not change. As a consequence,changes of this pattern should reflect changes in the spinconfiguration at the edge of the dot. If the spin configura-tion has changed for one parity [e.g. 0; 12 ! 1;12] thepattern is swapped [10].In our sample we find not less than 5 regions withdifferent combinations of Kondo effect and spin blockade.These are marked with roman numbers I to V in Fig. 2.Therefore we have 4 transitions in between marked withsolid lines. Insets in these regions marked with white boxesin Fig. 2 are shown in detail in Fig. 3.Figure 3(a) shows the differential conductance again as afunction of VG and B for all 5 regions. In Fig. 3(b) tracesare shown reflecting the amplitude along a Coulomb peakinfluenced by spin blockade and along the Coulomb valleyabove showing Kondo conductance.In region I no Kondo conductance and thus no chess-board pattern is observed since the barriers connecting thedot to the leads are too opaque to allow for second ordercotunneling. Nevertheless a clear bimodal pattern of spinblockade is visible.In region II Kondo conductance sets in (probably notspin- 12 Kondo [12]) and we can observe a clear chessboardpattern. We find that finite Kondo conductance appearsabove an unsuppressed peak amplitude. Therefore theKondo effect is connected to a spin down electron addedto the edge of the dot.This pattern is swapped in region III. Here we find theKondo effect above the suppressed peak amplitude. Thusthe Kondo effect is induced by a spin-up electron.-0.4-0.5-0.6-0.7-0.8-0.9-1.0-1.1-1.2)Vm(VGIIIIIIIVVSourcenia rDVGXXXXx20x1FIG. 2 (color online). Differential conductance G as a functionof B and VG (dark for high G, white for low G). On the right ofthe dashed line a regular chessboard pattern is observed due toKondo effect and spin blockade. The combination of both effectsyields five different regions. The transitions between theseregions are marked with solid lines. They are studied in detaillater at the positions marked with crosses. Inset: SEM picture ofour device.PRL 97, 176801 (2006) P H Y S I C A L R E V I E W L E T T E R Sweek ending27 OCTOBER 2006176801-2While region IV corresponds to region II, region Vshows again the features of region III.Now that we have identified these 5 regions we willfocus on the details of the transitions between them. This isdone exemplarily at the transition from region III to regionIV.In Fig. 4(a) we have plotted the peak amplitude in grayscale as a function of B and the peak number. The resultingplot is comparable to the original measurement without theCoulomb valleys. What is an alternating behavior of peakamplitudes now becomes a pattern of lines with negativeslope. A change of this pattern should directly reflect achange in the way electronic spins enter the dot. This inturn corresponds to a change of the spin configuration inthe edge of the dot which is exactly what is observed inFig. 4(a). Lines (dashed) with a strong amplitude below thetransition from III to IV (which is marked with a solid line)corresponding to spin-down transport become weak abovethe transition now showing spin-up transport. In analogythose lines (dotted) with a weak amplitude below thetransition become strong above the transition. This isshown in more detail in Fig. 4(b). Traces along linesmarked dashed and dotted in (a) are plotted as a functionof the peak number. A clear crossing of the peak ampli-tudes is visible between peak 40 and 41. Thus the origin forthe swap of the total pattern at the transition from region IIIto IV is identified with the spin blockade signal. The spinfilling mechanism has swapped and the spin configurationhas changed for one parity. The spin configuration under-lying the Kondo effect is not changed as the Kondo effect isnot influenced by this transition. Thus the change in spinpolarization must have happened for the parity, where noKondo effect appeared.Similar analyses were made at all other transitions. Theresults are shown in Fig. 5. Again two neighboring lineswere investigated for each transition as shown before inFig. 4. But this time for each transition the ratio of theamplitude of these lines is plotted as a function of the peaknumber. If there was no spin blockade, one would expectboth peaks to be equal and thus the ratio would be 1. Wefind a swap in the peak ratio at the transitions I to II, II toIII, and III to IV which indicates a change in the spinconfiguration at these transitions. At the first transitionno Kondo effect is visible. At the other two transitions nosignificant influence is found on the Kondo chessboardpattern. As discussed before, this implies that the spinconfiguration for the parity underlying the Kondo effectis not changed although two swaps of the spin blockadeand thus two changes of the spin polarization have oc-curred (one at II to III, another at III to IV). In our opinion48320.150.082IIIIV)b()a(FIG. 4 (color online). (a) Peak amplitude as a function of Band peak number at the transition from III to IV showing onlyfeatures of spin blockade. What is a bimodal pattern in Fig. 2now comes out as a pattern of lines with negative slope. At thetransition the amplitude of these lines swaps, reflecting a changeof the spin configuration. Strong lines become weak and viceversa. (b) Line amplitude along the lines marked dashed anddotted in (a). A crossing appears between peaks 40 and 41.)Vm(VG-1190-1250)Vm(VG-990-1040)Vm(VG-780-820)Vm(VG-645-685)Vm(VG-485-520IIIIIIIVV4.23.84.54G(e /h)2G(e /h)2954520G(e /h)2G(e /h)2904013090G(e /h)2G(e /h)213070145120G(e /h)2G(e /h)2135110145130G(10 e /h)-3 2G(e /h)2)b()a(FIG. 3 (color online). (a) Enhanced plots of the insets markedin Fig. 2. In all five regions amplitude modulations of theCoulomb peaks appear due to spin blockade. Apart fromregion I a clear chessboard pattern is visible due to the Kondoeffect as well. The combination of both effects changes fromregion to region. In II and IV the Kondo effect goes along with astrong amplitude of the Coulomb peak below while the pattern isswapped in III and V. (b) The combination of both effects comesout clearer with the amplitudes of peaks and valleys plotted as afunction of B. For each region the lower graph shows the spinblockade, the upper graph shows the Kondo effect.PRL 97, 176801 (2006) P H Y S I C A L R E V I E W L E T T E R Sweek ending27 OCTOBER 2006176801-3this is not possible if the spin polarization would havechanged twice in the same direction [e.g., 0; 12 ! 1;12 !1; 32]. If so, the spin configuration would have changed forboth parities which should have affected the Kondo effect.Instead, we believe to have observed a switching of thepolarization back and forth [e.g., 0; 12 ! 1;12 ! 0;12].Thus, only for one parity (the one without the Kondoeffect) the configuration is changed.The last transition from region IV to region V is differ-ent. Here the spin blockade stays unchanged, instead wefind a swap of the Kondo pattern marked with circles inFig. 5. We believe that this is due to a sudden change of thenature of the Kondo effect. This might have happenedwithout changing the spin configurations, as no swap inthe spin blockade is observed. However, the slope of thetransition line from region IV to region V marked with asolid line in Fig. 2 implies a different explanation. Theslope seems to fit very nicely the slopes of all othertransitions. Thus one would expect the same physicalorigin to be responsible. This could be possible if twoswaps at once are assumed changing the spin configurationfor both parities [e.g., 0; 12 ! 1;32]. In this case the spinblockade is not affected and the change in the nature of theKondo effect is just due to a new spin configuration.In conclusion, we have found multiple transitions of thespin configuration in a lateral quantum dot in high mag-netic fields as predicted theoretically. These transitions aredetected as changes of a combined spin blockade or Kondoeffect chessboard pattern. They appear either as a swap ofthe spin blockade pattern or as a swap in the Kondo pattern.Regardless of the different form of appearance, the slopesof all transitions yield a common origin. They reflect achange of the spin configuration at the edge of the two-Landau-level quantum dot with increasing electron num-ber. In addition, the combination of spin blockade andKondo effect indicates that a change of the spin polariza-tion back and forth is observed rather than a continuouslyincreasing spin polarization.This work has been supported by BMBF.*Electronic address: rogge@nano.uni-hannover.de[1] L. P. Kouwenhoven, C. M. Marcus, P. L. McEuen,S. Tarucha, R. M. Westerveld, and N. S. Wingreen, inMesoscopic Electron Transport, edited by L. L. Sohn,L. P. Kouwenhoven, and G. Schön, Series E Vol. 345(Kluwer, Dordrecht, 1997), p. 105.[2] D. Loss and D. P. DiVincenzo, Phys. Rev. A 57, 120(1998).[3] 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).[4] J. Kondo, Prog. Theor. Phys. 32, 37 (1964).[5] L. I. Glazman and M. E. Raikh, JETP Lett. 47, 452 (1988).[6] T. K. Ng and P. A. Lee, Phys. Rev. Lett. 61, 1768 (1988).[7] P. L. McEuen, E. B. Foxman, J. Kinaret, U. Meirav, M. A.Kastner, N. S. Wingreen, and S. J. Wind, Phys. Rev. B 45,11 419 (1992).[8] M. Stopa, W. G. van der Wiel, S. De Franceschi,S. Tarucha, and L. P. Kouwenhoven, Phys. Rev. Lett. 91,046601 (2003).[9] A. Wensauer, M. Korkusinski, and P. Hawrylak, Phys.Rev. B 67, 035325 (2003).[10] D. Kupidura, M. C. Rogge, M. Reinwald, W. Wegscheider,and R. J. Haug, Phys. Rev. Lett. 96, 046802 (2006).[11] M. Ciorga, A. Wensauer, M. Pioro-Ladriere,M. Korkusinski, J. Kyriakidis, A. S. Sachrajda, andP. Hawrylak, Phys. Rev. Lett. 88, 256804 (2002).[12] C. Fühner, U. F. Keyser, R. J. Haug, D. Reuter, and A. D.Wieck, Phys. Rev. B 66, 161305(R) (2002).[13] M. Keller, U. Wilhelm, J. Schmid, J. Weis, K. vonKlitzing, and K. Eberl, Phys. Rev. B 64, 033302 (2001).1.61.00.4peak)yellav(Peak number(valley)FIG. 5 (color online). For transitions I to IV the ratio of theamplitude of lines similar to those in Fig. 4(b) is plotted as afunction of the peak number (squares). Swaps corresponding tochanges of the spin configuration appear at the transitions I to II,II to III, and III to IV. No swap was observed at the lasttransition. Here the Kondo pattern swaps (circles). Please notethat the data were not taken at the same magnetic field but at thepoints marked with crosses in Fig. 2.PRL 97, 176801 (2006) P H Y S I C A L R E V I E W L E T T E R Sweek ending27 OCTOBER 2006176801-4

Multiple transitions of the spin configuration in quantum dots

Abstract

Similar works

Full text

Available Versions

Institutional Repository of Leibniz Universität Hannover