We demonstrate the operation of a quantum spin pump based on cyclic
radio-frequency excitation of a GaAs quantum dot, including the ability to pump
pure spin without pumping charge. The device takes advantage of bidirectional
mesoscopic fluctuations of pumped current, made spin-dependent by the
application of an in-plane Zeeman field. Spin currents are measured by placing
the pump in a focusing geometry with a spin-selective collector.Comment: related papers available at http://marcuslab.harvard.ed

Marcus, C. M.

Potok, R. M.

Umansky, V.

Watson, Susan K.

English

arXiv

Watson, Susan

Potok, R.

M. Marcus, C.

Copenhagen University Research Information System

u n i ve r s i t y  o f  co pe n h ag e n  Københavns UniversitetExperimental Realization of a Quantum Spin Pump Watson, Susan;  Potok, R.; M. Marcus, C.; Umansky, V.Published in:Physical Review LettersDOI:10.1103/PhysRevLett.91.258301Publication date:2003Citation for published version (APA):Watson, S., Potok, R., M. Marcus, C., & Umansky, V. (2003). Experimental Realization of a Quantum SpinPump. Physical Review Letters, 91(25), 258301. https://doi.org/10.1103/PhysRevLett.91.258301Download date: 02. Feb. 20201Experimental Realization of a Quantum Spin PumpSusan K. Watson*†, R. M. Potok†, C. M. Marcus†, and V. Umansky‡*Department of Physics, Middlebury College, Middlebury, VT 05753, USA†Department of Physics, Harvard University, Cambridge, MA 02138, USA‡Braun Center for Submicron Research, Weizmann Institute of Science, Rehovot 76100,IsraelWe demonstrate the operation of a quantum spin pump based on cyclic radio-frequency excitation of a GaAs quantum dot, including the ability to pump purespin without pumping charge. The device takes advantage of bidirectionalmesoscopic fluctuations of pumped current, made spin-dependent by the applicationof an in-plane Zeeman field. Spin currents are measured by placing the pump in afocusing geometry with a spin-selective collector.Using electron spin to encode information in semiconductors holds promise for inte-grating computation and storage [1] and, in coherent systems, is expected to provide sig-nificantly increased immunity from environmental decoherence compared with conven-tional charge-based electronics [1, 2]. Among the needed elements for any spin-basedelectronic system is a device that generates a spin current, the analog of a battery in con-ventional electronics. Candidates for such devices include injection schemes based onmagnetic semiconductors [3, 4] and ferromagnetic metals [5, 6], ferromagnetic resonancedevices [7], and a variety of spin-dependent pumps [8-14].In this Letter, we demonstrate the operation of such a quantum-dot–based spinpump—including the ability to pump pure spin without pumping charge—using a gate-defined lateral quantum dot fabricated on a GaAs/AlGaAs heterostructure. Pumping of2charge using cyclic gate voltages applied to a phase-coherent dot has been the subject ofnumerous investigations (mostly theoretical) in the past several years [15-20]. Quantumpumps are closely related to classical charge pumps using Coulomb blockade [21, 22] aswell as higher-frequency mesoscopic photovoltaic effects [20, 23-25] and photon-assistedtunneling [26]. A recent proposal [8] (MCM) considered a quantum-dot-based chargepump in the presence of sizable Zeeman splitting, and showed that such a device wouldfunction as a phase-coherent spin pump. An important feature of the MCM proposal isthat it remains operational regardless of whether the pumped current arises from adiabaticpumping [15-18, 20], mesoscopic rectification [18, 27, 28], or photovoltaic mechanisms[20, 23] as long as the fluctuations of pumped current are larger than the average, so thatboth positive and negative current can be generated and controlled by external parameterssuch as device shape or applied magnetic flux.In order to realize the spin pump device experimentally, radio-frequency (rf) sinu-soidal voltages were applied to two shape-defining gates of a quantum dot, producing adc current through the quantum dot due to a combination of adiabatic pumping and recti-fication effects. As discussed in detail below, while pumped charge can be directly meas-ured directly across the device, measuring the pumped spin is more subtle, and in the pre-sent set-up is detected using an electron focusing configuration with a quantum pointcontact operating as a spin detector [29, 30].Due to quantum coherence, the direction of the pumped current is a mesoscopicallyfluctuating quantity with zero average. In the absence of an external magnetic field,B|| = 0, the two spin states are degenerate and the pumped currents for spin up (I!) andspin down (I!) are identical, fluctuating together as control parameters are swept (this is3also the case for mesoscopic rectification [28]). In this zero-field case, pumping induces anet charge current Ic = I!+ I! ∀ 0, but no net spin current, Is = I! ∀ I! = 0, as illustratedschematically in Fig. 1a. For sufficiently strong in-plane magnetic fields, g#∃B|| >(kT, %), spin-up and spin-down pumped currents are uncorrelated. Here, % is the levelbroadening due to escape and dephasing, g ~ –0.4 is the electron g factor, and #B is theBohr magneton. In this high-field case, pumped charge is comprised of independent con-tributions of I! and I! (Fig. 1b), and in general a nonzero spin current exists. In practice, itis straightforward in this regime to tune the charge current to zero (using gate-defined dotshape or a small applied perpendicular magnetic flux) resulting in a pure spin current.The variance of the pumped charge (spin) current, Ic,s, is given by!"! #" ! !!" ∀ !#" ∃ "!!!# ! " !!" ∃ !!!#% & . At large B||, where I! and I! become uncorrelated!!!! ∀ !# ∃ , the typical spin current Is becomes nonzero and the variance of Ic decreases bya factor of two compared to its low field value, where !!!! ∀ !!!  (neglecting the effects oftime-reversal symmetry and spin-orbit coupling [13]).To detect the presence of a spin current, we take advantage of a spin-sensitive elec-tron focusing geometry (inset, Fig. 2), which allows the pumped current to be focusedinto a collector quantum point contact (QPC), as shown in Fig. 2. In moderate in-planefields,   !∀B|| #~ 3T , the collector QPC has been shown to act as a spin-sensitive detectorwhenever its conductance gc is tuned (by gate voltages) to !" ! !#" $  [29, 30]. In thisspin-sensitive regime, the base-collector voltage reflects the polarization of the currentimpinging upon the collector QPC.  As a control, when the collector QPC is non-spin-4sensitive, which is achieved—even in high fields—by setting !∀!"# !#! $ , the base-collector voltage signal reflects the total charge current impinging on the collector QPC.The complete system, comprising the quantum-dot spin pump plus the QPC-focusingtest structure, was fabricated on a GaAs/AlGaAs 2DEG using e-beam patterned CrAudepletion gates and nonmagnetic (PtAuGe) ohmic contacts. The high-mobility material! ∀ !"! # #$%!"&# ∃#$ ∃#% &  was useful for obtaining good focusing but is not necessary forthe operation of the spin pump itself. This mobility, and sheet density ! ! !"# ∀!$!!"##% ,gave a mean free path of !"!! . The quantum dot, which has an area of ! ! "#$!"% , istypically operated with one fully open channel in each of its point contact leads,!"#$%! " !"#$%# " ### & .Focusing was first tested and calibrated using a current-bias configuration!"#$% !!&’∀ # . Results are shown in Fig. 2. Next, two sinusoidal signals at 10 MHz withcontrollable phase difference, !, were applied (via synchronized Agilent 33250 synthe-sizers) to two of the confining gates of the dot: !"#$%! $! ∀ # !&’! ∃ !! "#$ %$! ∀ ,!"#$%! $! ∀ # !&’! ∃ !! "#$ %$ ∃&! ∀ . Applying ac gate voltages of 70 mV (comparable to thecharacteristic gate-voltage scale of gate-induced mesoscopic conductance or pumpingfluctuations (see Fig. 3)) induced a dc current through the dot on the scale of ~ 10–100pA, measured using an Ithaco 1211 current amplifier with input impedance ~20 ∀ (muchlower than the ohmic contact resistance of ~1k∀.) The rf applied to the gates was modu-lated at 11 Hz to allow lock-in detection of both the pumped current, measured throughthe base-emitter circuit, and the voltage across the collector QPC.5The sinusoidal dependence of pumped current on !, ! !∀ # ! !""#$ !∀ #  (Fig. 3a, inset) isconsistent with both adiabatic quantum pumping [17, 19] and capacitively coupled recti-fication [28]. However, the fact that the magnitude of current is typically larger than oneelectron per cycle (=1.6 pA at 10 MHz) suggests that the pumped current is dominated byrectification rather than adiabatic pumping. Again, this does not affect the performance ofthe spin pump.Figure 3 shows pumped current and collector voltage at !!! ! ""  for both spin-selective and nonselective settings of the collector QPC, as a function of dc voltage onone of the shape-defining gates of the quantum dot [31]. The point contacts of the dotwere each set at !!! " , the pumping amplitude was !! ! !" ! #$"!  and the phase was! ∀ !# " . These data illustrate our main experimental observation: when the collectorQPC is set to !"! !#! $ , and hence is not spin selective, the collector voltage closelyfollows the pumped current. In contrast, when the collector QPC is spin selective,!"! !#" $ , the collector voltage appears unrelated to the pumped total charge current.The fact that only the spin-selective detector shows a signal unrelated to the total currentmeans that a spin current, fluctuating independently from the total current, is being gen-erated by the pump. One may readily identify in Fig. 3 several zeros of the total currentand see that the spin currents measured at these values of !"#!  are nonzero. At thesepoints, the pump operated as a pure spin pump, producing tens of spins per cycle, withzero net charge being pumped.The corresponding control experiment at !!! ! " (Fig. 4) again compares collectorvoltages measured at !"! !#! $  and !"! !#" $ . In this case, there is little dependence ofthe collector voltage on the collector QPC conductance. This behavior is expected when6the collector QPC is not spin selective and the quantum dot pump produces no spin po-larized current.In summary, we have demonstrated a mesoscopic spin pump using an ac drivenphase-coherent quantum dot in a Zeeman field. Spin current—including pure spin cur-rent, without any charge current—is detected using a spin-sensitive focusing technique[29, 30]. While this experiment required the application of a sizeable in-plane magneticfield, one can expect similar results using permanent magnets microfabricated along withthe quantum dot. This would be particularly effective in materials with a larger g factorthan GaAs. It is of interest to clarify how spin-orbit coupling affects the operation of thepump [13]. We speculate that in strong spin-orbit materials it may be sufficient to breaktime-reversal symmetry with a small applied field (on the scale of a few flux quantathough the dot, typically of order 0.01T for a square-micron dot area). These interestingextensions await further experimental investigation.We thank Joshua Folk for valuable discussions and assistance in carrying out themeasurements, and Piet Brouwer for useful discussions. Research at Harvard was sup-ported by the DARPA-SpinS program and the National Science Foundation under DMR0072777. R. Potok acknowledges support of an ARO-QC Fellowship though the ArmyResearch Office. S. Watson acknowledges support from Middlebury College and the Na-tional Science Foundation (DMR-0074930).7References [1] S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnar, M.L. Roukes, A. Y. Chtchelkanova, and D. M. Treger, Science 294, 1488 (2001). [2] Semiconductor Spintronics and Quantum Computation, D. Awschalom, N. Samarth,and D. Loss, (eds.), New York: Springer (2002). [3] R. Fiederling, M. Keim, G. Reuscher, W. Ossau, G. Schmidt, A. Waag, and L. W.Molenkamp, Nature 402, 787 (1999). [4] Y. Ohno, D. K. Young, B. Beschoten, F. Matsukura, H. Ohno, and D. D. Awscha-lom, Nature 402, 790 (1999). [5] W. Y. Lee, S. Gardelis, B. C. Choi, Y. B. Xu, C. G. Smith, C. H. W. Barnes, D. A.Ritchie, E. H. Linfield, and J. A. C. Bland, J. Appl. Phys. 85, 6682 (1999). [6] P. R. Hammar, B. R. Bennett, M. J. Yang, and M. Johnson, Phys. Rev. Lett. 83, 203(1999). [7] Y. Tserkovnyak, A. Brataas, and G. E. W. Bauer, preprint (cond-mat/0208091); Y.Tserkovnyak, A. Brataas, and G. E. W. Bauer, Phys. Rev. Lett. 88, 117601 (2002). [8] E. R. Mucciolo, C. Chamon, and C. Marcus, Phys. Rev. Lett. 89, 146802 (2002). [9] Junling Wu, Baigeng Wang, and Jian Wang, Phys. Rev. B 66, 205327 (2002). [10] T. Aono, Phys. Rev. B 67, 155303 (2003). [11] Wei Zheng, Junling Wu, Baigeng Wang, Jian Wang, Qingfeng Sun and Hong Guo,preprint (cond-mat/ 0211460). [12] P. Sharma, and C. Chamon, Phys. Rev. Lett. 87, 096401 (2002).[13] M. Governale, F. Taddei, and R. Fazio, preprint (cond-mat/ 0211211).8 [14] Martin J. Stevens, Arthur L. Smirl, R. D. R. Bhat, Ali Najmaie, J. E. Sipe, and H.M. van Driel, Phys. Rev. Lett. 90, 136603 (2003). [15] B. Spivak, F. Zhou, and M. T. B. Monod, Phys. Rev. B 51, 13226 (1995). [16] F. Zhou, B. Spivak, and B. Altshuler, B. Phys. Rev. Lett. 82, 608 (1999). [17] P. W. Brouwer, Phys. Rev. B 58, 10135 (1998).[18] M. Switkes, C. M. Marcus, K. Campman, and A. C. Gossard, Science. 283, 1905(1999). [19] T. A. Shutenko, I. L. Aleiner, and B. L. Altshuler, Phys. Rev. B 61, 10366 (2000). [20] M. G. Vavilov, V. Ambegaokar, and I. L. Aleiner, Phys. Rev. B 63, 195313 (2001). [21] H. Pothier, P. Lafarge, C. Urbina, D. Esteve, and M. H. Devoret, Europhys. Lett. 17,249 (1992). [22] L. P. Kouwenhoven, A. T. Johnson, N. C. van der Vaart, C. J. P. M. Harmans, andC. T. Foxon, Phys. Rev. Lett. 67, 1626 (1991).[23] V. I. Fal'ko, Europhyics Letters. 8, 785 (1989).[24] A. A. Bykov, G. M. Gusev, Z. D. Kvon, D. I. Lubyshev, and V. P. Migal, JETPLetters 49, 13 (1989).[25] L. DiCarlo, C. M. Marcus and J. S. Harris Jr., preprint (cond-mat/ 0304397).[26] L. P. Kouwenhoven, S. Jauhar, J. Orenstein, P. L. McEuen, Y. Nagamune, J. Moto-hisa, and H. Sakaki, Phys. Rev. Lett. 73, 3443 (1994).[27] H. Linke, W. Sheng, A. Lofgren, H. Q. Xu, P. Omling, and P. E. Lindelof, Euro-physics Letters 44, 341 (1998); H. Linke, T. E. Humphrey, A. Lofgren, A. O.Sushkov, R. Newbury, R. P. Taylor and P. Omling, Science 286, 2314 (1999).[28] P. W. Brouwer, Phys. Rev. B 63, 121303 (2001).9 [29] R. M. Potok, J. A. Folk, C. M. Marcus, and V. Umansky, Phys. Rev. Lett. 89,266602 (2002). [30] J. A. Folk, R. M. Potok, C. M. Marcus, and V. Umansky, Science 299, 679 (2003). [31] To compensate for a small, unintentional cross-coupling between the collector QPCvoltage and the gates of the emitter-dot, the current data shown in Figs. 3 and 4,measured at various collector gate voltages, are shifted horizontally (by < 20mV) tobring the traces into alignment. Collector voltage traces, reflecting either spin po-larization or total current, depending on setting of the collector QPC, are then shiftedhorizontally by the same amount as their corresponding current trace. Similarly, thecollector voltage exhibits a smooth background that shifts linearly with Vdc1 of theemitter dot due to capacitive cross-coupling. This smooth background has been sub-tracted from traces in Figs. 3 and 4.10(a) (b)4003002001000-100Counts-20 0 20IPump (A)4003002001000-100Counts-20 0 20IPump (A)EZ0x10-12-100-50050100-300 -250 -200 -150 -100 -50Shape  or  B⊥IcIsB||  00x10-12-100-50050100Current-300 -250 -200 -150 -100 -50Shape or B⊥B||=0I↑ , I↓IcIs≠I↑ , I↓Figure 1. Schematic illustration of how mesoscopic pumping fluctuations plus Zeemansplitting can give rise to independent fluctuations of charge current Ic = I!+ I! and spincurrent Is = I! ∀ I!, based on Ref. 8. (a) At B|| = 0 one has I! = I! and hence Is = 0. (b) Atlarge in-plane fields, B|| > (kT, #), (see text) spin degeneracy is lifted, I! is uncorrelatedwith I!, and in general Is ∀ 0. In this case, one may even have a pure spin pump when Is ∀0 while Ic = 0.1186420Collector Voltage (µV)-250 -200 -150 -100 -50 0 50B⊥ (mT)Figure 2. The base-collector voltage as a function of perpendicular magnetic field, B!.The first (green dot) and second (red dot) focusing peaks in the base-collector voltageoccur when the spacing between the emitter (quantum dot) and the collector (QPC) is amultiple of the cyclotron diameter. To find the focusing peaks, a current bias of 1 nA wasapplied across the dot. Inset: Electron micrograph of the dot/focusing device, with addedcircuit and schematic trajectories. Electrons emitted from the quantum dot emitter, “E”,follow ballistic trajectories through the base region, “B”, into the collector, “C”. Ac volt-ages Vgate1 and Vgate2 are applied to shape-defining gates.12(a) -20 -10 0 10I (pA)φ pi/2 pi 3pi/2 2pi200150100500-50Pumped Current (pA)-350 -300 -250 -200 -150 -100(b)0.60.40.20.0-0.2Collector Voltage (µV)-350 -300 -250 -200 -150 -100Vdc1 (mV)B|| = 4T0gc = 2e2/hgc < e2/hFigure 3. (a) The pumped charge current at !!! ! "" and ! ∀ !# "  as a function of dotshape, controlled by dc gate voltage Vdc1. Traces at slightly different collector QPC set-tings, both with !"! !#! $  (gray and black) are similar, and are also similar to the tracewith !"! !#" $  (green). This is not surprising, as the collector QPC should not affectpumping by the emitter. Inset: Pumped current as a function of the phase ! between theVgate1 and Vgate2. (b) Collector voltages (relative to the base region) on the second focus-ing peak under the same conditions as corresponding traces in (a). For spin-nonselectivecollector QPC, !"! "#" $ , (gray and black) the collector voltages track pumped current,indicating that the voltage measures the total charge current. For spin-selective collectorQPC !"! !#" $  (green), the collector voltages are distinctly different from the pumpedcurrent and from traces at !"! "#" $ , indicating a nonzero spin current.13-0.2-0.10.00.1Collector Voltage (µV)-180 -160 -140 -120 -100 -80 -60Vdc1(mV)B|| = 0gc=2e2/hgc < e2/hFigure 4. Collector voltage as a function of dot shape for !!! ! "  at two different collectorQPC settings with !"! !#" $  and one with !"! "#" $ . Unlike the situation at!!! ! "" ,the collector voltage is not sensitive to the conductance of the collector QPC. This is an-ticipated as there is no spin selectivity of the collector QPC nor is there a pumped spincurrent from the dot.

Experimental Realization of a Quantum Spin Pump

Experimental Realization of a Quantum Spin Pump

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