Constructive role of non-adiabaticity for quantized charge pumping
B. Kaestner, C. Leicht, P. Mirovsky, V. Kashcheyevs, E. V. Kurganova, U. Zeitler, K. Pierz, H. W. Schumacher
aa r X i v : . [ c ond - m a t . m e s - h a ll ] J u l Constructive role of non-adiabaticity for quantized chargepumping
B. Kaestner ∗ , C. Leicht ∗ , P. Mirovsky ∗ , V. Kashcheyevs †, ∗∗ , E. V. Kurganova ‡ , U.Zeitler ‡ , K. Pierz ∗ and H. W. Schumacher ∗ ∗ Physikalisch-Technische Bundesanstalt (PTB), Bundesallee 100, 38116 Braunschweig † Faculty of Computing, University of Latvia, Riga LV-1586, Latvia ∗∗ Faculty of Physics and Mathematics, University of Latvia, Riga LV-1002, Latvia ‡ Nijmegen High Field Magnet Laboratory, Toernooiveld 7, 6525 ED Nijmegen, The Netherlands
Abstract.
We investigate a recently developed scheme for quantized charge pumping based on single-parameter modulation.The device was realized in an AlGaAl-GaAs gated nanowire. It has been shown theoretically that non-adiabaticity isfundamentally required to realize single-parameter pumping, while in previous multi-parameter pumping schemes it causedunwanted and less controllable currents. In this paper we demonstrate experimentally the constructive and destructive role ofnon-adiabaticity by analysing the pumping current over a broad frequency range.
Keywords: single electrons pumps
PACS:
Pumping transport mechanisms have attracted muchinterest as an alternative means to generate charge andspin currents in the absence of a bias voltage. The pump-ing current results from periodic modulation of certainsystem parameters of a nanostructure connected to leads.Of particular interest has been the quantized regimewhen the current varies in steps of e · f as a function ofthe system parameters, where e is the electron charge and f is the frequency of modulation.Much effort has been devoted to the adiabatic regime,when the variation of the parameters is slow compared torelaxation times of the system, and current quantizationhas been achieved almost 20 years ago [1]. Recently, ascheme has been developed in which only one parameteris varied [2, 3] and therefore non-adiabaticity is an essen-tial requirement to achieve pumping [4]. In this regimethe system is driven out of equilibrium, which was previ-ously considered to counteract the quantized regime [5].In the following we will demonstrate both, the destruc-tive and constructive role of non-adiabaticity, dependingon the pumping frequency f .The device is similar to those used in [3]. A schematicis shown in Fig. 1(a) and the corresponding potentiallandscape U ( x ) along the channel in (b). It was realizedin an AlGaAs/GaAs heterostructure. A 700 nm wide con-striction with a smooth curvature was generated insidethe two-dimensional electron gas by etching the dopedAlGaAs layer. The device was contacted at source (S)and drain (D) using an annealed layer of AuGeNi. Theconstriction is crossed by Ti-Au finger gates G1 and G2.A quantum dot (QD) with a quasibound state y is formedby applying sufficiently large negatice voltages V and V FIGURE 1. (a) Schematic of the device structure. (b)Schematic of the potential landscapes during loading and un-loading as generated by the device in (a). to G1 and G2, respectively. An additinoal sinusoidal sig-nal of power P RF is coupled to G1. In this way the energy e of the quasibound state drops by D E L below the chem-ical potential m of the leads during the first half-cycleand can be loaded with an electron [see Fig. 1(b)]. Dur-ing the second half-cycle, e is raised sufficiently fast by D E U above m and can be unloaded to the right. Hence acurrent is driven through the sample. Details of the mech-anism can be found in [6].The pumped current I as a function of V and V Constructive role of non-adiabaticity for quantized charge pumping December 6, 2018 1
IGURE 2.
Pumping current as a function of V and V for two different powers. Contours correspond to variation incurrent of 1.5pA is shown in Fig. 2 for two different powers. The mea-surements were performed at temperature T =
300 mK.Countours correpsond to variation in current of 1.5 pAand the plateaus to multiples of e f . The plateaus arebound for more positive V by insufficient unloading todrain and for more negative V by insufficient loadingfrom source [6]. Variation in P RF shifts this boundaryand allows calibration of the effective modulation am-plitude applied to the gate, as outlined in [7]. The stepedges along V are determined by escape of previouslycaptured source-electrons back to source [8]. The whitearea in Fig. 2 corresponds to the region, where electronsmay be loaded through the barrier at G2 and quantizedpumping breaks down.In order to determine the role of non-adiabaticity inthis pumping mechanism we analyse the frequency de-pendence at a point in V - V -space where both, the con-structive and destructive nature becomes visible, namelyfor V = −
126 mV and V = −
140 mV. The result isshown in Fig. 3. In order to extract the effects only dueto the f -dependence the voltage modulation amplitudeat G1 needs to be kept constant. To this end, the specificrf-power was determined for each frequency accordingto [7], and the I = e f - plateau was analysed. The contourcorresponding to I = . e f is shown in the inset of Fig. 3for each frequency ( f = , . . . ,
500 MHz). The contourwas only traced for the relevant step-edge region.The I ( f ) dependence implies that the average num-ber of pumped electrons per cycle, n p = I / e f , van-ishes as f is reduced, as expected when only a singlevoltage parameter is modulated close to the adiabaticlimit [4, 9, 3, 10]. From the inset of Fig 3 one can seethat this corresponds to a shift in the left border of the e f -plateau toward positive V . Since this step-edge marksthe transition where escape of previously captured elec-trons back to source is prevented [6, 8] the constructiveeffect of non-adiabaticity becomes visible: only when f is large enough, there will not be sufficient time for es-cape and the electron will contribute to I . -150 -140 -130 -120 -110-300-250-200-150-100 V i n m V V in mV
100 100010 -4 -3 -2 -1 C u rr en t I / e f Frequency f in MHz FIGURE 3.
Current normalized by e f as function of fre-quency. Inset shows traced contours for the relevant range in V - V -space. The arrow indicates the voltages where the currentwas measured. Increasing f beyond the optimal frequency range, n p reduces again as predicted in [3]. From the inset ofFig 3 one can see that this corresponds to a shift in theupper border of the e f -plateau toward negative V . Herethe destructive nature of non-adiabaticity is illustrated:since this step-edge corresponds to insufficient unloadingto drain [6] there is not sufficient time at such highfrequencies to empty the dot. Consequently the electroncannot contribute to the pumping current and n p drops.In general, driving a quantized current by a singlemodulation parameter, which is only possible in the non-adiabatic regime, is of fundamental importance in the de-velopment of a scalable quantum current standard [11]. Acknowledgements:
This work has been supported byEURAMET joint research project with European Com-munity’s 7 th Framework Programme, ERANET Plus un-der Grant Agreement No. 217257. C.L. has been sup-ported by International Graduate School of Metrology,Braunschweig. Funding by EuroMagNET under the EUContract No. RII3-CT-2004- 506239 is acknowledged.
REFERENCES
1. H. Pothier, et al. , Europhys. Lett. , 249–254 (1992).2. M. D. Blumenthal, et al. , Nature Physics , 343 – 347(2007).3. B. Kaestner, et al. , Phys. Rev. B , 153301 (2008).4. M. Moskalets, and M. Büttiker, Phys. Rev. B , 205320(2002).5. K. Flensberg, Q. Niu, and M. Pustilnik, Phys. Rev. B ,R16291–R16294 (1999).6. C. Leicht, et al. Physica E , 911 – 914 (2009).7. B. Kaestner, et al. , Appl. Phys. Lett. , 192106 (2008).8. V. Kashcheyevs, and B. Kaestner, Phys. Rev. Lett. ,186805 (2010).9. L. E. F. Foa Torres,
Phys. Rev. B , 245339 (2005).10. L. Arrachea, Phys. Rev. B , 249904(E) (2005). Constructive role of non-adiabaticity for quantized charge pumping December 6, 2018 2
1. V. F. Maisi, et al , New Journal of Physics , 113057(2009)., 113057(2009).