Highly Tunable Hybrid Quantum Dots with Charge Detection
C. Rössler, B. Küng, S. Dröscher, T. Choi, T. Ihn, K. Ensslin, M. Beck
HHighly Tunable Hybrid Quantum Dots with Charge Detection
Highly Tunable Hybrid Quantum Dots with Charge Detection
C. R¨ossler, a) B. K¨ung, S. Dr¨oscher, T. Choi, T. Ihn, K. Ensslin, and M. Beck Solid State Physics Laboratory, ETH Zurich, 8093 Zurich, Switzerland Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland (Dated: 10 November 2018)
In order to employ solid state quantum dots as qubits, both a high degree of control over the confinementpotential as well as sensitive charge detection are essential. We demonstrate that by combining local anodicoxidation with local Schottky-gates, these criteria are nicely fulfilled in the resulting hybrid device. To thisend, a quantum dot with adjacent charge detector is defined. After tuning the quantum dot to contain onlya single electron, we are able to observe the charge detector signal of the quantum dot state for a wide rangeof tunnel couplings.PACS numbers: 73.63.Kv, 73.63.Nm, 73.23.HkKeywords: Quantum Dot, Local Anodic Oxidation, Charge Readout, Single ElectronQuantum dots (QDs) are a playground for quantumengineered devices, since many system properties liketunnel coupling, energy spacing, etc. can be controlledand varied. In particular, electrostatically defined quan-tum dots, created by local depletion of a two-dimensionalelectron gas (2DEG) in an Al x Ga − x As heterostructure,allow to build charge- and spin-qubits . To this end,both a high degree of tunability of the confinement po-tential as well as the capability to sense the charge stateof the QD are needed. By employing Schottky-split-gatesit is possible to tune the local electrostatic potential in away that only one electron is left in the QD . Measur-ing the conductance of a nearby quantum point contact(QPC) facilitates to determine the charge state of theQD even if no measurable current flows through the QD .However, electrostatic screening of metal gates betweenQD and QPC strongly decreases the readout fidelity ascompared to fabrication techniques without metal gates,like etching or local anodic oxidation (LAO) . But thelatter fabrication techniques have the disadvantage of alow tunability because the confinement potential is pre-defined after fabrication. Tackling this issue by employ-ing a patterned top gate appears to sacrifice the readoutcapabilities of LAO defined QDs . The combination of lo-cal Schottky-gates with LAO promises to combine highlytunable confinement potentials with good detector read-out fidelity.The fabrication is carried out on an Al x Ga − x As het-erostructure. The 2DEG resides at the heterointerface, z ≈
40 nm beneath the surface. The 2DEG’s sheet den-sity is n S = 4 . × m − with a Drude mobility of µ = 33 m / Vs, as determined in Van-der-Pauw geometryat a temperature of T = 4 . a) Electronic mail: [email protected] I QPC I QD G1 G2 G3 G4 200 nm FIG. 1. (color online) AFM micrograph of the sample surface(black). The vertical and diagonal oxide lines are 10 nm highand define a QPC in the underlying 2DEG. The 2DEG arealabeled G4 on the left hand side is used to capacitively controlthe current through the QPC. Applying voltages to the 30 nmthick Schottky gates G1, G2 and G3 (yellow) defines a QD. V TIP ∼ −
30 V to the AFM tip at ambient conditions,the heterostructure is locally oxidized and the underly-ing 2DEG is depleted . Writing oxide lines (vertical anddiagonal lines in Fig. 1) left of the QD-gates defines aQPC. In a pioneering work on combining Schottky-gateswith LAO , the e-beam lithography was done after LAO.Hence, the alignment had to be done by e-beam lithog-raphy with respect to pre-defined markers, limiting theaccuracy to ∆ x ∼
50 nm . We find that the accuracy ofpositioning the oxide line is limited by the AFM lithogra-phy step to ∆ x ∼
10 nm and can easily be compensatedin the experiment by applying appropriate voltages to thegates. On the right side of the central oxide line a QD(white dashed circle in Fig. 1) is defined between gatesG1, G2, G3 and the oxide line.Applying voltages V (cid:46) − . V = 0. Applying positive gate-voltages during cooldown should create a depleting (negative) potential once thegates are set to zero at low temperature. It turns outthat this so called pre-biased cooldown works very wellon the shallow-2DEG structure employed here. Addi-tionally a bias V can be applied to the QPC-circuit a r X i v : . [ c ond - m a t . m e s - h a ll ] S e p ighly Tunable Hybrid Quantum Dots with Charge Detection 2 g Q D ( µ S ) I Q P C ( n A )
10 0.5 1.0 1.5 2.0 V G1 (V) T el = 100 mK dV SD-QD = 5 µV V G2 = -0.25 V V G3 = -0.1 V V = 0.05 V -0.4 -0.5 -0.6 (a) (b) V SD-QPC = 500 µV dV G2 = 50 µV V G4 = -0.015 V g T C ( µ S ) (c) -0.2 -0.1 0 -0.45 FIG. 2. (a) Differential conductance of the QD g QD , plot-ted as a function of gate voltage V G1 . Maxima in g QD areCoulomb oscillations. For gate voltages V G1 < − .
57 V (left),no more Coulomb oscillations are observed. (b) Currentthrough the QPC I QPC , plotted for the same gate voltages.Kinks in I QPC are caused by a change of the QD occupancy byone electron. (c) Transconductance g TC = dI QPC /dV G2 , mea-sured by modulating voltage V G2 and detecting dI QPC withlock-in technique. Local minima reflect the charge occupancyof the QD. with respect to the QD-circuit, thereby acting as an in-plane-gate.The source-drain current of both circuits is measuredat an electron temperature of T el ≈
100 mK as a functionof the voltages applied to the Schottky gates. Figure 2(a)shows the differential conductance g QD of the QD-circuit,measured with lock-in technique as a function of the volt-age applied to gate G1. Oscillations in g QD indicate thata QD is defined between the central oxide line and gatesG1, G2 and G3, as sketched in Fig. 1. Since gate G1also defines one tunnel barrier of the QD, the ampli-tude of the Coulomb oscillations decreases rapidly untilno measurable current flows for V G1 < − . I QPC through the QPCis shown in Fig. 2(b). Stepping V G1 to lower values de-creases I QPC due to capacitive crosstalk between the gateand the QPC. On top of that, I QPC increases step-likewhen the occupancy of the QD changes by one electron.Vertical dashed lines emphasize that the steps in I QPC co-incide with maxima in g QD . Moreover, the QPC is stillsensitive to the charge state of the QD when g QD be-comes unmeasurably small. The step height in Fig. 2(b)is ∆ I QPC /I QPC ≈
10 % at V G1 ≈ − . Technique: Schottky Hybrid Oxidation∆ I QPC /I QPC : 1 ... ...
15 % 5 ...
40 %TABLE I. QPC read-out efficiency ∆ I QPC /I QPC of QDs fab-ricated by different methods. Values obtained from . which is reduced when depleting large areas in order todefine a double QD. Table I shows typical readout ef-ficiencies of QDs fabricated by different methods. Thestep height of the hybrid structures lies in between typ-ical values of purely Schottky- and purely AFM-definedQDs, with the spread being due to different sample ge-ometries and QPC pinch-off slopes.Figure 2(c) shows the transconductance g TC = dI QPC /dV G2 measured by modulating the voltage V G2 and detecting dI QPC with lock-in technique. Thetransconductance minima directly represent the chargeoccupancy of the QD . As expected, the peak shapeof transconductance minima and Coulomb oscillationsare identical when the QD is weakly coupled to the leads.In contrast, the peak shape shows clear deviations in thecase of strong coupling. For example, the rightmost threeCoulomb peaks are asymmetric in direct transport, butsymmetric in the transconductance dip. This deviationhas to our knowledge not been observed before in directtransport and demonstrates the high fidelity of our de-tector readout.In order to explore the tunability of our scheme, an-other sample with similar geometry is tuned to a veryasymmetric configuration where it is only coupled tothe 2DEG underneath gate G1 ( V G1 > − . V G2 < − . V G3 = − g TC , plotted in falsecolors as a function of V G1 and V G2 . The transconduc-tance is finite and positive throughout the whole param-eter range, indicating that the QPC is neither pinched offnor insensitive to changes in the local electrostatic poten-tial. Single resonances with different slopes (marked byblack arrows) are caused by trapped states in the environ-ment, most likely in the doping layer or in the oxide line.A series of Coulomb resonances (white arrows) exhibitsthe same slope of ∆ V G1 / ∆ V G2 ≈
4, indicating that theycorrespond to charging events of the same QD. Moreover,the stronger coupling of gate G1 as compared to G2 con-firms that the QD has been ”pushed” away from gatesG2 and G3, towards the oxide line and gate G1. EachQD resonance is characterized by an abrupt end at verynegative V G1 (bottom) and a washed out regime for lessnegative V G1 (top). This observation is expected fromthe sample’s design, where gate G1 controls the heightof the tunnel barrier between QD and 2DEG. Making V G1 more negative and therefore increasing the tunnelbarrier reduces the tunnel rate between QD and 2DEGuntil it is comparable to the gate modulation frequencyof f LI = 193 Hz and the QD can not compensate thegate modulation by electron tunnelling. The full widthat half maximum FWHM ≈ g TC is dominated by the modulation amplitude dV G2 . Forsmaller tunnel barriers, the leftmost two resonances startighly Tunable Hybrid Quantum Dots with Charge Detection 3 -2 -1.8 -1.6 -1.4 -1.2 -1-200-150-100-500 V [V] V c n t [ m V ] I_{pcA-tc} [V] (EV1407_Bgamma/pcA-TC.vs.9plA.5cnt.completeMeas.cfg) V G ( V ) V G2 (V) -0.05 -0.20 -0.15 -0.10 -1.8 -1.4 -1.0 -0.8 -1.2 -1.6 -2.0 T el = 100 mK V SD-QPC = 0.5 mV dV G2 = 5 mV V G3 = -2 V V G4 = -0.33 V V = +0.06 V
0 1
2 3 4 5 FIG. 3. (color online) Transconductance g TC = dI QPC /dV G2 in false colors from g TC = 2 × − S (blue) to g TC =12 × − S (red), plotted as a function of V G1 and V G2 . Localminima are caused by Coulomb resonance of the QD (whitearrows) or trapped states in the environment (black arrows).Between the QD resonances, the electron number is fixed (la-beled from 0 to 7). to broaden at gate voltages of V G1 (cid:38) − .
08 V. This ob-servation indicates that due to the reduced tunnel barrierheight, the tunnel broadening exceeds 1 meV, which cor-responds to a tunnel rate of Γ = FWHM / h (cid:38) × Hz.Taking these two values of the tunnel barrier as refer-ences, we can estimate the coefficient relating top gatevoltage and tunnel rate to be of the order of 12 mVper decade. This is in good agreement with tunnel ratemeasurements on QDs with a comparable Schottky-gatelayout .Observing each QD state over a wide range of tunnelcouplings strongly indicates that after the leftmost QDresonance, the QD is completely emptied of electrons.This enables us to label the number of electrons on theQD (”0” to ”7” in Fig. 3). The charging energy of thefirst two electrons of E C ∼
10 meV (determined fromthe slope ∆ E/ ∆ V G2 = 0 . × ∆ V SD / ∆ V G2 ) is among thelargest values reported for laterally defined QDs. Strik-ingly, the addition energy of the electronic states labeled2 and 6 is slightly larger than the adjacent addition en-ergies. These ”magic numbers” are expected from a two-dimensional confinement potential and have already beendiscussed in transport experiments on QDs . More-over, the tunnel broadening of the first two electronicstates sets in at V G1 ∼ − .
08 V, whereas the followingfour QD states begin to broaden at V G1 ∼ − .
11 V. Ob-serving the same tunnel broadening for different tunnelbarrier heights indicates different tunnel rates of the in-volved orbital states. Again, the observation of tunnel broadened states of a few-electron QD in the QPC signaldemonstrates the capabilities of the presented device.In conclusion, we fabricated a QD with adjacent QPCby combining Schottky-gates with local anodic oxidation.The resulting hybrid device combines the advantages ofboth techniques. Reduced screening of the charge de-tector facilitates good charge readout and the employedSchottky-gates demonstrate high tunability of the QD.Tuning the QD to the few-electron regime, we can detectthese charge states over a range of more than nine ordersof tunnel coupling. Signatures of shell filling effects areobserved both in the excitation energy and in the tunnelrate. Further improvement of the device geometry andthe extension to few-electron double QDs promises de-vices with very desirable properties in view of definingsolid state qubits.We acknowledge the support of the ETH FIRSTlaboratory and financial support of the Swiss Sci-ence Foundation (Schweizerischer Nationalfonds, NCCRNanoscience).
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