Parallel carbon nanotube quantum dots and their interactions

Karin Goß,1, ∗ Martin Leijnse,2 Sebastian Smerat,3 Maarten R. Wegewijs,4, 5 Claus M. Schneider,1 and Carola Meyer1

1Peter Grunberg Institut (PGI-6), Forschungszentrum Julich & JARA Julich Aachen Research Alliance, 52425 Julich, Germany2Center for Quantum Devices, Niels Bohr Institute,

University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark3Physics Department, Arnold Sommerfeld Center for Theoretical Physics,Ludwig-Maximilians-Universitat Munchen, 80333 Munchen, Germany

4Peter Grunberg Institut (PGI-2), Forschungszentrum Julich & JARA Julich Aachen Research Alliance, 52425 Julich, Germany5Institute for Theory of Statistical Physics, RWTH Aachen, 52056 Aachen, Germany

(Dated: August 30, 2012)

We present quantum transport measurements of interacting parallel quantum dots formed in thestrands of a carbon nanotube rope. In this molecular quantum dot system, transport is dominatedby one quantum dot, while additional resonances from parallel side dots appear, which exhibit aweak gate coupling. This differential gating effect provides a tunability of the quantum dot systemwith only one gate electrode and provides control over the carbon nanotube strand that carriesthe current. By tuning the system to different states we use quantum transport as a spectroscopictool to investigate the inter-dot coupling and show a route to distinguish between various side dots.By comparing the experimental data with master equation calculations, we identify conditions forthe tunneling rates that are required in order to observe different manifestations of the inter-dotcoupling in the transport spectra.

PACS numbers: 73.22.-f,73.63.Fg,73.23.Hk

I. INTRODUCTION

Carbon nanotubes (CNTs) are a versatile material forelectronics. In addition to extraordinary electronic1–4

and thermal5–7 transport properties, they are mechan-ically flexible and strong8–10. The current is carried bythe π-orbitals of the macromolecule and thus, the elec-tronic transport can be strongly influenced by the en-vironment. This feature can be exploited by using car-bon nanotubes as the functional element in detectors,e. g., gas sensors11,12. A different way of using this prop-erty is the functionalization of individual CNTs withmolecules to create new hybrid types of nano-devices suchas biosensors13,14 or spin valves15.

The interactions involved in such a functionalizationare not yet fully understood but are expected to alsoplay an important role in the transport properties ofother interacting π-systems such as graphene or indi-vidual molecules. A lot of effort is put into studyingquantized transport in these systems.16–29 In contrast tographene and individual molecules, quantum transporton clean, individual CNTs today is well established andunderstood.30–35 Therefore, it can be used as a spectro-scopic tool for the investigation of more complex multi-component devices. Within this context, CNTs bundledtogether in form of a rope represent a generic and read-ily available system to study the electrical transport ofinteracting molecules.

Recently, we investigated the electronic hybridizationbetween the parallel quantum dots (QDs) in a CNT ropesystem, when two electrochemical potentials of the dotsare in resonance.36 In this article, we focus instead onthe differential gating effect and the off-resonant effects.We investigate and discuss the influence of the relative

500nm

FIG. 1. (Color online) Atomic force micrograph of the parallelquantum dot device with gold contacts patterned on top of aCNT rope. Inset: Height profile z in the quantum dot regionbetween the contacts.

tunnel rates of the system and the coupling of the QDsto the leads.

This manuscript is structured as follows. After in-dicating the sample fabrication and measurement tech-niques in section II, we evaluate in section III the cou-pling and interaction parameters of four parallel quantumdots within the CNT rope. This section also includes adiscussion of the differential gating effect, which allowsto tune the system into in-resonance and off-resonancestates. Section IV compares master equation calcula-tions with quantum transport measurements in order toshow the effect of relative tunnel rates of parallel quan-tum dots. At last in section V, we briefly outline howto extract the true capacitive coupling between parallelquantum dots in the presence of a strongly asymmetriccoupling to one lead.

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V (

mV

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V (V)gate

(b)(a)

FIG. 2. (Color online) Differential conductance plot showing several charge states of the main dot. Secondary resonances ofthree different side dots A, B (in (a)) and C (in (b)) are indicated by arrows. The resonances are shifted by ∆V (i) (i = A,B,C)due to a capacitive inter-dot coupling. Note the multiplied differential conductance at positive bias voltage in panel (a).

II. SAMPLE & METHODS

We show quantum transport measurements of a CNTrope device with the distance between the gold contactsbeing patterned as 360 nm (see Fig. 1). The highly dopedSi substrate with SiO2 on top of it acts as backgate. TheCNTs are grown on substrate by the chemical vapourdeposition method using Fe/Mo as catalyst and methaneas the carbon precursor.37 The growth temperature is920 C, where a predominant growth of single-walled car-bon nanotubes and a small fraction of double-walledCNTs is expected38. The height profile taken from theatomic force micrograph in Fig. 1 in the quantum dot re-gion between the two contacts gives a height of ∼ 7 nm.Raman scattering measurements performed on the devicereported here, can clearly exclude an individual multi-walled CNT of a large diameter and prove the bundling ofseveral carbon nanotubes with diameters between 0.6 nmand 1.3 nm in the quantum dot region.39 The device ex-hibits a resistance of 290 kΩ at room temperature with alinear current-voltage characteristic indicating its metal-lic character. Low-temperature transport measurementsare performed in a dilution refrigerator at a base temper-ature of ∼30 mK.

III. MULTIPLE PARALLEL QUANTUM DOTS

Figure 2 shows the stability diagram of the CNT ropedevice measured at low temperatures, which exhibitsCoulomb diamonds as typical Coulomb blockade signa-tures and more atypical additional resonances. Previ-ously, we have shown that the observable features can beexplained by a formation of interacting parallel quantumdots in different strands of the rope.36 The Coulomb dia-

monds in Fig. 2 originate from one quantum dot which welabel as main dot and the secondary resonances markedby arrows originate from side dots formed in parallelCNTs within the rope. These secondary resonances arepart of a Coulomb diamond pattern with smaller slopes ofthe diamond edges owing to a weaker backgate couplingof the side dots.

Within the gate voltage range plotted in Fig. 2a andb, indications of three different side dots are observedas we will discuss in the following. Three main signa-tures are used to discriminate these three quantum dots.First, anticrossings caused by a tunnel coupling betweenquantum dot states on different dots can be observed

sidedot

maindot

FIG. 3. (Color online) Circuit diagram of a system of twoparallel quantum dots formed in two CNTs. The tunnel bar-riers connecting them to the same source (sc) and drain (dr)electrodes are characterized by a resistance R and a capac-itance C. The quantum dots interact via a tunnel couplingwith the hybridization amplitude t and a capacitive couplingwith the capacitance Cms.

3

QD i αgt αsc αdr |t| (meV) ∆V (i) (meV)main dot 0.05 0.36 0.59 - -

side dot A 0.019 0.765 0.216 0.1 0.40side dot B 0.007 0.074 0.919 0.075 0.20side dot C 0.006 0.939 0.055 6= 0 0.15

TABLE I. Coupling and interaction parameters of the quan-tum dots observed in Fig. 2.

at meeting points between resonance lines. This tunnelcoupling is characterized by a hybridization amplitude tas sketched in the circuit diagram of the quantum dotsystem in Fig. 3. Second, a capacitive coupling charac-terized by the capacitance Cms between the dots leads toa voltage shift ∆V (i) in the secondary resonances whenproceeding from one Coulomb diamond to the next. Thisenergy shift of a side dot level is caused by a potentialchange on the side dot due to the subsequent addition ofelectrons onto the main dot.

Third, the bias coupling, that is due to the interactionof the QDs with the leads, can be deduced from the slopesof the diamond edges in the stability diagram. In ourexperiments, the bias voltage is applied asymmetrically,i. e. the drain is kept grounded and the full bias win-dow is applied at the source electrode. Then, the slopesof the diamond edges of each quantum dot are given as+

αgt

1−αscand −αgt

αscfor the positive and the negative slope,

respectively.40 Here, αj = Cj/C is the dimensionless cou-pling parameter of the quantum dot to electrode j, whereC =

∑Cj is the total capacitance as defined for a single

quantum dot within the constant interaction picture.41

The coupling parameters αj deduced from Fig. 2 aresummarized in Tab. I. The parameters of the main dotare directly extracted from the observed diamond pat-tern. For the side dots, it is not possible to observe com-plete Coulomb diamonds. Considering each secondaryresonance separately, a large bias coupling, i. e. a strongcoupling to either the source or the drain electrode, hasto be considered. In the case of a large source coupling(αsc αdr), the positive slope becomes very steep, whilethe negative slope becomes flat. On the other hand, if thecoupling to the drain electrode is large, the opposite willbe observed: the positive slope is flat, while the negativeslope is steep. We interpret each secondary resonance tobe the flat slope of a diamond pattern, hence belongingto different side dots, labelled as A, B and C in Fig. 2.Due to its steepness, the second slope of each side dotdiamond is assumed to be obscured by the prominentmain diamond pattern. In order to obtain an estimatefor the coupling of the side dots to the electrodes, thisslope of the side dot diamonds is assumed to be the sameas for the main dot. If it was much smaller, it would beobservable as a resonance in the diamond pattern. Anevaluation with steeper slopes up to completely verticaldid not change the results significantly.

The coupling parameters found by this analysis aregiven in Tab. I. For side dot A and C we find a strongsource coupling, while side dot B exhibits a strong drain

(a)

(b)

N-1 N+10

N

t

FIG. 4. (Color online) (a) Schematic stability diagram of amain dot (red) in parallel to one side dot (green) in the regionof negative bias voltage. (b) Level alignment for three gatevoltages as indicated in (a) at a constant bias voltage. AtV 1gate, tunneling via both quantum dots is possible. Due to

the differential gating, it is possible to add one more electrononto the main dot, while the side dot occupancy does notchange for V 2

gate. At V 3gate, again tunneling via two dots - but

different states - is possible.

coupling. The coupling to the gate electrode is similarfor side dot B and C, while it is slightly stronger for sidedot A. A screening of particular CNTs by surroundingCNTs within the rope is a possible reason for a differentcoupling to the backgate. Furthermore, the asymmetriccoupling to one of the contacts is a clear indication fordifferent interface properties at the leads, which can orig-inate from a changing assembly of the rope along the QDregion.

Although all quantum dots in the system are controlledby the same gate electrode, the dot-dependent backgatecoupling creates a differential gating effect that is usedto tune the system into various states. This is illustratedin Fig. 4 for one main dot (red) and one side dot (green)where interactions between the QDs are neglected forsimplicity. At the first indicated position in the stabilitydiagram in Fig. 4a, the bias voltage and the gate voltageV 1gate are set such that tunneling via both quantum dots

is possible simultaneously. The level alignment for thissituation is sketched in the left panel of Fig. 4b: whilethe level on the main dot is in resonance with the chemi-cal potential of the drain (negative slope of the Coulombdiamond), the level on the side dot is in resonance withthe chemical potential of the source (positive slope ofthe secondary resonance). Keeping the bias voltage fixedand increasing the gate voltage to V 2

gate, lowers the maindot level below the bias window and fills the main dot

4

x2V

(m

V)

bia

s

B=10T(c)0 0.06(a)

(b)

SETSET

FIG. 5. (Color online) Differential conductance plots for magnetic field (a) B = 0 T, (b) B = 2 T and (c) B = 10 T. (b) Themain and secondary resonances as observed at B = 0 T are indicated in yellow. (c) Note the multiplied differential conductanceat negative bias voltage. For better visibility, main dot Coulomb diamonds are indicated in red.

permanently with one more electron (see central panelof Fig. 4b). The main dot is in Coulomb blockade, buttunneling via the side dot level is still possible. This is aparticular property of the parallel quantum dot systemin contrast to a setup with serial quantum dots. There,the transport via the whole device is fully blocked whenonly one of the dots is in Coulomb blockade.

Increasing the gate voltage further to V 3gate, tunes the

next higher energy level of the main dot into the biaswindow allowing again tunneling via both quantum dotsin parallel. While the level on the main dot had a higherenergy than the side dot level at V 2

gate, it exhibits a lower

energy at V 3gate, which – with only one gate electrode –

is solely possible with a differential gating effect. Thesituation where the electronic states of the two quantumdots are at the same energy, i. e. in resonance with eachother, is depicted in the inset of Fig. 4a. To probe thisin-resonance state and a possible hybridization of quan-tum dot levels, both levels need to be simultaneously inresonance with one of the electrode chemical potentials.From earlier investigations we know that the current iscarried by the bonding state of hybridized levels and thatthe wavefunction overlap is symmetric.36

Hence, the differential gating effect as it is observedhere, can be used to tune the quantum dot system into in-resonance and off-resonance states and provides a controlover which strand of the rope carries the current. Thisenables us to use quantum transport as a spectroscopictool for probing various properties of the system.

Now that it is clear how the differential gating effectcan be employed to characterize the parallel quantumdot system, we want to use it to distinguish between theside dots by evaluating their interaction parameters inthe following. From the discrete shift of a secondary reso-nance ∆V (i) between two subsequent main dot Coulombdiamonds, the capacitive inter-dot coupling can be ex-tracted. This shift is found to be twice as large for res-onance A in comparison to resonance B (see Tab. I).For side dot C, an even smaller capacitive coupling isfound. The second interaction is the tunnel coupling tothe main dot, as mentioned above. A hybridization be-tween states on two different quantum dots causes ananticrossing between resonance lines. The gap betweena bonding and an anti-bonding state observable at theanticrossings corresponds to ∆E = 2|t|, where t is thehybridization amplitude.36 From a high resolution mea-surement (shown in Ref. 36), |t| can be estimated to be0.1 meV and 0.075 meV for A and B, respectively. Forside dot C, a magnitude for the hybridization amplitudecannot be accurately determined. However, the clearbending of resonance lines indicate that a hybridizationindeed occurs also for these quantum dot states. Hence,the different magnitude of the interactions between thequantum dots gives evidence that Fig. 2 contains the fin-gerprints of one main dot connected in parallel to threeside dots.

A further evidence for interpreting the secondary reso-nances as three side dots can be given from a distinct

5

SET

SET

(a)

(b)

FIG. 6. (Color online) Schematic stability diagram of a maindot (red) in parallel to one side dot (green) in the region ofpositive bias voltage. The voltage shift ∆V (i) occurs in (a) atthe Coulomb diamond edge and in (b) in the SET regime ofthe main dot.

evolution with increasing magnetic field. Figures 5aand b show the stability diagram of the main dot andthe secondary resonance B at a magnetic field B = 0 Tand 2 T, respectively. While at B = 0 T, the sec-ondary resonance is passing the Coulomb blocked regionat Vbias ≈ −0.6 mV, it appears at a more negative biasvoltage for B = 2 T. Figure 5c presents several chargestates of the main dot at B = 10 T. At this high mag-netic field, no secondary resonances can be observed atnegative bias voltages, where the signatures of side dotB and C could be measured at zero magnetic field (seeFig. 2). In contrast, enhanced secondary resonances canbe observed at positive bias voltage indicating electronstunneling favourably via side dot A. The contrary evo-lution of the secondary resonances in a magnetic fieldconfirms once again the presence of several parallel sidedots.

Comparing the secondary resonances A in Fig. 5c withthose in Fig. 2a, two differences can be observed in thesingle electron tunneling (SET) region of the main dot.First of all, excited states of side dot A are visible, whichcause parallel secondary resonances with equal couplingand interaction parameters. A detailed discussion con-cerning these excited states can be found elsewhere.36

Second, the voltage shift ∆V (A) of the secondary reso-nance is found to occur within the SET regime (see thearrow in Fig. 5c), and not at the edge of the subsequentCoulomb diamond. This effect is best visible for the sec-ondary resonance with the lowest energy and has its ori-gin in the relative tunneling rates of the main dot andthe side dots, which will be discussed in the next section.

In this first section, we showed how a differential gatingeffect enables the identification and characterization ofseveral parallel quantum dots. A strong bias coupling isfound for the side dots in the setup. By tuning to in-resonance and off-resonance states of the system, variousinteractions can be probed. Furthermore, the differential

gating is used to control which one of the strands withinthe rope carries the current.

IV. RATE-DEPENDENT QUANTUMTRANSPORT FEATURES

B

A

FIG. 7. (Color online) Differential conductance plot exhibit-ing a shifted main resonance (arrows). The secondary reso-nances of side dot A and B are indicated in yellow.

Figure 6 depicts two possible observations in the SETregion of a main dot in parallel to a capacitively coupledside dot (a hybridization of quantum dot states is ne-glected for simplicity). In the first case (a), the voltageshift ∆V (i) occurs exactly at the diamond edge of theright diamond, where an additional electron is filled ontothe main dot. The second case (b) shows the up-shiftedsecondary resonance already in the SET regime of themain dot. This observation can be made if an electronresides for a long time on the main dot state within thebias window due to a reduced tunneling rate towards thedrain electrode. This is the effect mentioned in sectionIII which can be observed in Fig. 5c for the main dotand side dot A. In a magnetic field (B = 10 T), theconductance via the main dot is very low (faint Coulombdiamonds) indicating reduced tunneling rates of the maindot. Furthermore, the shift of the secondary resonanceis found to occur in the SET regime, and not at the di-amond edge. At lower bias voltages, where an unshiftedresonance is expected (dotted line), no conductance canbe measured, in analogy to Fig. 6b.

A similar effect with the same physical origin can beobserved in Fig. 7a, which shows another transport mea-surement at B = 0 T at similar charge states as in Fig. 2.The secondary resonance of side dot B is observed sim-ilarly to the previous measurement. The position of the

6

N+1N

(b)

I

II

(a)

case I case II

FIG. 8. (Color online) (a) Differential conductance caculatedby master equations using the model of two interacting par-allel quantum dots. Black arrows indicate the shift of themain resonance appearing at the secondary resonance (yel-low arrow). (b) Schematic drawing of electron tunneling viatwo parallel CNT quantum dots. Γs

sc/dr and Γmsc/dr are the

tunneling rates from source (sc) and drain (dr) to the sidedot s (green) and the main dot m (red), respectively. (I) IfΓssc Γs

dr, the side dot is mainly unoccupied and electronscan tunnel via the main dot like in an uncoupled quantumdot. (II) In the case of Γs

sc Γsdr, an additional electron re-

sides on the side dot most of the time and electrons tunnelingvia the main dot can only tunnel via a state shifted in energyby the capacitive inter-dot coupling.

secondary resonance from side dot A is difficult to recog-nize due to a low conductance in this particular measure-ment. Instead, a shift of the diamond edge ∆V (m) canbe observed close to the meeting point of the secondaryresonance with the main resonance. This is - like thevoltage shift in the secondary resonances - a manifesta-tion of the capacitive coupling between the main dot andside dot A. In a system of capacitively coupled quantumdots, the chemical potential of the quantum dots will mu-tually depend on each other. Hence, resonance lines ofany dot – not only a side dot – are expected to shift whenthe number of electrons on the parallel quantum dot ischanged. That means, that also the tunneling of an addi-

tional electron via a side dot state changes the potentialfor the electrons on the main dot and a shifted main dotdiamond edge is expected at energies higher than the re-spective secondary resonance, i. e. in the single electrontunneling regime of the side dot. This effect causes theobserved shift in Fig. 7. As we will see in the following,the relative tunnel rates of quantum dot states are thedecisive parameter for a shift of resonances.

We use master equation calculations with an analogousmodel as in Ref. 36, describing a parallel double quan-tum dot (containing the main dot and side dot A) withina constant interaction model42 extended to account forinteractions between the quantum dots. Figure 8a showsa calculated stability diagram according to this model.Similar to the measurement, the main dot diamond edgeis shifted at the crossing of the secondary resonance. Thecalculations assume a larger capacitive coupling than ob-served in the experiment in order to enhance the visibilityof the effect.

In the calculated stability diagram, the shifted maindot diamond edge appears only for particular relativetunneling rates from the leads to the quantum dots. Thefollowing discussion assumes one state on each quantumdot to be within the bias window and the applied biasvoltage to be positive. The left panel (case I) of Fig. 8bdepicts a situation, where the tunneling rates for the stateon the side dot are Γssc < Γsdr, while Γmsc = Γmdr > Γsdr isassumed for the main dot. Then, the side dot state ismainly unoccupied, because electrons will immediatelytunnel out of the dot into the drain. Therefore, elec-trons tunneling via the main dot will not experience anadditional potential, because the probability to have anelectron on the side dot at the same time is low. As aresult, the diamond edge in the stability diagram will ap-pear as a continuous resonance line and exhibit no shiftas for uncoupled QDs (see resonance I in Fig. 8a).

For the calculation shown in Fig. 8a, the tunnelingrates for the side dot are assumed to be reversed, i. e.Γssc > Γsdr, as depicted in the right panel (case II) ofFig. 8b. For the main dot, Γmsc = Γmdr > Γssc is assumed.This leads to the following situation in the SET regime(i. e., above the side dot resonance): the state on theside dot is mainly occupied, and transport predominantlytakes place via a state on the main dot, which is shiftedin energy due to the inter-dot capacitive coupling. Then,the conductance in the original diamond edge (side dotnot occupied) is suppressed, whereas the shifted diamondedge (side dot occupied) appears enhanced, which causesthe higher conductance in resonance II in Fig. 8a.

This configuration of tunneling rates also suppressesthe conductance through the side dot, hence the sec-ondary resonance appears less pronounced. This is con-sistent with the experimentally found weak conductanceof the secondary resonance of side dot A in Fig. 7.

In conclusion, by reproducing the experimental obser-vations with master equation calculations, we have shownthat the energy and the conductance of the resonancesin the stability diagram of interacting parallel quantum

7

dots strongly depend on the tunnel rates into particularquantum dot states. Hence, the tunneling rates of onequantum dot dictate the relative conductance for the res-onances of the parallel quantum dot and are decisive forthe observation of their energy splitting.

V. EVALUATING THE TRUE CAPACITIVECOUPLING STRENGTH

As we have shown above, a shift in the resonance linesof the side dot as well as of the main dot is a mea-sure of the capacitive coupling between parallel quantumdots. However, here we find the magnitude of the shiftof the main resonance to be ∆V (m) ≈ 0.2 meV, whereas∆V (A) ≈ 0.4 meV is obtained from the voltage shift ofthe secondary resonance. This discrepancy can be ex-plained by considering the difference in the bias couplingof side dot A and the main dot. In fact, the voltage off-set due to a capacitive inter-dot coupling and also themagnitude of the anticrossing gap depend on the biascoupling, which we described in section III. A large αsc

will increase the observable shift of resonances, because∆V (i) = Ums/(1 − αsc(i)), where αsc is the source cou-pling of the dot corresponding to the shifting resonanceand Ums is the true capacitive coupling strength. Thevalues of the shifts are thus always upper bounds for theactual capacitive inter-dot coupling.

Considering the source coupling of the main dot andthe side dot A in Tab. I, a shift of

∆V (m) = ∆V (A)1− αsc(A)

1− αsc(m)= 0.15 meV (1)

is expected for the main dot resonance. This value iscomparable to the ∆V (m) deduced from the shift of themain resonance, taking into account the experimental er-ror. In principle, the source coupling of the main dot ismore reliable than the ones of the side dots, because noassumptions had to be made for obtaining them. Hence,we evaluate the true capacitive inter-dot coupling be-tween main dot and side dot A from the shifted maindiamond edge and obtain UmA = 0.13 meV. Althoughseveral side dots are interacting with the main dot, onlyside dot A is coupled strongly enough to shift the maindot resonances in energy.

VI. SUMMARY & CONCLUSIONS

In summary, we discussed a multi-component molec-ular transport device employing quantum transport as

a spectroscopic tool. We use a carbon nanotube ropeas a molecular model system, which exhibits rich char-acteristics in its transport spectra. The formation ofmultiple parallel quantum dots is concluded from sec-ondary resonances. A differential gating effect due to adot-dependent gate coupling allows for tuning the quan-tum dot system into various states using only one gateelectrode. By tuning to in- and off-resonance states ofthe system, quantum transport spectroscopy can distin-guish several parallel quantum dots by their coupling andinteraction properties, as we have shown on three sidedots coupled in parallel to one main dot. Furthermore,the differential gating provides a control over the carbonnanotube strand carrying the current.

The distinct coupling of the quantum dots to the leads,their interactions and the impact of relative tunnelingrates lead to a variety of features in the transport spec-tra which we discussed in depth. By reproducing theexperimental data with master equation calculations, wehave identified the requirements for observing an energyoffset due to a possible interaction between parallel quan-tum dots. Concentrating on the off-resonance quantumtransport, we have found that a capacitive inter-dot cou-pling is not only observable in a shift of secondary res-onances, but additionally can manifest itself in shiftingthe edges of otherwise regular Coulomb diamonds. Theexact position and appearance of such a shift depends onthe relative tunneling rates through the parallel quantumdots.

Our results provide the basis for understanding quan-tum transport via parallel quantum dots, which is animportant issue in molecular transport where a large va-riety of hybrid transport devices with new functionalitiesare expected.

ACKNOWLEDGMENTS

We thank H. Schoeller and U. Schollwock for fruitfuldiscussions and S. Trellenkamp for e-beam writing, aswell as S. Estevez Hernandez, H. Kertz, H. Pfeifer, W.Harneit and J. Lauer for technical assistance. We ac-knowledge the DFG (FOR 912) and the European UnionSeventh Framework Programme (FP7/2007-2013) underagreement no 270369 (ELFOS) for funding.

∗ Current address: 1. Physikalisches Institut, UniversitatStuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany;karin.goss@pi1.physik.uni-stuttgart.de

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