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Giant Magnetoconductance Oscillations in Hybrid Superconductor−Semiconductor Core/Shell Nanowire Devices Ö . Gül,†,∥,⊥ H. Y. Günel,*,†,‡,⊥ H. Lüth,† T. Rieger,† T. Wenz,† F. Haas,† M. Lepsa,† G. Panaitov,§ D. Grützmacher,† and Th. Schap̈ ers*,† †

Peter Grünberg Institute (PGI-9) and JARA-Fundamentals of Future Information Technology, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany ‡ Institute of Semiconductor Electronics, RWTH Aachen University, 52074 Aachen, Germany § Peter Grünberg Institute (PGI-8) and JARA-Fundamentals of Future Information Technology, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany ABSTRACT: The magnetotransport of GaAs/InAs core/shell nanowires contacted by two superconducting Nb electrodes is investigated, where the InAs shell forms a tube-like conductive channel around the highly resistive GaAs core. By applying a magnetic field along the nanowire axis, regular magnetoconductance oscillations with an amplitude in the order of e2/h are observed. The oscillation amplitude is found to be larger by 2 orders of magnitude compared to the measurements of a reference sample with normal metal contacts. For the Nbcontacted core/shell nanowire the oscillation period corresponds to half a flux quantum Φ0/2 = h/2e in contrast to the period of Φ0 of the reference sample. The strongly enhanced magnetoconductance oscillations are explained by phase-coherent resonant Andreev reflections at the Nb-core/shell nanowire interface. KEYWORDS: GaAs/InAs core/shell nanowires, magnetoconductance oscillations, Josephson effect, superconducting electrodes, Andreev reflection, reflectionless tunneling

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semiconductor represents, in principle, an exchange of a Cooper pair at the interface. In this letter we address the question, how interference effects in a tubular conductor realized by a GaAs/InAs core/ shell nanowire are affected when the normal metal contacts are replaced by superconducting electrodes, i.e., when Andreev reflection contributes to the transport. Previously a number of experiments have been performed on structures, where either two superconducting electrodes are connected by an Aharonov−Bohm-type normal-conducting ring9−13 or where a superconducting fork-like structure covers a normal conducting wire.14−16 In most cases a period of half a flux quantum Φ0/2 = h/2e was observed in the transport, except for the ballistic structure,13 where a period of Φ0 was reported. In another study critical current modulations in an axial magnetic field are observed for an InAs nanowire contacted with superconducting leads; however, the modulations are not assigned to a flux quantum periodicity but rather to interferences in a Josephson contact.17 The geometry of our structure differs from the previously investigated ones: our device is a tubular conductor laterally connected to two

emiconductor core/shell nanowires with a conducting shell and an insulating core are ideal nanostructures for the study of quantum interferences and/or quantum transport through coherent angular momentum states.1,2 In an axially oriented magnetic field the magnetoconductance of the core/ shell nanowire oscillates with a period of a single flux quantum Φ0 = h/e.1−6 The observed effects can be interpreted in terms of diffusive transport along the tube-like conducting shell through quantum states, which are coherent along the shell circumference. A variation of the magnetic flux through the shell changes the occupation of current carrying angular momentum quantum states periodically in Φ0. In those investigations normal metal contacts at both ends of the wire enabled current flow through the highly conducting shell along the wire axis. When the normal metal contacts are replaced by superconducting electrodes, the transport through the superconductor−nanowire interface can be described by the Andreev reflection process.7,8 Here, an electron from the semiconductor side approaching the superconducting contact generates a Cooper pair within the superconductor by retro-reflection of a positively charged hole, i.e., a missing electron in the Fermi sea of a highly degenerate semiconductor. The latter propagates time-reversed (in opposite direction) along the electron path in the semiconductor. The propagation of electrons and correlated holes on equal but time-reversed paths in the © XXXX American Chemical Society

Received: July 9, 2014 Revised: September 26, 2014

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dx.doi.org/10.1021/nl502598s | Nano Lett. XXXX, XXX, XXX−XXX

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superconducting leads at each end. Furthermore, by using a bottom-up approach for the nanowire growth a very small ringshaped cross section can be achieved, which is inaccessible by other fabrication methods. For a direct comparison, a reference sample with normal metal leads instead of the superconducting electrodes was also prepared. The direct comparison of both types of samples reveals that the magnetoconductance of the device with superconducting contacts oscillates with a period of Φ0/2 with a much higher amplitude than the normal conducting counterpart. We explain the observed phenomena by means of phase-coherent resonant Andreev reflection. Growth, Device Fabrication and Measurement Setup. For the growth of the GaAs/InAs core/shell nanowires by molecular beam epitaxy, a GaAs (111)B substrate covered with ∼6 nm SiOx was employed.1,18 The self-catalyzed GaAs core nanowire was grown at a substrate temperature of 620 °C for 1.5 h. A Ga flux corresponding to a planar growth rate of 0.095 μm/h and an As4 beam equivalent pressure (BEP) of 10−6 Torr were used. Subsequently, the catalyzing Ga droplets were consumed by As. In order to increase the thickness of the GaAs wire, an additional GaAs shell was grown for 40 min at 590 °C while increasing the As4 BEP to 8 × 10−6 Torr. (The increased thickness of the core was chosen to reduce the magnetic field required to obtain a magnetic flux quantum for a given cross section. A smaller magnetic field is desirable in order to keep the superconducting state in the Nb electrodes.) Hereafter, the substrate temperature and the As4 BEP were lowered to 490 °C and 10−6 Torr, respectively. Using an In rate of 0.125 μm/h, the InAs shell was grown for 25 min. Finally, the wires had a core diameter of about 180 nm with an InAs shell thickness of around 40 nm. In Figure 1a, a scanning electron micrograph of an as-grown GaAs/InAs core/shell nanowire is shown. The fact that InAs does not grow on the small end part can be attributed to the wurtzite structure of the GaAs core in this section.18,19 After the growth, nanowires were mechanically transferred to a Si(100) substrate, which was covered with a 200 nm thick SiO2 layer. For the subsequent processing steps the substrate was prepatterned with alignment markers. The device fabrication was realized by standard electron beam lithography and lift-off. The 100 nm thick superconducting Nb film was deposited by magnetron sputtering. To obtain a transparent superconductor−nanowire interface, Ar+ sputtering was employed just before Nb deposition. The superconducting gap Δ of the Nb electrodes has been extracted from a temperature-dependent resistance measurement of a Nb thin film where we have found the critical temperature as Tc ≈ 8 K corresponding to a superconducting gap of Δ = 1.3 meV.20 A scanning electron micrograph and a schematic illustration of the Nb-core/shell nanowire junction are shown in Figure 1b,c. In addition to the structures with superconducting Nb electrodes, reference samples with normal metal Ti/Au contacts were also prepared. From low-temperature transport measurements with normal metal contact electrodes we estimate the carrier concentration, mobility, and mean free path to be n ≈ 1017 cm−3, μ ≈ 500 cm2/(Vs), and le ≈ 5 nm, respectively. A detailed room-temperature electrical characterization of our GaAs/InAs core/shell nanowires as well as band structure calculations by self-consistent Schrödinger−Poisson solver for different shell thicknesses can be found in ref 1. Comprehensive low-temperature magnetotransport investigations of normal metal-contacted GaAs/InAs core/shell nanowires are reported in ref 2.

Figure 1. (a) Scanning electron micrograph of the as-grown GaAs/ InAs core/shell nanowire. The uncovered section of the GaAs core (in yellow) is due to the wurtzite crystal structure in this section of the GaAs core. (b) Scanning electron micrograph of the measured sample with superconducting electrodes separated by 150 nm. (c) Schematic illustration of the sample layout. The magnetic field B∥ is oriented along the nanowire axis. (d) Interference of retro-reflected electrons (e) and holes (h) at two points at a superconductor (S)−normal conductor (N) interface. Φ is the magnetic flux. Details of the electron and hole paths are determined by elastic scattering. (e) Corresponding illustration of interfering electron and hole trajectories in the nanowire shell.

The measurements of superconducting Nb-contacted nanowires were performed in a He-3 cryostat with a base temperature of 0.3 K and magnetic fields up to 6 T. The measurements were performed on three samples with the same core diameter and shell thickness, but different Nb contact separations of 150, 200, and 350 nm. While the periodic conductance oscillations as well as enhanced oscillation amplitude were observed for all samples, here, we present a consistent data set of a single sample with a contact separation of 150 nm. The reference structures with the Ti/Au normal metal electrodes were measured in a variable temperature insert with a base temperature of 1.8 K and a maximum field of 13 T. The structure was measured in a two-terminal configuration. This sample had a contact finger separation of 260 nm. Results and Discussions. Basic Transport Properties. Before we address the flux periodic phenomena observed when the magnetic field is aligned axially, we first introduce the basic transport characteristics of the Nb-core/shell nanowire junction. A set of current−voltage (IV) characteristics for temperatures between T = 0.4 and 3.4 K at zero magnetic field is shown in Figure 2a. Although no clear Josephson supercurrent is observed, the IV characteristics are nonlinear at temperatures below 2.8 K with a smaller slope around zero bias current. The observed slight voltage drop around zero-bias is due to the fact that the thermal smearing is larger than the Josephson coupling energy.21 From the bias current range, where the slope of the IV characteristics increases, a switching current of around Ic ≈ 12 nA is estimated. The magnitude of Ic is strongly affected by the normal state resistance RN of the junction, i.e., the switching current is small if RN is large. The B


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reflections.25,26 At temperatures exceeding 2.4 K the differential resistance is constant, i.e., the IV characteristics are linear in accordance to the results shown in Figure 2a. For further characterization of the Nb-core/shell nanowire Josephson junction the effect of a perpendicular magnetic field B⊥ on the supercurrent has been investigated. In Figure 2c, dV/dI is plotted as a function of B⊥ and bias current. The monotonous decay of the supercurrent with increasing magnetic field is evident and can be attributed to the small size of the junction. The absence of a Fraunhofer diffraction pattern in these so-called narrow junctions has been explained by quasi-classical theory27 and demonstrated in various experiments.28−31 Magnetoconductance Oscillations. We now turn to the measurements, where the magnetic field B∥ is aligned along the axis of the GaAs/InAs core/shell nanowire, as it is depicted in the schematic illustration of Figure 1c. Thus, the cross section of the nanowire is penetrated by a magnetic flux. As can be seen in Figure 3a, the differential resistance dV/dI of the

Figure 2. (a) IV characteristic of a Nb-core/shell nanowire junction at temperatures between 0.4 and 3.4 K at zero magnetic field. (b) Differential resistance dV/dI as a function of bias voltage of the Nbcore/shell nanowire junction at temperatures ranging from 0.8 to 3.0 K at B = 0. The curves are offset by 100 Ω. The labels (1) and (2) indicate the peaks in the differential resistance. The inset shows the dV/dI at 0.3 K for a larger bias voltage range. (c) Color-coded differential resistance dV/dI vs perpendicular magnetic field and bias current at a temperature of 0.3 K.

normal state resistance, determined at bias voltages larger than 2Δ has a relatively large value of 3.6 kΩ. The value of RN includes the resistance of the nanowire segment as well as the contact resistance. The latter is due to a barrier at the Nb−nanowire interface, which causes a nonideal interface transparency. From the excess current measurement, the contact interface transparency has been estimated to be approximately 0.5.22 Apart from the Josephson effect, where a supercurrent flows between both Nb electrodes, especially at finite bias a smaller slope of the IV characteristics can also originate from the so-called reflectionless tunneling mechanism.23,24 Here, quantum interference effects of normal and Andreev reflected electrons and holes result in an excess conductance of the superconductor−nanowire interface. We will address this issue in more detail in connection with the measurements in an axial magnetic field. In Figure 2b (inset), the differential resistance dV/dI of the junction is shown as a function of bias voltage at a temperature of 0.3 K at B = 0. The measurement has been performed by a standard lock-in technique with an excitation current of 5 nA. At bias voltages below about 2 mV, which is in the order of 2Δ/e, dV/dI decreases due to the additional contribution of Andreev reflection to the transport. As can be seen in Figure 2b, two peaks, labeled by (1) and (2), are found at a bias voltage of about 0.27 and 0.16 mV, respectively. With increasing temperature these maxima slightly shift toward zero bias, while they vanish completely at 2.2 K. A possible origin of these peaks is the induced superconductivity in the nanowire shell right underneath the Nb electrodes. The resulting gap in the density of states can lead to additional features in the differential resistance due to multiple Andreev

Figure 3. (a) Differential resistance dV/dI of the Nb-core/shell nanowire structure as a function of an axial magnetic field B∥. The inset shows the measurement in an extended magnetic field range. (b) Magnetoresistance of the core/shell nanowire with normal metal (Ti/ Au) leads. The inset shows a magnified detail of the oscillations between 3 and 4 T. (c) Magnetoconductance G in units of e2/h for both types of structures. (d) Fourier transforms of the magnetoconductance oscillations. The spectra were rescaled in height for better comparison.

superconducting Nb-contacted core/shell nanowire exhibits a pronounced series of periodic oscillations in the magnetic field range −0.8 T < B < 0.8 T. For larger magnetic fields the oscillations vanish, cf. Figure 3a, inset. The absence of oscillations at the normal state of superconductor (B > Bc) is attributed to the low Nb−nanowire interface transparency. From the cross section area of the core part of the nanowire (A = 2.5 × 10−14 m2), we calculate the period of the magnetoresistance oscillations exactly to be half a flux quantum Φ0/2 = h/2e [cf. Figure 3a (upper scale)]. The Fourier transform of the magnetoresistance is shown in Figure 3d. A sharp frequency peak at 11.7 T−1 corresponding to a period of 85 mT (Φ0/2 periodicity) can be seen. To get more insight into the effect of coupling superconducting electrodes to a core/shell nanowire, the magnetoresistance of the reference structure contacted with normal C


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nanowires contacted by normal metal electrodes, resolving the Φ0/2 periodicity in normal conducting structures by ensemble averaging was previously shown to be possible.2 Φ0/2 periodic oscillations are interesting because, contrary to Φ0 periodic oscillations, the sign of the oscillation amplitude at zero flux provides information about the presence of spin−orbit interaction in the nanowire channel. Indeed, in ref 2, an oscillation maximum in conductance is reported for slightly thinner GaAs/InAs core/shell nanowires and attributed to the presence of spin−orbit coupling in the tubular InAs channel. Next we focus on the bias current dependence of the magnetoresistance oscillations. In Figure 5a, the color-scaled

metal Ti/Au electrodes was investigated. The corresponding measurement, performed at a temperature of 1.8 K up to a magnetic field of 13 T, is shown in Figure 3b. Here, oscillations in the magnetoresistance can be seen as well. However, there is a striking difference compared to the measurements on the Nbcontacted core/shell nanowire. For the Ti/Au-contacted samples the oscillations remain up to the largest applied magnetic field of 13 T, while the oscillation period corresponds to a single flux quantum Φ0 instead of Φ0/2. The latter can also be seen in the Fourier transforms shown in Figure 3d. To compare the periodicity as well as the amplitude of the oscillations of both samples, the corresponding magnetoconductances are shown Figure 3c for a magnetic field between −1 and 1 T after subtracting the slowly varying background. Apart from the obvious difference in the oscillation period, i.e., twice as large for the Ti/Au-contacted wire, one also finds a significantly larger oscillation amplitude for the Nb-contacted sample. Indeed, for the latter the maximum peak-to-peak amplitude is larger than 2 (e2/h), which is at least 200 times larger than that of the Ti/Au-contacted nanowire reference sample. To further elucidate the influence of superconducting contacts, the magnetoconductance has been measured at different temperatures for superconductor and normal metalcontacted core/shell nanowires, respectively. For the sample with superconducting leads, the Φ0/2 periodic conductance oscillations persist up to 2.0 K (Figure 4a). Above that

Figure 5. (a) Differential resistance dV/dI vs bias current and magnetic field at 0.3 K for the Nb-contacted core/shell nanowire. The labels (1) and (2) indicate the position of the subgap peaks. (b) Resistance modulations δR as a function of bias current and magnetic field at 0.3 K. Here, the slowly varying background resistance was subtracted. (c) Selected differential resistance curves at a fixed field of 0, 20, and 40 mT, respectively. The gray arrows indicate the change δR with magnetic field.

differential resistance dV/dI is plotted against bias current and magnetic field for the Nb-contacted core/shell nanowire. These measurements have been performed at T = 0.3 K as a function of bias current with a stepwise increasing axially oriented magnetic field. The dark stripes found at bias currents of around 80 and 50 nA, indicated by the labels (1) and (2), correspond to the peaks in the differential resistance shown in Figure 2b. These peaks merge at a magnetic field of about 1 T. At zero current bias, dV/dI oscillates with a period of Φ0/2, as discussed above. These oscillations die off at a field of around 0.5 T. In order to better resolve the current bias dependence, the resistance modulations δR are plotted in Figure 5b as a function of bias current and magnetic field. Here, δR was calculated by subtracting from dV/dI the slowly varying background magnetoresistance at a fixed bias current. The oscillations remain up to a bias current of 60 nA, being considerably larger than Ic. At a bias current of around 30 nA, the phase of the magnetoresistance modulations δR is shifted by π. This phase shift is further visualized in Figure 5c. At zero magnetic field the modulation of dV/dI is strongest, comprising a dip at zero bias current and pronounced maxima at ±25 nA. When the magnetic field is increased to 40 mT (about half a oscillation

Figure 4. (a) Magnetoconductance in units of e2/h of the Nbcontacted nanowire for various temperatures between 0.4 and 2.0 K. The curves are offset for clarity. (b) Corresponding measurements for the Ti/Au-contacted nanowire for temperatures between 1.8 and 20 K.

temperature the oscillations vanish. This temperature matches the temperature, at which the IV curve becomes linear and the modulations in the differential resistance disappear (cf. Figure 2a,b). Thus, the presence of the large conductance oscillations is directly related to the Andreev reflection at the superconductor−nanowire boundary. It should be noted that above 2.0 K the Nb electrodes are still in the superconducting state although the effect on the magnetoconductance is suppressed. A different behavior is observed for the nanowire with normal metal contacts. As shown in Figure 4b, the Φ0 periodic oscillations are maintained up to a temperature of 9 K. Furthermore, the oscillations remain observable up to magnetic fields of several Tesla. We note that, while Φ0/2 periodic oscillations are not visible in the conductance of the present D


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of the two types of carriers, electrons and retro-reflected holes. This is in agreement with our experimental findings. Thus, in our interpretation the Φ0/2 modulations originate from the transmission along the circumference through two points at each single superconductor−nanowire interface (cf. Figure 1e), rather than from the transport between the two superconducting electrodes through the weak link. By applying a magnetic field along the nanowire axis the transmission through each contact interface is modulated with a period of Φ0/2. It was shown theoretically that the transmission rate through the interface is largely enhanced due to constructive interference, which explains the large amplitude.24,32 In other words, electrons and holes encircling the nanowire axis between successive Andreev reflections at two points of each single superconductor−nanowire interface contribute to the oscillations. This process is resonant because only one lead is involved: electrons and correlated holes are Andreev-reflected at the same lead. Since all single processes of back and forward traveling carriers contribute to the transport, a very large modulation of G in the order of e2/h is observed for the sample with superconducting leads, while the modulation is 2 orders of magnitude lower for the reference sample with normal metal leads. In principle, one could also take into account multiple Andreev reflections between both superconducting electrodes. In this case, the interference of Andreev pairs traversing the junction would also give rise to regular oscillations. However, under voltage bias the superconducting phase difference between both electrodes is not fixed, so that no significant contribution to a regular interference pattern is expected. In contrast, for a single Nb electrode the phase difference between two reflection points is fixed; thus, the interference is welldefined. As already mentioned above, we attribute the features labeled (1) and (2) in Figure 5a to multiple Andreev reflections between both superconducting electrodes. In principle, according to eq 2, a phase accumulation and thus a biasdependent conductance oscillation might also occur with increasing energy E. However, in that case the bias voltageposition of the features (1) and (2) should oscillate with an additionally applied magnetic field. As can be inferred from Figure 5a, this is not the case. Summary and Conclusions. In summary, we demonstrated enhanced magnetoconductance oscillations in a GaAs/ InAs core/shell nanowire connected to superconducting leads. Owing to the Andreev reflection processes, a flux period of Φ0/2 is found, in contrast to a period of Φ0 for the normal metal-contacted reference sample. The much larger oscillation amplitude is attributed to phase-coherent resonant Andreev reflections at a single superconductor−semiconductor interface, analogous to the phenomena of reflectionless tunneling. These results may pave the way for novel hybrid phase-based switching and sensing devices combining the tunable electronic properties of semiconductors with the long-range coherence of superconductors.

period) the depth of the minimum at zero bias current is smaller, thus δR changes from a local minimum to a maximum. The opposite behavior is found at around ±25 nA; here, the side maxima are pushed downward, leading to changes from a local maximum to a minimum, thus causing the π-phase shift with respect to magnetoresistance oscillations at zero bias current. The physical origin of the Φ0/2 periodic oscillations observed in the Nb-core/shell nanowire device is based on transport of two types of charge carriers, electrons and Andreev holes, being retro-reflected at the InAs−Nb interface. To explain the physical origin in more detail, we refer to the phenomena of reflectionless tunneling.23,24,32 Since only a minor supercurrent was observed in our structures, while the oscillations were observed up to 60 nA, contributions related to the Josephson effect are neglected. As illustrated in Figure 1d, reflectionless tunneling originates from the constructive interference of Andreev pairs traversing a path between two arbitrary points at a single superconductor−normal conductor interface where they undergo successive Andreev reflections. For this process it is essential that the carriers have a chance to backscatter to the interface, i.e., by diffusive transport in the normal conductor. The interference can be tuned by changing the energy E of the particle or by applying a magnetic field B. According to van Wees et al.,24 the electrons and holes accumulate a phase of ⎤ ⎡ E ⎥L + 2π Φ/Φ0 ϕe,h = ±⎢kF ± 2 (ℏ kF/m*) ⎦ ⎣

(1)

while propagating between the two points at the interface where they are Andreev reflected. Here, kF is the Fermi wave vector in the normal conductor, E the energy relative to the Fermi energy, m* the effective mass, L the path length between two retro-reflections at the interface, and Φ the enclosed flux. The total phase accumulation of the electron and the Andreevreflected hole is Δϕ =

2EL Φ + 2π (Φ0 /2) (ℏ2kF/m*)

(2)

In a diffusive conductor, the path lengths L and the enclosed flux are different for different pairs of phase-coherently connected retro-reflections. Thus, only at B = 0 and E = 0 constructive interference is achieved for all loops, resulting in a largely enhanced conductance due to the increased transmission probability through the interface. Whereas at finite values of B and E, each loop acquires a different phase leading to a strong decrease of conductance, as it was observed experimentally.23,33,34 Unlike in the case of a compact diffusive normal conductor with irregularly shaped electron and hole path loops (cf. Figure 1d), in our sample the loops between two arbitrary Andreev reflection points are geometrically well-defined, due to the space limitations imposed by the tubular shell geometry. As illustrated in Figure 1e, the cross section of the core/shell nanowire is partly covered by the superconducting Nb electrode. The retro-reflected hole and electron trajectories connected by the superconductor encircle a magnetic flux Φ. In contrast to a disordered diffusive normal conductor, the flux Φ between different pairs of retro-reflections is fixed and determined by the well-defined core cross section A. Consequently, the accumulated phase Δϕ is identical for all pairs. According to eq 2, a period of Φ0/2 is expected because

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AUTHOR INFORMATION

Corresponding Authors

*(H.Y.G.) E-mail: [email protected]. *(Th.S.) E-mail: [email protected]. Present Address

∥ Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, Netherlands.

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Author Contributions

(27) Cuevas, J. C.; Bergeret, F. S. Phys. Rev. Lett. 2007, 99, 217002. (28) Angers, L.; Chiodi, F.; Montambaux, G.; Ferrier, M.; Guéron, S.; Bouchiat, H.; Cuevas, J. C. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 77, 165408. (29) Frielinghaus, R.; Batov, I. E.; Weides, M.; Kohlstedt, H.; Calarco, R.; Schäpers, Th. Appl. Phys. Lett. 2010, 96, 132504. (30) Chiodi, F.; Ferrier, M.; Guéron, S.; Cuevas, J. C.; Montambaux, G.; Fortuna, F.; Kasumov, A.; Bouchiat, H. Phys. Rev. B 2012, 86, 064510. (31) Günel, H. Y.; Batov, I. E.; Hardtdegen, H.; Sladek, K.; Winden, A.; Weis, K.; Panaitov, G.; Grützmacher, D.; Schäpers, Th. J. Appl. Phys. 2012, 112, 034316. (32) Marmorkos, I. K.; Beenakker, C. W. J.; Jalabert, R. A. Phys. Rev. B 1993, 48, 2811−2814. (33) Popinciuc, M.; Calado, V. E.; Liu, X. L.; Akhmerov, A. R.; Klapwijk, T. M.; Vandersypen, L. M. K. Phys. Rev. B 2012, 85, 205404. (34) Günel, H. Y.; Borgwardt, N.; Batov, I. E.; Hardtdegen, H.; Sladek, K.; Panaitov, G.; Grützmacher, D.; Schäpers, Th. Nano Lett. 2014, 14, 4977−4981 PMID: 25118624..

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These authors contributed equally to this work.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank David P. DiVincenzo and Janine Splettstößer for fruitful discussions, Herbert Kertz for assistance during the measurements, and Stefan Trellenkamp for electron beam writing.

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REFERENCES

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