Letter pubs.acs.org/NanoLett
Crossover from Josephson Effect to Single Interface Andreev Reflection in Asymmetric Superconductor/Nanowire Junctions H. Y. Günel,*,†,‡ N. Borgwardt,† I. E. Batov,†,¶,§ H. Hardtdegen,† K. Sladek,† 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 ¶ Institute of Solid State Physics, Russian Academy of Sciences, Chernogolovka, 142432 Moscow district, Russia § Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Russia ∥ Peter Grünberg Institute (PGI-8) and JARA-Fundamentals of Future Information Technology, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany S Supporting Information *
ABSTRACT: We report on the fabrication and characterization of symmetric nanowire-based Josephson junctions, that is, Al- and Nb-based junctions, and asymmetric junctions employing superconducting Al and Nb. In the symmetric junctions, a clear and pronounced Josephson supercurrent is observed. These samples also show clear signatures of subharmonic gap structures. At zero magnetic field, a Josephson coupling is found for the asymmetric Al/InAs-nanowire/Nb junctions as well. By applying a magnetic field above the critical field of Al or by raising the temperature above the critical temperature of Al the junction can be switched to an effective singleinterface superconductor/nanowire structure. In this regime, a pronounced zero-bias conductance peak due to reflectionless tunneling has been observed. KEYWORDS: InAs nanowire, superconducting electrodes, Andreev reflection, Josephson effect, asymmetric junctions, reflectionless tunneling urrently, the field of mesoscopic superconductor/semiconductor hybrid structures experiences a kind of renaissance, owing to recent experimental studies on the detection of Majorana Fermion states.1−3 In these experiments, a superconducting electrode is employed to induce a topological superconducting phase in a semiconductor nanowire by means of the proximity effect. At the ends of the nanowire, Majorana bound states are formed, which can be detected in the electronic transport. The proximity effect can also be utilized to realize a nanowire-based Josephson junction. Here, a semiconductor nanowire is connected by two closely spaced superconducting electrodes. In most cases, low-band gap materials, that is, InAs or InN, comprising a surface accumulation layer, are chosen, because they ensure highly transparent contacts between the nanowire surface and the superconductor.4−8 In addition, Ge/Si core/shell nanowirebased Josephson junctions have also been realized, opening up the route for integration in Si nanowire circuits.9 A striking advantage of employing a semiconductor as a normalconducting bridge is the possibility to control the Josephson supercurrent by means of the field effect. A number of fascinating experiments on fundamental aspects on quantum transport have been conducted on nanowire-based junctions, that is, supercurrent reversal,10 Kondo-enhanced Andreev
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© XXXX American Chemical Society
tunneling,11 hot electron injection,12 or a Josephson quantum electron pump.13 So far, most of experiments on superconductor/semiconductor−nanowire junctions have been conducted in a symmetric junction geometry, that is, a semiconductor nanowire coupled by two identical superconducting electrodes with the same energy gap. In our approach, we realized an asymmetric junction with two different superconductors, comprising a different critical temperature Tc and critical magnetic field Bc. To be more specific, we employed Nb and Al as superconducting materials, where the former has a considerably larger Tc and Bc. Thus, by increasing the temperature or magnetic field, the junction can be transferred from the Josephson regime to a single interface nanowire/ superconductor junction. In order to obtain a complete picture on the nanowire/superconductor interface properties, we first studied the transport properties of symmetric junctions. Subsequently, an asymmetric junction was investigated. As mentioned above, the asymmetric junction provides the advantage to achieve Josephson coupling at zero magnetic Received: April 11, 2014 Revised: August 5, 2014
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field, that is, when the Al electrode is in the superconducting state. Whereas Andreev reflection of quasiparticles at a single Nb/InAs−nanowire interface can be studied when the superconductivity is suppressed in the Al electrode, for example, by means of a small magnetic field. As an interesting feature, in the latter case a distinct zero-bias conductance peak due to reflectionless tunneling14−16 was observed. Hence, in an asymmetric junction the transport can be switched by increasing the temperature or the magnetic field from the Josephson regime, governed by the superconducting phase, to a single interface transport regime. Making use of that feature an asymmetric superconductor−nanowire junction can provide additional design options for samples used in connection with the search for Majorana Fermion states, because the coupling properties of the larger-gap superconductor to the semiconductor nanowire can be determined in more detail. Experimental Section. Highly doped n-type InAs nanowires were grown by selective area metal organic vapor phase epitaxy without using catalyst material. Details of the growth parameters can be found elsewhere.7,17 The device fabrication process has been realized by standard electron beam lithography via double layer electron beam resist, metal deposition, and lift-off. A 100 nm thick superconducting Nb layer was deposited by magnetron sputtering, while for the 100 nm thick Al layer electron beam evaporation was employed. In the latter case, a 5 nm thick Ti interface layer was inserted. Two different types of hybrid structures were fabricated, that is, symmetric junctions (Al/InAs-nanowire/Al, Nb/InAs-nanowire/Nb) and asymmetric junctions (Al/InAs-nanowire/Nb). For the symmetric junctions, the contact electrodes were fabricated in a single electron beam lithography step. Whereas for the asymmetric junctions, we have used two electron beam lithography steps aligned to each other. In order to obtain a high contact transparency of the semiconductor/superconductor interface, Ar+ milling was employed prior to metal deposition to remove native oxides on the nanowire surface. For the Al and Nb layers, a critical temperature Tc of 1.9 and 7.2 K was determined, respectively. Scanning electron microscopy (SEM) images of typical symmetric Al- and Nbbased junctions are presented in Supporting Information. An image of an asymmetric junction can be found in Figure 2a (inset). The electrical transport measurements were carried out in a He-3 cryostat with a base temperature of 0.3 K in a magnetic field up to 7 T. The measurement DC lines were equipped with RC filters to eliminate electrical noise. The electrical measurements were done in a quasi 4-terminal setup with two separated contacts on each Nb electrode. The differential resistance dV/ dI measurements were performed using standard lock-in technique by superimposing a small AC signal at a frequency of 17.3 Hz and an amplitude of 5 nA to the junction DC bias current. The dimensions of the investigated junctions as well as their basic transport properties are given in Table 1. Regarding the basic transport properties, from low-temperature measurements at 4 K on nanowires contacted with normal metal electrodes a resistivity of ρ = 1.8 × 10−5 Ωm, a carrier concentration of n = 1 × 1019 cm−3, an elastic mean free path of le = 15 nm, and a diffusion constant of + = 170 cm2/s were determined. Using + and superconducting gap of the electrodes ΔAl,Nb the normal metal coherence length ξN = (ℏ+ /ΔAl,Nb)1/2 was calculated,18 that is, 300 and 100 nm for the Al and Nb interface, respectively.
Table 1 parameters
Al-J1
Al-J2
Nb-J1
Nb-J2
Nb-J3
Al−NbJ1
L (nm) d (nm) Ic (nA) RN (kΩ) Eth (meV) L/ξN
60 115 500 0.11 3.5 0.2
285 140 213 0.21 0.16 0.95
150 140 110 0.5 0.56 1.5
70 85 -2.1 2.5 0.7
170 95 -4.15 0.44 1.7
210 135 25 1.3 0.29 -
Sample parameters: length (L) and diameter (d) of samples were obtained from scanning electron microscopy images, critical current (Ic) values were extracted from the current−voltage characteristics, normal state resistance (RN) of the samples were determined from the bias current−voltage characteristics at voltages V ≫ 2ΔAl,Nb/e, thouless energy (Eth), and superconducting coherence length in the nanowire (ξN) were determined from the normal state transport measurements.
Results and Discussion. Symmetric Junctions. The current−voltage (IV) characteristics measurements of symmetric junctions have been carried out and the results are presented in the Supporting Information. At low temperatures and zero magnetic field, a pronounced supercurrent has been observed for both Al- and Nb-based symmetric junctions. The critical current values Ic of the junctions are given in Table 1. Owing to the higher critical temperature of Nb the supercurrent in the Nb-based junctions persists up to 4.8 K, while for the Al-based junctions it persists up to 1.5 K. Similar results have been found in magnetic field-dependent measurements, that is, the supercurrent is suppressed at 200 mT in Nb-based junctions7 and at around 20 mT in the Al-based junctions (cf. see Supporting Information). We next focus on the measurement results of subharmonic gap structures of the junctions. In Figure 1a, the differential resistance dV/dI as a function of bias voltage V at various temperatures is plotted for a symmetric Al-based junction (Al-J1). The observed dips in dV/dI are evidence of multiple Andreev reflections.19,20 At 0.4 K, we observed subharmonic gap features at Vn = 2ΔAl/en, for n
Figure 1. Differential resistance dV/dI versus bias voltage V (a) for sample Al-J1 and (b) for sample Nb-J2 at various temperatures. The curves are vertically shifted for clarity. The black dashed lines follow the temperature evolution of the subharmonic gap structures. The color-scale dV/dI as a function of B and V (c) for sample Al-J2 at T = 0.3 K and (d) for sample Nb-J3. B
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= 1, 2 and ΔAl = 140 μeV the superconducting energy gap of Al. With increasing temperature ΔAl decreases, leading to a shift of the subharmonic gap structures toward zero bias. The corresponding measurements for a typical symmetric Nbbased junction (Nb-J2) are depicted in Figure 1b. In contrast to the Al-based structures, here the subharmonic gap structures corresponding to 2ΔNb/e and ΔNb/e evolve as peaks. The subharmonic features vanish at temperatures above 4 K. There is a large number of experimental studies found in literature where peaks in the dV/dI curves at Vn = 2Δ/en for the superconducting Nb-based junctions are reported,5,21−25 while for the superconducting Al-based junctions dips in the dV/dI curves were observed.4,6,9,26,27 Both observations are confirmed by our measurements. It has been theoretically shown by Cuevas et al.18 that in diffusive mesoscopic SNS junctions the shape of the subharmonic gap structures is affected by the ratio of L/ξN. For L/ξN ≪ 1, the subharmonic gap structure consists of a set of pronounced conductance maxima at voltages 2Δ/ne. With increasing the ratio L/ξN, the amplitude of the modulations of the subharmonic gap structure progressively washes out. In addition, at some bias voltages associated with the subharmonic gap structure the conductance peaks evolve into dips at intermediate lengths of the SNS junctions L ∼ ξN. As can be seen, the observed behavior of the subharmonic gap structures in the differential resistance is qualitatively similar to the theoretical calculations.18 Figure 1c shows the color-scaled differential resistance of an Al-based junction (Al-J2) as a function of B and V at a temperature of 0.3 K. It can clearly be seen that the feature corresponding 2ΔAl bends toward zero bias and its amplitude is diminishing with increasing magnetic field. This behavior is because the superconducting energy gap value reduces when the magnetic field is increased. Above the critical field of Al (∼13 mT) all modulations in dV/dI vanish. For the Nb-based junctions, the critical field is much higher, that is, ∼3 T, therefore the subharmonic gap features remain at considerably larger fields, as confirmed by the corresponding data (sample Nb-J3) shown in Figure 1d. The position of the peaks shifts according to the decrease of the superconducting gap with increasing field. Asymmetric Junctions. We now turn to the experimental results on the asymmetric Al/InAs-nanowire/Nb junction (Al− Nb-J1). The corresponding SEM image of the junction is depicted in Figure 2a (inset) while the junction parameters are summarized in Table 1. The IV characteristics are shown in Figure 2a. As can be seen, a Josephson coupling is detected in the junction at zero field and low temperature. The differential resistance dV/dI versus bias voltage is shown in Figure 2b. The measurement has been performed at zero magnetic field at T = 0.3 K, thus both electrodes are in the superconducting state. Close to zero bias, one finds a dip in the differential resistance that is due to the Josephson coupling. Corresponding to the superconducting gap of Nb a pronounced peak is observed at ΔNb/e = 1.1 meV. The peak observed at 0.13 meV can be assigned to the gap of Al: ΔAl/e. Furthermore, an additional feature is found at around 0.5 meV (marked by ★). The first two structures are consistent with the theoretical model by Hurd et al.,28 where features corresponding to the superconducting gaps of the two superconductors are expected. The assignment is also confirmed by the magnetic field dependent measurements of the differential resistance dV/ dI shown in Figure 3a,b. Owing to the large critical field of Nb the peak at 1.1 meV remains at the same position within the
Figure 2. (a) The IV characteristics of the asymmetric Al/InAsnanowire/Nb junction (sample Al−Nb-J1) at different temperatures. The inset shows the corresponding SEM image of the junction. (b) Differential resistance dV/dI versus bias voltage at T = 0.3 K and B = 0 T. The arrows indicate the subharmonic gap structures.
Figure 3. (a) Color-scale plot of dV/dI of the asymmetric Al/InAsnanowire/Nb junction (sample Al−Nb-J1) as a function of magnetic field and bias voltage at 0.3 K. (b) dV/dI versus bias voltage at different magnetic fields, the corresponding parameter range is indicated by the dashed frame in (a). The curves are shifted for clarity.
magnetic field range shown here but vanishes at the critical magnetic field of Nb (∼3T) (not shown). In contrast, the feature assigned to the superconducting gap of Al moves toward zero bias within 13 mT, the critical field of Al. Interestingly, the structure at around 0.5 meV remains at the same position when the magnetic field is varied, even above the critical field of Al. This clearly indicates that the peak is related to the Nb/nanowire interface. The origin of this peak might arise from sequential Andreev reflection processes at a single Nb/nanowire interface. In addition, the amplitude of the peak in the differential resistance reduces at around zero magnetic field at which the Al is in the superconducting state, as can be seen in Figure 3a. The physical origin of this decrease in the C
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thus one can conclude that the process of reflectionless tunneling mainly occurs close to the Nb/nanowire interface. In contrast to the model of Marmorkos et al.,16 the area is considerably smaller than the area limited by the coherence length ξN = 100 nm. However, our result is in accordance with experiments on graphene/superconductor interface, where also a significantly smaller effective area was extracted compared to the area limited by the coherence length.30 From the measurement at B = 20 mT shown in Figure 4a a characteristic voltage V★ of 0.015 mV, corresponding to the full width half-maximum, was determined. The value was extracted at a finite field being slightly larger than Bc,Al, in order to suppress any contribution due to the Josephson effect. A comparison with the Thouless energy of that junction (cf. Table 1) reveals that eV★ is much smaller than Eth. A possible reason is that a degraded nanowire/Nb interface due to Ar+ sputter cleaning leads to enhanced disorder and a reduced effective diffusion constant.31 In Figure 4b, one finds that the amplitude of the zero-bias peak monotonously decreases with increasing temperature. As can be seen in Figure 4d, where the normalized peak height is plotted, the zero-bias peak vanishes completely at 5 K, confirming that this feature is related to the superconducting property of Nb. Summary and Conclusion. In summary, we have fabricated and characterized symmetric and asymmetric nanowire-based Josephson junctions using superconducting Al and Nb electrodes. At low bias current regime, the symmetric junctions exhibited a pronounced Josephson supercurrent. The critical current decreased monotonously with the magnetic field. From a comparison of the subharmonic gap features in symmetric Al- and Nb-based junctions, we found that the different normal metal coherence length resulted in peaklike features in the differential resistance in case of Nb-junctions, while diplike features were observed in case of Al-based junction. In the asymmetric Al/InAs-nanowire/Nb junction, a Josephson supercurrent was observed as well. By applying a small magnetic field, the Al electrode could be transferred into the normal conducting state, which allowed to realize a single superconductor/nanowire interface. Here, a pronounced peak in the differential conductance was observed, which is explained by reflectionless tunneling. We could demonstrate that by means of an asymmetric junction, the transport can be switched from the Josephson regime, where two superconductive electrodes are phasecoherently coupled via a semiconductor nanowire, to a regime, where a single superconductor/nanowire interface governs the transport properties. Our approach might be useful for the design and characterization of structures for the investigation of Majorana bound states using superconductor/nanowire hybrid structures. In order to confirm their existence, the transport through a single superconductor/nanowire interface1,2 can be investigated. Here, the presence of the observed zero-bias conductance peak is a necessary, but not sufficient, condition for the existence of these states and ruling out alternative explanations is a serious challenge.32 Alternatively, junctions with two superconducting electrodes connected by a semiconductor nanowire can also be employed.3,33 As theoretically predicted, signatures of Majorana bound states are expected to appear in measurements of the multiple Andreev reflection current and the Josephson effect.34 Our route using an asymmetric junction might allow to combine both approaches and by that help to obtain a more complete picture.
resistance is due to superconducting correlations induced in the InAs−nanowire by the proximity effect in the transmissive Al/ InAs−nanowire junction. It should be noted that in our measurements of dV/dI versus bias voltage we did not find any indications of subharmonic gap structures where a combination of both superconducting gap energies are involved, as it was theoretically predicted by Hurd et al.28 In Figure 3b, dV/dI versus bias voltage is shown at different magnetic fields. At small magnetic fields B < 10 mT, when the asymmetric junction is in the superconducting state, the Josephson coupling leads to a dip in the differential resistance at zero bias. However, above the critical field of Al (13 mT) the Josephson coupling between the Nb and Al electrodes must be suppressed. Nevertheless, a dip in the differential resistance remains even at higher magnetic fields. We assign this feature to the phenomena of reflectionless tunneling at the nanowire/Nb interface.15,16,29 The underlying mechanism is based on coherent multiple normal and Andreev reflections at the interface leading in total to an enhanced conductance. It is essential that the transport is diffusive, so that there is a chance that (retro)reflected carriers are backscattered to the interface. In order to discuss this phenomenon in more detail, the differential conductance dI/dV was measured at different magnetic fields and temperatures. As can be inferred from Figure 4a, the conductance peak decreases with increasing magnetic field. In Figure 4c, the
Figure 4. (a) Differential conductance vs bias voltage of sample Al− Nb-J1 at various magnetic fields at T = 0.3 K. The curves are vertically shifted for clarity. (b) Corresponding measurements at various temperatures at B = 0. (c) Normalized conductance G0/G0.1 mV as a function of B, with G0 and G0.1 mV the differential conductance at 0 and 0.1 meV, respectively. (d) Corresponding plot as a function of temperature.
normalized differential conductance G0/G0.1 mV is plotted, taking the conductance at 0.1 mV as a reference. It rapidly decreases with increasing magnetic field up to 1.5 T. The enhancement of the conductance completely vanishes for magnetic fields larger than the critical field of the Nb electrode. As a characteristic field B★ for the suppression of the enhanced conductance, we estimated a value of 1.5 T. According to theory,16 B★ corresponds to the situation that during reflectionless tunneling process the phase coherent loops enclose a single magnetic flux quantum h/e. Using B★ = 1.5 T we assessed an effective area of 2800 nm2. This area is smaller than the area of the normal-conducting bridge of the junction, D
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(18) Cuevas, J. C.; Hammer, J.; Kopu, J.; Viljas, J. K.; Eschrig, M. Phys. Rev. B 2006, 73, 184505. (19) Octavio, M.; Tinkham, M.; Blonder, G. E.; Klapwijk, T. M. Phys. Rev. B 1983, 27, 6739−6746. (20) Flensberg, K.; Hansen, J. B.; Octavio, M. Phys. Rev. B 1988, 38, 8707−8711. (21) Gao, J.; Heida, J.; van Wees, B.; Klapwijk, T.; Borghs, G.; Foxon, C. Surf. Sci. 1994, 305, 470−475. (22) Lachenmann, S. G.; Kastalsky, A.; Friedrich, I.; Förster, A.; Uhlisch, D. J. Low Temp. Phys. 1997, 106, 321−326. (23) Chrestin, A.; Matsuyama, T.; Merkt, U. Phys. Rev. B 1997, 55, 8457−8465. (24) Richter, A.; Koch, M.; Matsuyama, T.; Merkt, U. Supercond. Sci. Technol. 1999, 12, 874−876. (25) Lachenmann, S. G.; Förster, A.; Uhlisch, D.; Schäpers, Th.; Kastalsky, A.; Golubov, A. A. Appl. Supercond. 1999, 6, 681−688. (26) Du, X.; Skachko, I.; Andrei, E. Y. Phys. Rev. B 2008, 77, 184507. (27) Nilsson, H. A.; Samuelsson, P.; Caroff, P.; Xu, H. Q. Nano Lett. 2012, 12, 228−233. (28) Hurd, M.; Datta, S.; Bagwell, P. F. Phys. Rev. B 1996, 54, 6557− 6567. (29) Giazotto, F.; Pingue, P.; Beltram, F.; Lazzarino, M.; Orani, D.; Rubini, S.; Franciosi, A. Phys. Rev. Lett. 2001, 87, 216808. (30) Popinciuc, M.; Calado, V. E.; Liu, X. L.; Akhmerov, A. R.; Klapwijk, T. M.; Vandersypen, L. M. K. Phys. Rev. B 2012, 85, 205404. (31) Neurohr, K.; Golubov, A. A.; Klocke, Th.; Kaufmann, J.; Schäpers, Th.; Appenzeller, J.; Uhlisch, D.; Ustinov, A. V.; Hollfelder, M.; Lüth, H.; Braginski, A. I. Phys. Rev. B 1996, 54, 17018−17028. (32) Finck, A. D. K.; Van Harlingen, D. J.; Mohseni, P. K.; Jung, K.; Li, X. Phys. Rev. Lett. 2013, 110, 126406. (33) Churchill, H. O. H.; Fatemi, V.; Grove-Rasmussen, K.; Deng, M. T.; Caroff, P.; Xu, H. Q.; Marcus, C. M. Phys. Rev. B 2013, 87, 241401. (34) San-Jose, P.; Cayao, J.; Prada, E.; Aguado, R. New J. Phys. 2013, 15, 075019.
ASSOCIATED CONTENT
S Supporting Information *
IV characteristics of the symmetric junctions, differential resistance of the asymmetric junction, and figures of typical current−voltage characteristics of a symmetric Al-based junction (sample Al-J1) and Nb-based junction (sample NbJ1) at different temperatures and dV/dI versus bias voltage at different magnetic fields. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected]. *E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank H. Lüth for fruitful discussions, H. Kertz for assistance during the measurements, and S. Trellenkamp for electron beam writing. I.E.B. acknowledges the Russian Foundation for Basic Research and the Russian Ministry of Education and Science, Project No. 14Y.26.31.0007, for financial support.
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REFERENCES
(1) Mourik, V.; Zuo, K.; Frolov, S. M.; Plissard, S. R.; Bakkers, E. P. A. M.; Kouwenhoven, L. P. Science 2012, 336, 1003−1007. (2) Das, A.; Ronen, Y.; Most, Y.; Oreg, Y.; Heiblum, M.; Shtrikman, H. Nat. Phys. 2012, 8, 887. (3) Deng, M. T.; Yu, C. L.; Huang, G. Y.; Larsson, M.; Caroff, P.; Xu, H. Q. Nano Lett. 2012, 12, 6414−6419. (4) Doh, Y.-J.; van Dam, J. A.; Roest, A. L.; Bakkers, E. P. A. M.; Kouwenhoven, L. P.; Franceschi, S. D. Science 2005, 309, 272−275. (5) Frielinghaus, R.; Batov, I. E.; Weides, M.; Kohlstedt, H.; Calarco, R.; Schäpers, Th. Appl. Phys. Lett. 2010, 96, 132504. (6) Nishio, T.; Kozakai, T.; Amaha, S.; Larsson, M.; Nilsson, H. A.; Xu, H. Q.; Zhang, G.; Tateno, K.; Takayanagi, H.; Ishibashi, K. Nanotechnology 2011, 22, 445701. (7) 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. (8) Abay, S.; Nilsson, H.; Wu, F.; Xu, H.; Wilson, C.; Delsing, P. Nano Lett. 2012, 12, 5622−5625. (9) Xiang, J.; Vidan, A.; Tinkham, M.; Westervelt, R. M.; Lieber, C. M. Nat. Nanotechnol. 2006, 1, 208−213. (10) van Dam, J. A.; Nazarov, Y. V.; Bakkers, E. P. A. M.; Franceschi, S. D.; Kouwenhoven, L. P. Nature 2006, 442, 667−670. (11) Sand-Jespersen, T.; Paaske, J.; Andersen, B. M.; GroveRasmussen, K.; Jørgensen, H. I.; Aagesen, M.; Sørensen, C. B.; Lindelof, P. E.; Flensberg, K.; Nygård, J. Phys. Rev. Lett. 2007, 99, 126603. (12) Roddaro, S.; Pescaglini, A.; Ercolani, D.; Sorba, L.; Giazotto, F.; Beltram, F. Nano Res. 2011, 4, 259−265. (13) Giazotto, F.; Spathis, P.; Roddaro, S.; Biswas, S.; Taddei, F.; Governale, M.; Sorba, L. Nat. Phys. 2011, 7, 857−861. (14) Kastalsky, A.; Kleinsasser, A. W.; Greene, L. H.; Bhat, R.; Milliken, F. P.; Harbison, J. P. Phys. Rev. Lett. 1991, 67, 3026−3029. (15) van Wees, B. J.; de Vries, P.; Magnée, P.; Klapwijk, T. M. Phys. Rev. Lett. 1992, 69, 510−513. (16) Marmorkos, I. K.; Beenakker, C. W. J.; Jalabert, R. A. Phys. Rev. B 1993, 48, 2811−2814. (17) Wirths, S.; Weis, K.; Winden, A.; Sladek, K.; Volk, C.; Alagha, S.; Weirich, T. E.; von der Ahe, M.; Hardtdegen, H.; Lüth, H.; Demarina, N.; Grützmacher, D.; Schäpers, Th. J. Appl. Phys. 2011, 110, 053709. E
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