Letter pubs.acs.org/NanoLett
Anomalous Zero-Bias Conductance Peak in a Nb−InSb Nanowire−Nb Hybrid Device M. T. Deng,† C. L. Yu,† G. Y. Huang,† M. Larsson,† P. Caroff,‡ and H. Q. Xu†,§,* †
Division of Solid State Physics, Lund University, Box 118, S-221 00 Lund, Sweden I.E.M.N., UMR CNRS 8520, Avenue Poincaré, BP 60069, F-59652 Villeneuve d’Ascq, France § Department of Electronics and Key Laboratory for the Physics and Chemistry of Nanodevices, Peking University, Beijing 100871, China ‡
S Supporting Information *
ABSTRACT: Semiconductor InSb nanowires are expected to provide an excellent material platform for the study of Majorana fermions in solid state systems. Here, we report on the realization of a Nb−InSb nanowire− Nb hybrid quantum device and the observation of a zero-bias conductance peak structure in the device. An InSb nanowire quantum dot is formed in the device between the two Nb contacts. Due to the proximity effect, the InSb nanowire segments covered by the superconductor Nb contacts turn to superconductors with a superconducting energy gap ΔInSb ∼ 0.25 meV. A tunable critical supercurrent is observed in the device in high back gate voltage regions in which the Fermi level in the InSb nanowire is located above the tunneling barriers of the quantum dot and the device is open to conduction. When a perpendicular magnetic field is applied to the devices, the critical supercurrent is seen to decrease as the magnetic field increases. However, at sufficiently low back gate voltages, the device shows the quasi-particle Coulomb blockade characteristics and the supercurrent is strongly suppressed even at zero magnetic field. This transport characteristic changes when a perpendicular magnetic field stronger than a critical value, at which the Zeeman energy in the InSb nanowire is Ez ∼ ΔInSb, is applied to the device. In this case, the transport measurements show a conductance peak at the zero bias voltage and the entire InSb nanowire in the device behaves as in a topological superconductor phase. We also show that this zero-bias conductance peak structure can persist over a large range of applied magnetic fields and could be interpreted as a transport signature of Majorana fermions in the InSb nanowire. KEYWORDS: Majorana fermion, InSb nanowire, topological superconductor, zero-bias conductance peak mass (m* ∼ 0.015me). These properties should allow to generate a helical liquid in the InSb nanowire, by applying a relatively small magnetic field, and a nontrivial topological superconductor,17−19 which supports a pair of Majorana fermions, by coupling the InSb nanowire to an s-wave superconductor under experimentally feasible conditions. The s-wave superconductor will introduce superconductivity into the InSb nanowire by the proximity effect30 and the external magnetic field will then drive the strongly spin−orbit coupled nanowire system to a topological superconductor phase through Zeeman splitting. The giant Landé g-factor of InSb27,28 guarantees a significantly large Zeeman splitting at a magnetic field well below the critical magnetic field of the swave superconductor. A topological superconductor nanowire can be achieved by covering an entire InSb nanowire with an s-wave super-
T
he search for Majorana fermions is one of the most prominent fundamental research tasks in physics today.1−5 Majorana fermions are an elusive class of fermions that act as their own antiparticles.6 Although an extensive effort has been made worldwide in particle physics, Majorana fermions have so far not been convincingly discovered in free space. In recent years, numerous proposals7−21 for probing Majorana fermions in solid state systems have been suggested. The most recent ones are to explore a topological superconductor phase of a strong spin−orbit coupled semiconductor nanowire in the proximity of an s-wave superconductor.17−19 These proposals have stimulated a new wave of searches for Majorana fermions in solid state systems.22−26 Epitaxially grown InSb nanowires are the most promising material systems for the formation of hybrid devices with an swave superconductor in which zero-energy Majorana fermions can be created under the application of an external magnetic field of a moderate strength. InSb nanowires27−29 possess a large electron g factor (|g*| ∼ 30 − 70), a strong spin−orbit interaction strength (with a spin−orbit interaction energy in the order of ΔSOI ∼ 0.3 meV), and a small electron effective © XXXX American Chemical Society
Received: October 9, 2012 Revised: November 21, 2012
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conductor. However, two technical difficulties for probing Majorana fermions in such a system may arise. First, it may become difficult for an applied magnetic field to penetrate through the superconductor due to the Meissner effect. To get a sufficiently large Zeeman splitting, a strong magnetic field may have to be applied. This could lead to the suppression of the superconductivity in the s-wave superconductor. Second, it is also technically difficult to perform electrical measurements in such a superconductor-covered nanowire system. One way of solving the difficulties would be to lay down an InSb nanowire on the surface of an s-wave superconductor and detect the Majorana fermions using a scanning tunneling microscopy setup. However, to perform such an experiment at an ultralow temperature can be extremely challenging. In this work, we solve these technical difficulties by employing an InSb nanowire quantum dot based Josephson junction structure with two Nbbased contacts. Here, Nb is employed because it has a high superconducting critical magnetic field31 and thus a strong magnetic field can be applied to achieve a sufficiently large penetration field into the InSb nanowire (see Supporting Information). The most important advantage of using such a Josephson junction configuration is that the entire InSb nanowire can be tuned to a topological superconductor by the proximity effect and zero-energy Majorana fermions present in the InSb nanowire can be detected by using the two Nbbased contacts in a standard transport measurement setup. Our Nb−InSb nanowire−Nb hybrid quantum device with a structure schematically shown in figure 1a is fabricated from a high crystalline quality, zinc blende InSb segment of an epitaxially grown InSb/InAs heterostructure nanowire (see Supporting Information for details). Figure 1b shows a scanning electron microscope (SEM) image of the fabricated device. Shown as in figure 1a, in the device, there is a Ti/Au layer at the bottom side of the chip, serving as a global back gate to the nanowire. By tuning the voltage applied to this back gate, Vbg, the chemical potential in the nanowire beneath the superconductors can be tuned, as can be seen from the change in the overall transparency of the Josephson junction device (see Supporting Information). The fabricated devices is first characterized by the transport measurements over a large range of Vbg. At sufficiently high Vbg, the device is relatively open and show a strong Josephson supercurrent (see Supporting Information), as observed in an InSb nanowire based Josephson junction with two Al contacts.30 The presence of a strong supercurrent may hinder the experimental identification of the transport signatures of Majorana fermions in the system. To avoid this problem, we have tuned our device to a low conductance region in which the quasi-particle transport shows the Coulomb blockade characteristics at a low temperature. In the following, we will focus on measurements in the Coulomb blockade regions in which the Josephson supercurrent is strongly suppressed. Figure 1c displays the differential conductance of the device shown in figure 1b measured at the base temperature T = 25 mK and a magnetic field B = 0 T as a function of source-drain bias voltage Vsd and back gate voltage Vbg (charge stability diagram). Here, a clear quasi-particle Coulomb blockade diamond structure is seen, indicating the formation of a quasi-particle quantum dot in the InSb nanowire junction region between the two superconductor contacts. From the Coulomb diamond structure, we can determine that the quasiparticle addition energy of the quantum dot is ∼7 meV, which is much larger than the superconductor energy gap ΔNb of Nb.
Figure 1. Device layout and characterization. (a) Schematics showing a side view (left panel) and a cross-section view (right panel) of the structure of the Nb−InSb nanowire−Nb junction device studied in this work. The device is made from the zinc blende InSb segment of an InAs/InSb heterostructure nanowire with two Ti/Nb/Ti (3 nm/80 nm/5 nm) contacts on a SiO2 capped, highly doped Si substrate, using electron beam lithography, sputtering, and lift-off process. (b) SEM image of the fabricated Nb−InSb nanowire−Nb junction device. In this device, the diameter of the InSb nanowire is about 65 nm, the separation between the two Nb based contacts is about 110 nm, and the lengths of the InSb nanowire sections covered by the two Nb based contacts are about 740 and 680 nm, respectively. (c) Differential conductance on a color scale measured for the device shown in part b as a function of source-drain bias voltage Vsd and back gate voltage Vbg (charge stability diagram) at the base temperature of T = 25 mK and a magnetic field of B = 0 T. The measurements show a quasi-particle Coulomb blockade diamond structure with a quasi-particle addition energy ΔEadd ∼ 7 meV to the InSb nanowire quantum dot. The weak vertical stripes of high conductance seen in the Coulomb blockade region arise from multiple Andreev reflections with the superconductor energy gaps, ΔNb and ΔInSb, related, respectively, to the two Nb based contacts and the two proximity-effect-induced superconducting InSb nanowire segments covered by the Nb based contacts. (d) Differential conductance as a function of Vsd measured for the device shown in part b at Vbg = −11.1 V, i.e., along the white dashed line in part c, and T = 25 mK, and at different magnetic fields applied perpendicularly to the substrate and to the InSb nanowire. The measured curves are successively offset by 0.02 e2/h for clarity. Here, multiple Andreev reflection induced conductance peaks due to the presence of the superconductor energy gaps ΔNb and ΔInSb can be identified and are labeled for clarity. The dashed lines that mark the peak positions are used as guidelines. (e) Differential conductance as a function of Vsd measured for the device shown in part b at Vbg = −11.1 V, corresponding to the white dashed line in part c, and B = 0 T, and at different temperatures. Here, the measured curves are successively offset by 0.06 e2/h for clarity. The multiple Andreev reflection induced conductance peaks are again seen in the measurements and are labeled in the figure. The dashed lines are used once more as guidelines. B
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topological superconductor, supporting the pair of the remaining zero-energy Majorana fermions (see Supporting Information for the results of our modeling and simulation), which are located at the two ends of the entire nanowire and are therefore strongly coupled to the Nb contacts. Cooper pairs can move between the two Nb contacts via the Majorana fermion states, leading to an enhancement in the zero-bias conductance. We will show below that such an enhancement in zero-bias conductance could be observed in our Nb−InSb nanowire−Nb quantum device in the quasi-particle Coulomb blockade regime. We first present our magnetic field dependent measurements of the differential conductance for the device at Vbg = −11.1 V for which the device is in a quasi-particle Coulomb blockade region. Figure 2a shows the results of the measurements. Here, a low conductance gap can be clearly identified in the small
Inside the Coulomb blockade region, vertical stripe features of high conductance can be identified. These high conductance stripe features are due to multiple Andreev reflections. Figure 1d shows the differential conductance traces measured at a fixed back gate voltage of Vbg = −11.1 V (i.e., along the white dashed line cut in figure 1c) and the base temperature T = 25 mK for different magnetic fields B applied perpendicularly to the substrate and thereby to the nanowire. Here, we can clearly observe six conductance peaks in each measured curve, roughly located symmetrically around Vsd = 0 V. The four peaks at larger |Vsd| arise from the first- and second-order multiple Andreev reflections, associated with the superconductor energy gap ΔNb of the Nb contacts as indicated in the figure. The two peaks at smaller |Vsd| arise from the first-order multiple Andreev reflections, associated with the proximity effect induced superconductor energy gap ΔInSb of the InSb nanowire.32 The |Vsd| positions of all these peaks show weak dependences on B at the magnetic fields of B ≤ 4.5 T, indicating that the critical magnetic field of the thin Nb contacts is large and goes well beyond 4.5 T. The measurements also imply that the Nbcontacted InSb nanowire segments remain in a superconductor phase in the presence of these applied magnetic fields. Figure 1d shows the differential conductance traces measured at Vbg = −11.1 V and B = 0 T for different temperatures. Here, we observe a weak temperature dependences of the |Vsd| positions of the conductance peaks, indicating that the values of the critical temperature Tc are high and go beyond 1 K in the Nb and the proximity effect induced InSb nanowire superconductors. Furthermore, from the measured multiple Andreev reflection conductance peaks shown in figures 1d and 1e, we can deduce ΔNb = 1.55 meV and ΔInSb = 0.25 meV in agreement with the measurements reported in refs. 22 and 32. To search for Majorana fermions, we drive the Nb-contacted InSb nanowire segments in our device from a trivial superconductor phase to a nontrivial topological superconductor phase. This is done by applying an external magnetic field B perpendicularly to the nanowire (and also to the substrate). The magnetic field introduces a Zeeman energy Ez = 1/2|g*|μBB̃ , where μB = eℏ/2me is the Bohr magneton, g* is the effective g-factor, and B̃ is the magnetic field actually applied on the Nb-contacted InSb nanowire segments. The phase transition from the trivial superconductor phase to the nontrivial topological superconductor phase in the Nbcontacted InSb nanowire segments occurs at Ez = (ΔInSb2 + μ2)1/2, where μ is the chemical potential.14 It is difficult to accurately determine the strength of the externally applied magnetic field BT at which the phase transition in the InSb nanowire occurs. However, using the Nb thin film value of λL ∼ 130 nm for the magnetic field penetration depth (see Supporting Information), and the g-factor of |g*| ∼ 30−70 and the superconductor energy gap of ΔInSb ∼ 0.25 meV for the InSb nanowire, we can estimate that the lower limit value of BT is in the range 0.25−0.58 T. When there is no coupling between the two Nb-covered InSb nanowire segments in the device, each of the two nanowire segments in a topological superconductor phase should support a pair of Majorana fermions located at the two ends of the segment.21 When the two topological superconducting InSb nanowire segments are coherently connected via a quasi-particle quantum object, e.g., quantum dot, the interaction between a pair of nearby zero-energy Majorana fermions leads to the creation of a pair of normal fermion states at finite energies. The entire nanowire will then behave as a
Figure 2. Signature of the zero-bias anomaly in the Nb−InSb nanowire−Nb hybrid quantum device. (a) Differential conductance on a color scale as a function of source-drain bias voltage Vsd and magnetic field B applied perpendicularly to the substrate and to the InSb nanowire measured for the device shown in figure 1b at Vbg = −11.1 V (corresponding to the white dashed line in figure 1c) and T = 25 mK. A pronounced zero bias conductance peak is seen to emerge when the magnetic field exceeds ∼1 T. (b) Same measurements as in part a, but with a high magnetic field resolution. Here, the zero-bias conductance peaks are more clearly seen and appear in both the positive and the negative magnetic field direction. (c) Same measurements as in part b, but the differential conductance traces measured in the region marked by the dashed square in part b are shown. Here, the measured curves are successively offset by 0.05 e2/h for clarity. In this figure, in addition to the zero-bias conductance peak, two side differential conductance peaks are seen to appear at finite Vsd. (d) Differential conductance as a function of B at Vsd = 0 V (black curve) corresponding to a line plot along Vsd = 0 V in part c. Here, it is seen that the zero-bias conductance shows a plateau structure. The slope in the plateau could be due to a change in the background conductance with increasing B in the region, as indicated by the differential conductance measurements at Vsd = 1 mV (red curve). C
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would simply be the result of a supercurrent transistor effect and, as the magnetic field is further increased, the conductance peak should shift to finite bias voltages, which is again not consistent with our observation shown in figure 2. To further test the possibility of a simple magnetic field induced levelshifting mechanism, we shown in figure 3a high-resolution
source-drain bias voltage region. This low conductance gap structure can be attributed to the presence of the superconductor energy gap ΔInSb in the Nb-contacted InSb nanowire segments. More importantly, figure 2a shows the emergence of a pronounced high zero-bias conductance peak structure as the magnetic field exceeds ∼1 T. To see this high zero-bias conductance peak structure more clearly, we show in Figure 2b the corresponding high-resolution magnetic field dependence measurements. Here, two high zero-bias conductance peak structures, located symmetrically with respect to zero magnetic field, can be clearly identified. Figure 2c shows close-up traces for visualization of the details in the region of the measurements marked by a dashed square in figure 2b. Here, we see that the differential conductance shows a distinct peak structure at zero bias voltage at magnetic fields of B ∼ 1−2.5 T. In addition, along with the zero-bias conductance peak, there are two side peaks. The origin of the two side peaks is not known, but one possible cause for the two side peaks could be transport through the two normal fermion states created as a result of the annihilation of the pair of Majorana fermions adjacent to the InSb nanowire quantum dot, as predicted by our theoretical calculations presented in the Supporting Information. Figure 2d shows a trace of the differential conductance at zero bias voltage, where the zero-bias conductance peak structure is seen to appear as a plateau. Figure 2d also shows a corresponding trace of the differential conductance measured at a finite bias voltage of Vsd = 1 mV. A comparison between the two traces may imply that the small slope seen in the zero-bias conductance plateau is due to a change in the background differential conductance with increasing Vbg. This zero-bias conductance plateau structure is consistent with the physical picture that a pair of Majorana fermions can be created in a certain range of the applied magnetic fields for which the entire InSb nanowire is in a topological superconductor phase. In a Josephson junction device, there are several other mechanisms that can cause a zero-bias conductance peak, such as the Kondo effect, supercurrent, and high order multiple Andreev reflections. For the Kondo effect, irrespective of half or integer spin Kondo effect, an associated zero-bias conductance peak should split and move to finite bias voltage positions with an increasing magnetic field. In a recent experiment,26 a zerobias conductance peak due to the Kondo effect in a Al-based Josephson junction device was observed at weak magnetic fields (about 10−20 mT), for which the splitting of the Kondo peak could not be clearly resolved. However, in our measurements, the zero-bias conductance peak appear at much stronger magnetic fields (about 1.2−2.7 T) and it does not show splitting over about a 1.5 T range of magnetic fields. Therefore, the zero-bias conductance peak we have observed in our experiment could not be a feature of the Kondo effect. Supercurrent and high order multiple Andreev reflections can also give a zero-bias conductance peak. However, in both cases, the zero-bias conductance peak will decrease with an increasing magnetic field. This is clearly not consistent with our observations, and therefore, all these superconductivity effects cannot be considered as the physical origin of the zero-bias conductance peak that we have observed. One may also argue that an applied perpendicular magnetic field could change the energy level positions in the InSb nanowire quantum dot, leading to level shifting, due to, e.g., the Zeeman effect and thus occasionally turn the device to resonant conduction even if the device is in a Coulomb blockade region at B = 0 T. In such a case, the magnetic field induced zero-bias conductance peak
Figure 3. Zero-bias conductance peak and its gate voltage and temperature dependences. (a) High-resolution measurements of the differential conductance on a color scale as a function of Vsd and Vbg (charge stability diagram) for the device shown in figure 1b at B = 1.8 T, for which the device show a strong zero-bias conductance peak, and T = 25 mK. Here, only the measurements in the center of the Coulomb blockade region are shown. (b) Differential conductance on a color scale as a function of Vsd and temperature T measured for the device at B = 1.8 T and Vbg = −11.1 V. Here, it is seen that the zerobias conductance peak becomes hardly visible when the temperature goes above 350 mK. (c) Same measurements as in part b but for a line cut along Vsd = 0 V.
measurements of the charge stability diagram in the center of the quasi-particle Coulomb blockade region at B = 1.8 T for which the measurements show a strong zero-bias conductance peak (cf. figure 2). Clearly, the zero-bias conductance peak does not show any shift toward finite bias voltages as the back gate voltage changes, which is in a strong contrast to what would be suggested by the magnetic field induced level shifting mechanism. It should also be noted that in a recent theoretical work,33 it was predicted that weak antilocalization could induce a zero-bias conductance peak in a disordered Majorana nanowire. However, due to the inclusion of a quantum dot in our Nb−InSb nanowire−Nb device, the weak antilocalization induced zero-bias conductance peak should be suppressed by the Coulomb blockade effect. Overall, in absence of any other relevant physical mechanism or theory to date, the zero-bias conductance peak structure observed in the device shown in Figure 2b is most likely a transport signature of Majorana fermions in the InSb nanowire. Figures 3b and 3c show the temperature dependence measurements of the zero-bias conductance peak. Figure 3b displays the differential conductance measured at B = 1.8 T and Vbg = −11.1 V as a function of source-drain bias voltage Vsd and temperature T, while figure 3c shows the measured differential conductance trace at Vsd = 0. Here, we find that the zero-bias conductance peak decreases gradually as the temperature is increased and becomes to be hardly visible at a temperature T ∼ 350 mK (which corresponds to an energy scale of 32 μeV) and above. The exact physical mechanism of this temperature D
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gap evolution structure is also visible in Figures 2c and 4a. In Figure 4b, we clearly see that the gap almost vanishes again at the upper edge of the zero-bias conductance plateau and then reopens as the magnetic field is increased further. We have also fabricated and measured a normal metal−InSb nanowire quantum dot-superconductor device similar to the device reported in ref 22. As shown in the Supporting Information, the measurements show a weak zero-bias conductance peak structure in the same magnetic field region as we reported above. This zero-bias conductance peak structure could also arise from zero-energy Majorana fermions in the superconductor-contacted InSb nanowire in the normal metal-InSb nanowire quantum dot-superconductor device. In summary, we have studied a Nb−InSb nanowire−Nb hybrid quantum device by transport measurements and observed a zero-bias conductance peak structure at finite perpendicularly applied magnetic fields. At zero magnetic field, the Nb-contacted InSb nanowire segments are found to be in a trivial superconductor phase. As the applied magnetic field is increased, the entire InSb nanowire in the device, including the two Nb-contacted segments and the middle quantum dot junction segment, changes to a topological superconductor phase, supporting a pair of Majorana fermions. Cooper pair transport through the InSb nanowire via the Majorana fermion states could lead to the zero-bias conductance peak structure observed in this work. A further proof of the appearance of Majorana fermions in InSb nanowires would be the measurements of a SQUID structure in which the Josephson current is predicted to show a characteristic dependence on the phase difference φ between the two superconductor contacts.17,18,35
suppression of the zero-bias conductance peak is not known. One possible origin could be thermal excitation to normal fermion states 34 including, e.g., those created by the annihilation of the pair of Majorana fermions adjacent to the InSb quantum dot. Zero-bias conductance plateau-like structures have also been observed in other gate voltage regions. Figure 4a shows
Figure 4. Zero-bias conductance plateau structures at different back gate voltages. (a) Differential conductance as a function of sourcedrain bias voltage Vsd and magnetic field B applied perpendicularly to the substrate and to the InSb nanowire measured for the device at Vbg = −13 V and T = 25 mK. (b) Same as in part a but for Vbg = −15 V. (c) Same as in part a but the differential conductance measured as a function of B at Vsd = 0 V is plotted. (d) Same as in part c but for Vbg = −15 V.
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ASSOCIATED CONTENT
S Supporting Information *
Device fabrication, electrical characterization of the device reported in the main article, zero-bias conductance peak structure observed in the measurements of a Au−InSb nanowire quantum dot−Nb device, superconducting properties of the Ti/Nb/Ti trilayer, and theoretical model and simulation results. This information is available free of charge via the Internet at http://pubs.acs.org.
measurements of the differential conductance as a function of source-drain bias voltage Vsd and applied magnetic field B at a fixed back gate voltage of Vbg = −13 V, while Figure 4b shows the same type of measurements at Vbg = −15 V. Figures 4c and 4d show the corresponding traces of the measurements at the zero source-drain bias voltage. Figures 4a and 4c show that the zero-bias conductance has a value of ∼1.0e2/h at B = 0 T and stay approximately at a constant value as B increases. The zerobias conductance starts to increase quickly from B ∼ 1.3 T and reaches a plateau value of ∼1.3e2/h at B ∼ 2 T. The zero-bias conductance stays at the constant value until B = 2.8 T and then jumps to a lower value as a result of a charge rearrangement (see Figure 4a for a clear signature of the charge rearrangement). In fact, a plateau-like zero-bias conductance structure can still be identified after the charge rearrangement. Figures 4b and 4d show similar characteristics of the differential conductance. Here, the zero-bias conductance plateau can be identified to appear in a magnetic field range of 0.9−2.6 T, although it is superimposed by fluctuations and a visible slope. In addition, the differential conductance measurements in the small Vsd region are characterized by a gap at low magnetic fields, that nearly vanishes at the edge of the zero-bias conductance plateau and reopens as the magnetic field is continuously increased. This gap evolution behavior is similar to the one predicted in ref 19. Here we should note that such a
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Author Contributions
M. T. Deng participated in the development of the idea for the experiment, led and participated in the device fabrication, performed the measurements and the data analysis, and participated in the developments of the physical concepts for the observation and in the writing of the paper. C. L. Yu fabricated the device and participated in the measurements. G. Y. Huang performed numerical calculations. M. Larsson participated in the measurements. P. Caroff grew the InSb nanowires used for this work. H. Q. Xu had the idea for and initiated the experiment, participated in the data analysis, developed the physical concepts for the observation, wrote the manuscript, and supervised the whole project. All the authors discussed the results and commented on the manuscript. Notes
The authors declare no competing financial interest. E
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(24) Rokhinson, L. P.; Liu, X.; Furdyna, J. K. The fractional a.c. Josephson effect in a semiconductor−superconductor nanowire as a signature of Majorana particles. Nat. Phys. 2012, 8, 795−799. (25) Das, A.; Ronen, Y.; Most, Y.; Oreg, Y.; Heiblum, M.; Shtrikman, H. Zero-bias peaks and splitting in an Al−InAs nanowire topological superconductor as a signature of Majorana fermions. Nat. Phys. 2012, DOI: 10.1038/nphys2479. (26) Lee, E. J. H.; Jiang, X.; Aguado, R.; Katsaros, G.; Lieber, C. M.; De Franceschi, S. Zero-bias anomaly in a nanowire quantum dot coupled to superconductors. Phys. Rev. Lett. 2012, 109, 186802. (27) Nilsson, H. A.; Caroff, P.; Thelander, C.; Larsson, M.; Wagner, J. B.; Wernersson, L.-E.; Samuelson, L.; Xu, H. Q. Giant, leveldependent g factors in InSb nanowire quantum dots. Nano Lett. 2009, 9, 3151−3156. (28) Nilsson, H. A.; Karlström, O.; Larsson, M.; Caroff, P.; Pedersen, J. N.; Samuelson, L.; Wacker, A.; Wernersson, L.-E.; Xu, H. Q. Correlation-Induced Conductance Suppression at Level Degeneracy in a Quantum Dot. Phys. Rev. Lett. 2010, 104, 186804. (29) Nilsson, H. A.; et al. InSb Nanowire Field-Effect Transistors and Quantum-Dot Devices. IEEE J. Sel. Top. Quantum Electron. 2011, 17, 907−914. (30) Nilsson, H. A.; Samuelsson, P.; Caroff, P.; Xu, H. Q. Supercurrent and multiple Andreev reflections in an InSb nanowire Josephson junction. Nano Lett. 2012, 12, 228−233. (31) Bose, S.; Raychaudhuri, P.; Banerjee, R.; Ayyub, P. Upper critical field in nanostructured Nb: Competing effects of the reduction in density of states and the mean free path. Phys. Rev. B 2006, 74, 224502. (32) Deon, F.; et al. Proximity effect in a two-dimensional electron gas probed with a lateral quantum dot. Phys. Rev. B 2011, 84, 100506. (33) Pikulin, D. I.; Dahlhaus, J. P.; Wimmer, M.; Schomerus, H.; Beenakker, C. W. J. Zero-voltage conductance peak from weak antilocalization in a Majorana nanowire. arXiv 2012, DOI: arXiv:1206.6687. (34) Law, K. T.; Lee, P. A. Robustness of Majorana fermion induced fractional Josephson effect in multichannel superconducting wires. Phys. Rev. B 2011, 84, 081304. (35) Zazunov, A.; Egger, R. Supercurrent blockade in Josephson junctions with a Majorana wire. Phys. Rev. B 2012, 85, 104514.
ACKNOWLEDGMENTS This work was supported by the Swedish Research Council (VR), the Swedish Foundation for Strategic Research (SSF), the Chinese Scholarship Council (CSC), and the National Basic Research Program of the Ministry of Science and Technology of China (Nos. 2012CB932703 and 2012CB932700).
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