Direct Measurement of Current-Phase Relations in Superconductor

Pearl vortices occur in longer junctions, indicating suppressed superconductivity in aluminum, probably due to a proximity effect. Our observations es...
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Letter pubs.acs.org/NanoLett

Direct Measurement of Current-Phase Relations in Superconductor/ Topological Insulator/Superconductor Junctions Ilya Sochnikov,*,†,‡ Andrew J. Bestwick,∥ James R. Williams,∥ Thomas M. Lippman,§ Ian R. Fisher,†,§ David Goldhaber-Gordon,‡,§,∥ John R. Kirtley,†,‡ and Kathryn A. Moler†,‡,§,∥ †

Department of Applied Physics, Stanford University, Stanford, California 94305, United States Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, United States § Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, United States ∥ Department of Physics, Stanford University, Stanford, California 94305, United States ‡

ABSTRACT: Proximity to a superconductor is predicted to induce exotic quantum phases in topological insulators. Here, scanning superconducting quantum interference device (SQUID) microscopy reveals that aluminum superconducting rings with topologically insulating Bi2Se3 junctions exhibit a conventional, nearly sinusoidal 2π-periodic current-phase relations. Pearl vortices occur in longer junctions, indicating suppressed superconductivity in aluminum, probably due to a proximity effect. Our observations establish scanning SQUID as a general tool for characterizing proximity effects and for measuring current-phase relations in new materials systems.

KEYWORDS: Topological insulator, Majorana fermions, superconducting proximity effect, current-phase relation, Josephson junction, scanning SQUID microscopy

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these predictions have motivated our development of a technique to measure the current-phase relation. The current-phase relation can be measured by various methodologies, including radiofrequency superconducting quantum interference device (RF-SQUID)32 and direct current (DC)-SQUID.29 The main experimental advantage of the scanning SQUID technique, which we use here to measure the current-phase relation in superconductor/topological insulator/ superconductor junctions, is the contactless testing of many devices without the need to connect each individual device to external electronics. Variations from device to device can thus be tested easily. Local information on the London or the Josephson penetration depths is also important for interpreting phenomena such as the Fraunhofer interference of charge carriers in topological insulator/superconductor Josephson junctions. Scanning SQUID offers high magnetic-field sensitivity that is comparable to or better than the sensitivity of stationary SQUIDs for measuring mesoscopic superconducting structures33−35 without exposing the measured sample to additional fabrication steps. In addition, scanning SQUIDs provide valuable information about the spatial distribution of magnetic flux in superconductors,36 information that is not available in static SQUIDs.

ajor efforts are currently underway to test for the existence of Majorana fermions (see refs 1−3 and references therein) in semiconductors with strong spin−orbit coupling or in topological insulators.4−20 One class of proposals is based on inducing superconductivity in a topological insulator via proximity to a superconductor in a geometry such as a Josephson junction.21−23 Most experiments on such systems4−7,9−11,13,15−20 have been based on electronic transport, for example, voltage−current characteristics and Fraunhofer magnetic interference patterns. Yet, theoretical proposals to detect Majorana fermions are often formulated in terms of the current-phase relation of the superconductor/ topological insulator/superconductor Josephson junction.1,21−26 The current-phase relation is the dependence of the supercurrent across a Josephson junction on the phase change in the Cooper pair wave function across the junction. It can be sensitive to junction characteristics27 such as unconventional symmetry of the superconducting order parameter,28 or scattering and tunneling mechanisms through ferromagnetic29 and two-dimensional conducting30,31 junction materials. In topological insulator/superconductor systems such as the one explored in this work, the current-phase relation may potentially reveal the surface ballistic nature of an induced superconducting state25 or even the presence of Majorana fermions.21−23 Although many factors may complicate their experimental realization, as described throughout this Letter, © XXXX American Chemical Society

Received: March 17, 2013 Revised: May 29, 2013

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directly measure the postprocessing conductivity of the surface and bulk of the current devices given their sizes and geometries. Flakes of thickness d ≈ 100 nm, as determined by atomic force microscopy, were obtained from these crystals via mechanical exfoliation. Junction structures were fabricated via electron beam lithography with standard poly(methyl methacrylate) resist, followed by deposition of layers of Ti and Al (3 nm/40 nm; Figure 1). The thin Ti layer improves the conductivity of the Al/Bi2Se3 interface. We used a scanning SQUID susceptometer with two field coil and pickup loop pairs in a gradiometer configuration37 (Figure 1a shows only one pickup loop and field coil). The scanning apparatus was mounted in a 3He cryostat, with a sample base temperature of ∼500 mK, the temperature at which most of our measurements were performed. The whitenoise base levels of our scanning SQUID systems are typically below 1 μΦ0/(Hz)1/2,37 in the same range or better than the sensitivities of the best stationary SQUIDs. In this investigation we primarily operated the SQUID sensors in real-time magnetometry mode.34,39 The local magnetic field was swept relatively slowly by ramping the current through the field coil, inducing a local magnetic field. In a superconducting ring with a Josephson junction, the amount of applied magnetic flux piercing the ring, Φapl, will enforce a phase difference across the Josephson junction in the ring of φ = 2π (Φapl/Φ0), and induce supercurrents in the structure (Φ0 = h/2e is the superconducting flux quantum, h is the Planck constant, e is the electron charge). Then, the magnetic flux produced by the supercurrents in the structure is detected with the pickup loop. The latter can be calibrated to reflect the value of the concentric supercurrent, Is(φ) (Figure 1). This type of measurement reveals information not available in time-averaged measurements and yields information on dynamic processes occurring in a bandwidth up to a few kilohertz, such as vortex jumps and fluxoid transitions.33 We used this mode to measure the current-phase relation in superconducting rings with topological insulator Josephson junctions and to detect vortex jumps in a long superconductor/topological insulator Josephson junction. Figure 2a depicts the magnetic response of a ring with a Josephson junction; the flux, Φ, is coupled into the SQUID by the pickup loop, while the magnetic field is applied by ramping the current IFC in the field coil. The Φ(IFC) curve shown in Figure 2a was measured above the ring center (Figure 1a). We fit this measured response to the functional form

Here we employed scanning SQUID microscopy to investigate two kinds of structures combining the topological insulator Bi2Se3 and the s-wave superconductor Al: (i) an Al ring with a junction made of Bi2Se3, with a junction length L = 1 μm and a width of w = 50−100 nm (Figure 1a), and (ii) a

Figure 1. Two geometries for scanning SQUID studies of the superconductor/topological insulator/superconductor junctions. (a) Left, schematic of the setup for measuring the current-phase relation in an Al ring with a Bi2Se3 Josephson junction. A current is applied through the field coil (green); as a result, a supercurrent around the ring, Is, is induced in the superconducting loop with a topological insulator Josephson junction. This supercurrent modifies the magnetic flux, which is detected by the pickup loop of the SQUID sensor (brown).37 Spatial variation of the phase φ of the Cooper pair wave function occurs mainly across the junction and is set by the flux piercing the measured ring. The SQUID sensor can be moved (scanning imaging) to acquire the spatial dependence of the response from each ring. Right, scanning electron microscopy of a typical sample; the Bi2Se3 flake appears at right. (b) Left, schematic of a longer Josephson junction with width 50−100 nm and a junction length of 6 μm. The junction is smaller than the pickup loop (∼1.5 μm in radius), allowing direct magnetic imaging. Right, scanning electron microscopy of a sample with a brighter Bi2Se3 flake and darker Al pads. Scale bars, 1 μm.

junction whose two superconducting leads are not closed into a ring, with a junction length L = 6 μm μm and a width, w = 50− 100 nm (Figure 1b). The junction width is defined as the shortest distance between the two superconductors, and the length is the distance along the superconducting edges at the opening. The shorter junctions in the ring geometry allowed direct measurements of the current-phase relation; in the longer junction in the nonring geometry, we directly observed vortices in the junction leads. Single crystals of (Bi1−xSbx)2Se3 were synthesized by slow cooling a binary melt of Bi (99.9999%), Sb (99.999%), and Se (99.9999%) starting materials mixed at a ratio of 0.33:0.05:0.62. The actual proportion x of Sb in the single crystals was approximately 0.01, as measured in microprobe analysis. Bulk single crystals with dimensions 1 × 1 × 0.1 mm3 exhibited nonmetallic resistivity at low temperatures with a bulk carrier density of 7 × 1016 cm3, as deduced by Hall and Shubnikov−de Haas analysis.38 Postgrowth processing of the crystals may affect the surface and bulk Fermi level; we were unable to

Φ(IFC) = C0IFC + C1 sin(IFC/Ip + δ1) + C2 sin(2IFC/Ip + δ2)

where Ip is the period of oscillations in Φ(IFC) in the units of field coil current and δ1 and δ2 are phase shifts. We then decomposed this total response signal into a linear component, Φlinear = C0IFC (Figure 2b), and a periodic component, Φperiodic = Φ − C0IFC (Figure 2c). We interpreted the linear component as corresponding primarily to the signals induced by shielding currents flowing in Al outside of the junction and smaller shielding currents in the junction region, while the periodic component corresponds to Josephson currents through the topological insulator and along the ring circumference. The current through the junction and around the ring was extracted from the periodic component of the flux through the pickup loop using the estimated 2 pH mutual inductance between the B

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Figure 3. Periodicity of the oscillations in the current-phase relation. The main panel shows a fast Fourier transform of the field-periodic component of Φ(IFC), as measured above the center of one of the rings with a superconductor/topological insulator/superconductor junction. Φ(IFC) data prior to the fast Fourier transformation appear in the inset. A dominant Φ0 component in the sine (in-phase, red) parts and a smaller component in the cosine parts (out-of-phase, blue) are detected. A small negative Φ0/2 component is also detected in the sine component; these two frequencies are marked by arrows pointing up and down, respectively.

small negative sine component of the second harmonic. To improve the signal-to-noise ratio, we measured the oscillations over a wider field range (inset to Figure 3); these data was used to generate the main panel of Figure 3. Measurements of six rings with Bi2Se3 junctions, all of the same geometry, revealed similar current-phase relations that were nearly sinusoidal, Φ0-periodic, and carried a small negative Φ0/2 component (we designate this component as “negative” because the second harmonic component is antiphase with respect to the base sine component). The average amplitude of the second harmonic measured in five rings with junctions was ∼0.025 that of the first harmonic, varying between ∼0.015 and ∼0.042 in different rings (data not shown). The negative sinusoidal Φ0/2 component is consistent with the predicted forward “skewness” (described below) in the current-phase relation of superconductor/topological insulator/superconductor junctions at flux values equal to half-integer multiples of the flux-quantum.22,25,26 However, these measured circulating current versus phase curves can also be reproduced well within a theoretical model for a short bridge Josephson junction by assuming a sinusoidal current-phase relation in the junction and an inductance-related parameter β ≈ 0.1, so the forward skewness may be due to self-inductance effects and may not be indicative of exotic behavior.40,41 We now discuss the possible scenarios for unconventional current-phase relations in topologically nontrivial junctions. Kitaev predicted that the Josephson energy EJ could be 2π periodic but 2-valued, such that it appears to be 4π-periodic if the system preserves the fermion parity (in other words, the system stays on a single branch of the 2-valued energy).2,42 As a general point, any single junction with trivial superconducting leads cannot have a 4π-periodic current-phase relation in equilibrium because the state of each lead is only defined modulo 2π. In equilibrium, the current-phase relation is therefore expected to be 2π-periodic with deviations from sinusoidal behavior22 that may be as extreme as discontinuities25,26 in the current when the phase drop across the junction is close to half-integer multiples of 2π (φ = π, 3π, etc.). For this reason, we describe the predicted current-phase

Figure 2. Decomposition of the magnetic response of a ring with a superconductor/topological insulator/superconductor Josephson junction. (a) A typical flux vs field coil current curve measured close to the center of the ring in Figure 1a. (b) The linear component of the flux− current curve from part a. (c) The periodic component of the fluxcurrent curve from part a. The field coil current axis is expressed in units of the phase drop. The flux from the ring is expressed as Josephson current circulating in the ring (left ordinate). (d) The magnitude of the linear component of the flux-current curve mapped as a function of the SQUID sensor position above the ring produces an “image” of the Al regions (image size is 15 × 15 μm). (e) The amplitude of the oscillations mapped as a function of the SQUID sensor position generates an image of the flux coming from the Josephson currents flowing around the ring, hence the circular symmetry of the image (image size is 15 × 15 μm).

ring and the pickup loop. The resulting current-phase characteristic is displayed in Figure 2c. We measured the response curves, Φ(IFC), at various locations above the sample in a scanning/stepping mode. Each curve was acquired at a different location and decomposed as described above to generate two different images of the measured ring. The first image (Figure 2d) was constructed from C0. A comparison of the image in Figure 2d with the scanning electron microscopy image in Figure 1a indicates that stronger and weaker signals in C0 were observed above the Al parts and above the junction, respectively. The location of the junction can be inferred from this measurement. The second image, which is symmetric around the ring center (Figure 2e), was constructed using C1 and reflects the Josephson currents crossing the junction and circulating in the ring. These images demonstrate an effective method for magnetic imaging of complex structures involving Josephson junctions but also enable derivation of the quantitative characteristics of these structures, including the current-phase relation. Figure 3 demonstrates that the oscillations described above are Φ0-periodic and are primarily sinusoidal, with a small cosine component of the same periodicity that is possibly due to a very small residual magnetic field in the measurement system and a C

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exhibit 4π-periodic circulating current in our experimental method. We now turn to another factor that may influence the measured current passing through the junctions: vortices that may be induced in the superconducting leads. In order to observe possible induced vortices in the superconductor/ topological insulator/superconductor structures, we prepared a longer junction (Figure 1b). Figure 4a depicts the magnetic flux Φ measured at four locations above this long superconductor/ topological insulator/superconductor junction. When measured above the junction center (curve 1 and location 1 in Figure 4a), the response first rose linearly with the applied magnetic field (current through the field coil; arrow pointing up and right in Figure 4a). When the applied current exceeded ∼5 mA, vortices appeared in the junction, a behavior that manifested as jumps in Φ(IFC). At 7 mA, the current through the field coil was swept down, and Φ(IFC) was linear (field coil current I1; arrow pointing down and left in Figure 4a). At field coil currents smaller than ∼3 mA, vortices began to exit the junction region (three steps in Φ(IFC) indicated by vertical lines I2 − I3 in Figure 4a). Three additional Φ(IFC) curves, labeled as 2−4 in Figure 4a, show that the observation of vortices depends strongly on the location of the SQUID sensor above the sample. While Φ(IFC) at the junction center displayed a total of three jumps, on the lower part of the Bi2Se3 flake (location 2) only two vortex jumps were observed at currents I2 and I4 (curve 2), and on the upper half of the flake (location 3) only one vortex jump occurred at field coil current I3 (curve 3). No vortex jumps were observed above the Al pad, far away from the junction region (location 4). These results suggest that the vortices are not localized in the junction center, as we demonstrate in the spatial magnetic maps below. Spatial maps of flux-difference reveal the locations at which the above vortices were induced (Figure 4b). No vortices appeared at field coil current I1 (Figure 4b). At field coil current I2, we detected a vortex jump on the lower half of the flake, and a vortex jump appeared on the upper half of the junction at current I3 (Figure 4b). We observed an additional vortex jump on the lower half of the junction region at field coil current I4 (Figure 4b). These images confirm that the vortices prefer to enter those parts of the samples in which Al covers Bi2Se3. We measured the large Josephson junction in Figure 1b to assess whether there were any deviations in fluxoid quantization in the junction caused by, for example, flux-focusing effects or changes in the Josephson or London penetration depths originating in proximity effects. Scanning SQUID microscopy makes it possible to test for these effects in a straightforward way since the probes are local, as demonstrated in Figure 4. The observed vortex jumps suggest that the energy barrier for vortex entry is suppressed when Al sits atop the Bi2Se3 flake, probably due to a proximity effect between Bi2Se3 and Al. The more familiar outcome of the proximity effect is induced superconductivity in a normal conductor, but proximity to a normal conductor also suppresses superfluid density in the superconductor. Our observations at different locations in our devices show, surprisingly, that it is more energetically favorable for the vortices to occur in the Al on the bulk of the flake than in the junction itself. It is therefore possible that the pinning potential is weaker for Josephson vortices than for the vortices observed in Al covering Bi2Se3. However, it is also possible that a large Josephson penetration depth, as compared to the Pearl penetration depth, results in much weaker magnetic signals from the Josephson vortices as compared to the observed Pearl

relation in equilibrium as a 2π-periodic function that is sinusoidal with forward skewness. Full observation of the so-called 4π-periodic Josephson effect would require staying on a single branch of the two-valued energy throughout the measurement. In other words, the phase difference would have to be swept fast enough for the fermion parity to be conserved. It could also be possible to observe switching between the branches in such time-resolved measurements or to find signatures of switching behavior in noise measurements.43,44 The time scale on which fermion parity in nontrivial Josephson junctions may be violated has been discussed in the literature in terms of quasiparticle poisoning.21,24,45,46 More research is needed to understand this time scale, but we do not expect fermion parity to be conserved on the time scales of our measurement in this experimental system. Thus, it is not surprising that we do not detect a 4π-periodic Josephson effect. Even in situations where a superconducting channel may exist with a 4π-periodic Josephson effect, this exotic feature may be further masked by parallel channels that are purely 2πperiodic or more likely to be purely sinusoidal. For example, backscattering of propagating states at oblique incidence at the junction barrier may result in a significant 2π component in the current-phase relationship.23,47 A trivial bulk 2π contribution is also likely to occur.22,26 The influence of these factors may be reduced by preparing smaller junctions,22,26 which would be desirable for future experiments. For a ring that includes a Josephson junction, the detected dependence of circulating current on the applied magnetic flux may differ from the current-phase relation of the junction. For example, in rings with one nontrivial Josephson junction and one additional trivial Josephson junction (such as a weak link), the charging energy may introduce phase slips that open a gap in a 4π current-phase relation and thus make the current 2πperiodic.46 We do not expect such phase slips to be important in the current experiment because the annulus cross-section is not sufficiently small to require treating it as a weak link. Another parameter to consider for a ring geometry is the product of the self-inductance of the ring and the Josephson critical current, β = 2πLIc/Φ0. Veldhorst et al.48 considered a ring with two junctions: one trivial junction, whose currentphase relation is 2π periodic, and one nontrivial junction, whose current-phase relation is a sum of 2π periodic and 4π periodic components. They showed that an enhanced value of β increases the 4π-periodic component in the critical current relative to the 2π component.48 To check the relevance of these theoretical studies to ring with a single nontrivial junction, we performed similar calculations (unpublished) assuming one nontrivial junction in the ring with no externally applied current or voltage, different ratios of 4π and 2π components in the junction current-phase relationship, and different values of β. We found that a 4π component, if present in the junction’s current-phase relation, would be reflected in our circulating current vs applied flux characteristics. Given that our measured rings have only one junction, that they have relatively small self-inductance, and that the Josephson critical current values are relatively low, our technique is a direct method for probing the current-phase relationship. The above discussion indicates that there are many effects that may destroy the 4π-periodic nature of topologically nontrivial Josephson junctions. However, if the current-phase relation of a junction would be 4π-periodic, then a single (nontrivial) junction ring with no additional weak links would D

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vortices. In this scenario, the Josephson vortices would be present in the junction, but their magnetic signatures would be overshadowed by the magnetic signals from the observed vortices. Although the extended standalone junction presented here is longer than the junctions incorporated in the rings, it should also be in the short-junction limit in which the length is shorter than the Josephson penetration depth. According to our estimate based on the critical current of the small junctions, the Josephson penetration depth, λJ = [Φ0/(2πμ0(IC/(wd))(2λL + L))]1/2,49 is larger than the junction lengths in the present experiment: this formula yields λJ = 12.8−20.2 μm for the London penetration depth, λL = 50−200 nm (which has a large uncertainty), and IC ≈ 0.32 nA for junctions with dimensions w = 1 μm, d = 100 nm, and L = 100 nm. Therefore, we expect the extended junctions to behave similarly to the shorter junctions, for which we have shown critical current data. Note that the area of superconducting Al covering the Bi2Se3 flakes is much smaller in the shorter junctions incorporated in the rings than in the longer standalone junction (Figure 1). Therefore, fields applied to the rings with shorter junctions are not strong enough to induce vortices, and the measured current-phase relation would not be effected. In conclusion, we have used scanning SQUID microscopy to investigate proximity effect-induced phenomena and Josephson effects in superconducting Al rings with Josephson junctions made of the topological insulator Bi2Se3. We distinguished two components in the magnetic images: a linear response to the applied field related to the geometry of a sample and the London and Josephson penetration depths of these regions. This decomposition empowers direct contactless measurements of the current-phase relation in rings with Josephson junctions made of topologically insulating Bi2Se3. We found that the current-phase relation was nearly sinusoidal (Φ0periodic), with a small second harmonic Φ0/2 indicating a forward “skewness”. Further studies of surface superconductivity require preparation of superconductor/topological insulator/superconductor junctions with smaller dimensions, preferably made of thin topological insulator films with tunable Fermi levels. In scanning SQUID images of a larger Al/Bi2Se3/Al Josephson junction, we observed induced Pearl vortices as quantized jumps in magnetic flux from the junction; these vortices were distinct from Josephson vortices. We infer that the vortices were confined to the Bi2Se3 flake, probably because the superfluid density in the proximity region where Al covers Bi2Se3 is suppressed versus that in the Al pads on SiO2. The suppressed superfluid density would allow vortices to enter the Al/Bi2Se3 parts of the sample at relatively low magnetic fields. These findings imply that the superconductor/topological insulator/superconductor junctions do not behave as ideal junctions, possibly due to a strong proximity effect between the superconductor and the topological insulator. Our observations therefore highlight the necessity for more careful interpretation of data measured in such junctions by nonlocal probes, such as electrical resistance measurements of Fraunhofer interference. Local SQUID magnetometry may thus be an important complement to other techniques, such as transport measurements, for studying topological insulators in general.

Figure 4. Vortices in a superconductor/topological insulator/superconductor junction. (a) Flux vs field coil current curves (analogous to magnetization curves) reveal vortex jumps in the area of the superconductor/topological insulator/superconductor Josephson junction (depicted in Figure 1b). These data were measured at four SQUID sensor locations. Inset, schematic of the junction with the Bi2Se3 flake outlined in black (compare to Figure 1b); location 1, the junction gap; location 2, the lower half of the Bi2Se3 flake; location 3, the upper half of the Bi2Se3 flake; and location 4, the upper part of the Al pad. Dashed vertical lines (I1 − I4) indicate the applied current through the field coil at which the flux-difference images in b were measured. Arrows denote rising and lowering field coil current, corresponding to upward and descending branches of the flux-current curves, respectively. (b) Magnetic flux-difference images show vortex locations. These images were constructed by subtracting two sequential flux images taken at slightly different applied field coil currents ΔΦ(I) = Φ(I + ΔI) − Φ(I), where ΔI ≪ I3 − I2. These images are plotted for the descending branch of the flux-field curves. The sample structure is outlined in white. The four images correspond to the four values of the field coil current (I1 − I4) indicated on panel a.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. E

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Author Contributions

(12) Rokhinson, L. P.; Liu, X. Y.; 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. (13) Sacepe, B.; Oostinga, J.; Li, J.; Ubaldini, A.; Couto, N.; Giannini, E.; Morpurgo, A. Gate-tuned normal and superconducting transport at the surface of a topological insulator. Nat. Commun. 2011, 2, 575. (14) Veldhorst, M.; Molenaar, C.; Wang, X.; Hilgenkamp, H.; Brinkman, A. Experimental realization of superconducting quantum interference devices with topological insulator junctions. Appl. Phys. Lett. 2012, 100, 072602. (15) Veldhorst, M.; Snelder, M.; Hoek, M.; Gang, T.; Guduru, V.; Wang, X.; Zeitler, U.; van der Wiel, W.; Golubov, A.; Hilgenkamp, H.; Brinkman, A. Josephson supercurrent through a topological insulator surface state. Nat. Mater. 2012, 11, 417−421. (16) Williams, J.; Bestwick, A.; Gallagher, P.; Hong, S.; Cui, Y.; Bleich, A.; Analytis, J.; Fisher, I.; Goldhaber-Gordon, D. Unconventional Josephson effect in hybrid superconductor-topological insulator devices. Phys. Rev. Lett. 2012, 109, 056803. (17) Yang, F.; Qu, F.; Shen, J.; Ding, Y.; Chen, J.; Ji, Z.; Liu, G.; Fan, J.; Yang, C.; Fu, L.; Lu, L. Proximity-effect-induced superconducting phase in the topological insulator Bi2Se3. Phys. Rev. B 2012, 86, 134504. (18) Zareapour, P.; Hayat, A.; Zhao, S.; Kreshchuk, M.; Jain, A.; Kwok, D.; Lee, N.; Cheong, S.; Xu, Z.; Yang, A.; Gu, G.; Jia, S.; Cava, R.; Burch, K. Proximity-induced high-temperature superconductivity in the topological insulators Bi2Se3 and Bi2Te3. Nat. Commun. 2012, 3, 1056. (19) Zhang, D.; Wang, J.; DaSilva, A.; Lee, J.; Gutierrez, H.; Chan, M.; Jain, J.; Samarth, N. Superconducting proximity effect and possible evidence for Pearl vortices in a candidate topological insulator. Phys. Rev. B 2011, 84, 165120. (20) Cho, S.; Dellabetta, B.; Yang, A.; Schneeloch, J.; Xu, Z.; Valla, T.; Gu, G.; Gilbert, M. J.; Mason, N. Symmetry protected Josephson supercurrents in three-dimensional topological insulators. Nat. Commun. 2012, 4, 1689. (21) Fu, L.; Kane, C. Josephson current and noise at a superconductor/quantum-spin-Hall-insulator/superconductor junction. Phys. Rev. B 2009, 79, 161408(R). (22) Potter, A.; Fu, L. Anomalous supercurrent from majorana states in topological insulator Josephson junctions. arXiv 2013, 1303.1524. (23) Snelder, M.; Veldhorst, M.; Golubov, A.; Brinkman, A. Andreev bound states and current-phase relations in three-dimensional topological insulators. Phys. Rev. B 2013, 87, 104507. (24) Lutchyn, R.; Sau, J.; Das Sarma, S. Majorana fermions and a topological phase transition in semiconductor-superconductor heterostructures. Phys. Rev. Lett. 2010, 105, 077001. (25) Olund, C.; Zhao, E. Current-phase relation for Josephson effect through helical metal. Phys. Rev. B 2012, 86, 214515. (26) Ilan, R.; Bardarson, J.; Sim, H.; Moore, J. Detecting perfect transmission in Josephson junctions on the surface of three dimensional topological insulators. arXiv 2013, 1305.2210. (27) Golubov, A.; Kupriyanov, M.; Il’ichev, E. The current-phase relation in Josephson junctions. Rev. Mod. Phys. 2004, 76, 411−469. (28) Tsuei, C.; Kirtley, J.; Chi, C.; Yujahnes, L.; Gupta, A.; Shaw, T.; Sun, J.; Ketchen, M. Pairing symmetry and flux-quantization in a tricrystal superconducting ring of YBa2Cu3O7‑delta. Phys. Rev. Lett. 1994, 73, 593−596. (29) Frolov, S.; Van Harlingen, D.; Oboznov, V.; Bolginov, V.; Ryazanov, V. Measurement of the current-phase relation of superconductor/ferromagnet/superconductor pi Josephson junctions. Phys. Rev. B 2004, 70, 144505. (30) Girit, C.; Bouchiat, V.; Naaman, O.; Zhang, Y.; Crommie, M.; Zettl, A.; Siddiqi, I. Current-phase relation in graphene and application to a superconducting quantum interference device. Phys. Status Solidi B 2009, 246, 2568−2571. (31) Girit, C.; Bouchiat, V.; Naamanth, O.; Zhang, Y.; Crommie, M.; Zetti, A.; Siddiqi, I. Tunable graphene dc superconducting quantum interference device. Nano Lett. 2009, 9, 198−199.

I.S. designed the samples, performed the scanning SQUID measurements, and analyzed the data. A.J.B. designed, fabricated, and characterized the samples. J.R.W. assisted in designing the experiment and interpreting the data. T.M.L. assisted with the scanning SQUID measurements and data analysis. I.R.F. guided materials synthesis and characterization. D.G.G., J.R.K., and K.A.M. guided the experiments. I.S., J.R.K., and K.A.M. wrote the manuscript with contributions from all coauthors. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Jens Bardarson, Roni Ilan, Dmitry I. Pikulin, Eric M. Spanton, and Katja C. Nowack for fruitful discussions. Scanning SQUID measurements were supported primarily by the NSF Center for Probing the Nanoscale at Stanford University, NSF NSEC grant PHY-0830228, and also partially by NSF grant DMR-0803974. Sample fabrication was supported by the Keck Foundation. Materials synthesis and characterization were supported by the DOE Office of Basic Energy Sciences, under contract DE-AC02-76SF00515 (the authors thank Andrew S. Bleich and J. G. Analytis for their important role in this aspect of the work). Analysis of the experimental data and manuscript writing were supported by the Gordon and Betty Moore Foundation through grant GBMF3429.

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