Abstract
The recent development of superconducting spintronics has revealed the spintriplet superconducting proximity effect from a spinsinglet superconductor into a spinpolarized normal metal. In addition recently superconducting junctions using semiconductors are in demand for highly controlled experiments to engineer topological superconductivity. Here we report experimental observation of Andreev reflection in junctions of spinresolved quantum Hall (QH) states in an InAs quantum well and the spinsinglet superconductor NbTi. The measured conductance indicates a subgap feature and two peaks on the outer side of the subgap feature in the QH plateautransition regime increases. The observed structures can be explained by considering transport with Andreev reflection from two channels, one originating from equalspin Andreev reflection intermediated by spinflip processes and second arising from normal Andreev reflection. This result indicates the possibility to induce the superconducting proximity gap in the the QH bulk state, and the possibility for the development of superconducting spintronics in semiconductor devices.
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Introduction
A junction of superconductor and normal metal is a platform to observe superconducting proximity effect, in which the superconducting property penetrates to the normal metal. In a microscopic description of the proximity effect, an electron in the normal metal enters the spinsinglet superconductor, forming a Cooper pair with another electron with opposite spin, reflecting a hole into the normal metal, in a process called Andreev reflection (AR)^{1}. In this picture, no AR is expected in the case of a fully spin polarized normal metal, however recently, theoretical and experimental studies in junctions with spinpolarized normal metal, revealed existence of the spintriplet superconducting proximity effect^{2,3,4,5,6,7,8}. The spintriplet proximity effect is only allowed when spinflip processes intermediate “equalspin” AR, which is possible due to the presence of magnetization inhomogeneity or spinorbit interaction^{9,10}. Ferromagnetic metal has been utilized in experiments of superconducting spintronics to date. A semiconductor material however offers several advantages, including the control of carrier density and spin filling through electrical gating and magnetic field, and the possibility of ballistic transport in micron sized devices. Furthermore strong spinorbit interaction can be utilized in two dimensional electron gases (2DEGs) in narrow gap semiconductors such as InAs and InSb^{11,12,13,14}. These features favor the formation of spinpolarized states when the 2DEG is in the quantum Hall (QH) regime. Indeed, there are several experimental reports focusing on superconductorsemiconductor junctions in the QH regime^{15,16,17,18,19,20}. However, all of these experiments have focused on the spindegenerate QH states and the spintriplet proximity effect has yet to be experimentally addressed, despite theoretical predictions of spintriplet supercurrent in Josephson junctions with weak links of spin resolved QH edge channels^{10}. Additionally, if the superconducting proximity gap is induced into the spinresolved QH state, the system can be a topological superconductor^{21} and give a new platform to realize the Majorana Fermions^{22,23} whose signatures have recently been reported^{24,25,26,27,28,29,30,31}.
Here we report an experimental study on electron transport in junctions between spinresolved QH states and spinsinglet superconductors. We prepared junctions consisting of a high mobility InAs quantum well (QW) with NbTi contacts. The NbTi layers are contacted to the sides of the mesa containing the QW, minimizing the damage to the 2DEG. The 2DEG possesses a large gfactor, high mobility, and strong spinorbit interaction, all necessary ingredients for coexistence of superconductivity and spinresolved QH states. We observe spinresolved quantized steps at magnetic fields below the superconducting critical field, 7 T, and find that the differential conductance has a dip or a peak structure as a subgap feature in all QH plateautransition regimes of filling factor between 0 to 4. Additionally, we find two side peaks on the outer side of the subgap feature. We conclude that the structures observed here are a result of the equalspin AR between the spinresolved QH bulk states and the superconductor.
We fabricated junction devices from an InAs QW grown by molecular beam epitaxy^{32,33} with carrier density 3 × 10^{11} cm^{−2} and mobility 3 × 10^{5} cm^{2}V^{−1}s^{−1}. (The material stack is represented in Supplementary Information (SI)). The cross section of the device is schematically represented in Fig. 1(a). Sputtered NbTi with the critical field of 7.0 T and the critical temperature of 6.5 K contacts the edge of the 2DEG and a top gate structure is fabricated using an insulating layer of crosslinked PMMA (see SI for details). The optical microscope photo in Fig. 1(b) shows the top view of the device. The two junctions are separated by 20 μm, so this device is assumed to have two independent junctions. We measured the twoterminal differential conductance in a He3He4 dilution refridgerator with a base temperature of 50 mK.
Figure 1(c) shows the measured dI/dV vs. V_{sd} at B = 0 T. The dI/dV is enhanced in the range of −0.71 mV < V_{sd} < 0.71 mV. This conductance enhancement arises from AR^{1,34} and only appears for the bias voltage in the junction less than the superconducting bulk gap energy Δ_{ bulk }. Therefore, we evaluate the Δ_{ bulk } as approximately 0.35 meV. The observation of the subgap feature guarantees that the junction has enough quality to study AR between the superconductor and spinresolved QH state.
Figure 1(d) shows dI/dV vs. the top gate voltage, V_{tg}. dI/dV gradually decreases with decreasing V_{tg} and becomes pinched off for V_{tg} < −1.38 V. This indicates that the top gating efficiently varies the 2DEG carrier density but not necessarily near the junction. We measured dI/dV vs. V_{sd} for various values of V_{tg} to examine the effect of top gating on the subgap conductance. We derived the differential resistance as given by dV/dI = (dI/dV)^{−1} and then subtracted dV/dI measured at V_{sd} = 2.0 mV to eliminate the normal state resistance including a series resistance due to the InAs QW away from the junction. The result is shown in Fig. 1(e) for three different values of V_{tg} = 0, −0.45, and −0.625 V by the purple, blue, and green curve, respectively. It is clear to see that dV/dI(V_{sd}) − dV/dI(2.0 mV) displays a pronounced reduction (or conductance enhancement) within the gap, and the reduction increases as V_{tg} is made more positive. If the top gating only varies the carrier density away from the junction, the dV/dI reduction below the gap should be constant with V_{tg}. Therefore, the result of Fig. 1(e) indicates that the top gating is efficient enough to vary the carrier density in the InAs QW near the superconducting junction. In Fig. 1(e), V_{sd} to characterize the superconducting gap decreases as V_{tg} is made more positive. The V_{sd} shift is due to the change in the voltage dropped over the junctions when the series resistance of the 2DEG is altered. Schematics of the equivalent circuit for the device are shown in Fig. 1(f). In the constant voltage bias measurement, the effective junction voltage decreases as the carrier density of the QW decreases with decreasing V_{tg}. Herein the applied voltage of V_{sd} is assumed to only drop across the junctions in the saturation region. Therefore we evaluate \({{\rm{\Delta }}}_{bulk}\simeq 0.35\,{\rm{meV}}\).
In Fig. 2(a), we present plots of measured dI/dV as a function of V_{tg} at outofplane magnetic field B = 2.4 and 4.0 T. The welldefined plateaus at integer multiples of e^{2}/h which originate from the QH edge transport are clearly seen. From this observation, it is confirmed that the applied fields are strong enough to resolve the spin degeneracy, but significantly smaller than the critical field of the NbTi, implying that the superconductivity and the spinresolved QH states coexist. We note that the spinorbit energy α ⋅ σ × k can be estimated as 0.3 meV with α = 10^{−10} eVm^{14,35}. This energy is much smaller than Zeeman energy at 4 T, 10 meV (see SI). Consequently, we ignore the effective field from the spinorbit interaction in the spinresolved QH state.
dI/dV vs. V_{sd} measured in the range of V_{tg} between −1.5 V and 0 V is represented in Fig. 2(b), and (c) for B = 2.4 T, and 4.0 T, respectively. dI/dV traces measured for magnetic fields spanning the conductance range ne^{2}/h to (n + 1)e^{2}/h with n = 0, 1, 2... are shown in the separate panels to highlight the subgap structure in the transition regions between plateaus. For example, dI/dV at B = 2.4 T between 0 < dI/dV < e^{2}/h is shown in the leftmost panel of Fig. 3(b).
In the transition regions between the conductance plateaus, we find pronounced subgap features appearing as a dip, a peak and then a dip at around V_{sd} = 0 V from the lower to the upper plateau in all panels. Similar subgap features are previously reported for the junctions of two NbN superconductors and a spindegenerated QH state in an InAs QW^{15}. However, the underlying physics of the subgap feature remains to be elucidated. More interestingly in Fig. 2(b) and (c), the center peak appears broad in some traces and even split into two in others. In addition to a center dip or peak structure we observe a side peak. For example, it is clear to see two side peaks at V_{sd} = ±1.8 mV in addition to a peak at V_{sd} = 0 V for the curves at \(dI/dV\simeq 2.5{e}^{2}/h\) in the right panel of Fig. 2(c).
The subgap conductance enhancement indicated by the observation of a zerobias peak can be assigned to AR in the junction having a low potential barrier. In contrast, if the potential barrier is so large that normal reflection is more dominant than AR, a dip rather than a peak can appear according to the Blonder, Tinkham, and Klapwijk (BTK) theory^{34}. Therefore we assign the peak (dip) structure observed in the plateautransition regime to AR (normal reflection), and then the change of the subgap feature in Fig. 2(b) and (c) can be simply explained by considering the change of the junction potential barrier depending on V_{tg}. For the transport through the QH state it is well established that the dominant contribution arises from the QH bulk state in the plateautransition regime and from the QH edge state in the plateau regime. Herein, we deduce that the subgap feature, especially the peak structure is originated from AR in the junction between the superconductor and the spinresolved QH bulk state. A finite amount of equalspin AR can be expected for a 2DEG with strong spinorbit interaction according to recent theoretical studies^{9,10}. Therefore, we here assume coexistence of equalspin AR and normal AR, corresponding to AR intermediated with and without a spinflip process respectively, as schematically shown in Fig. 3(a).
This kind of subgap features might emerge due to the other origins. We discuss some of the origins here. First, recent theory predicts that the weak (anti)localization effect in the junction of a disordered normal metal and a superconductor^{36}. This effect is originated from closed trajectory of an electron and a retroreflected hole without consideration of any orbital motion invoked by the outofplane magnetic field. However, the orbital motion prevents the electron and the hole from making the closed trajectory. Therefore, this scenario is not assigned to the observed subgap feature. Second, the conductance enhancement can also be obtaind in the Kondo effect on the quantum dot. This is also not assigned the measured enhancement because our device structure is not a 0 or 1dimensional but 2dimensional system where the Kondo effect should appear as the resistance enhancement. Additionally the Kondo effect can easily collapse due to large Zeeman effect. Therefore we do not assume that the zerobias peak is due to the Kondo effect. Third, the similar subgap features observed in junctions of superconductor NbN and an InAs nanowire were reported^{37}. In this paper, the transient resonance is discussed as one of possible origins of the observed subgap features. The resonances arise when reflections at the interface between the bare segment and the NbTicovered segments induce constructive interference. Our data shows the clear trend of the subgap feature; the peak structure appears only in the plateau transition regime. Additionally, this trend reproduces at 2.4 T and 4.0 T, which give different cyclotron radius (<100 nm). This clear trend observed in the several QH plateau transition regimes at the different magnetic fields means that the subgap feature is strongly related to the QH effect, not the detail of the interface.
In order to more quantitatively interpret the subgap features including the side peaks, we construct a model based on the BTK theory. In this theory, the normalized differential conductance of the junction, G_{int}(V_{sd},Z,T,Δ), can be written as
where f(E),T,Δ and Z are the FermiDirac distribution function, temperature, superconducting gap and the dimensionless parameter representing the potential barrier in the junction, respectively. A(B) is the probability of the equalspin AR (normal reflection) defined in the BTK theory^{34}. However, this standard BTK theory cannot explain the coexistence of side peaks and subgap feature as observed in Fig. 2(b) and (c). Herein, to apply the BTK theory for such cases, we assume two different transport channels in the proximity region, labeled channel α in which the equalspin AR occurs and channel β with no spinflip process. A schematic representation of the transport in these channels is shown in Fig. 3(a). The channel α can generate the subgap features reflecting the conductance enhancement due to the equalspin AR, while the channel β can generate the side peaks reflecting the quasiparticle peaks of the superconducting bulk gap energy via normal reflection. Then, the normalized differential conductance of the junction can be written as
where \({G}_{{\rm{int}}}^{\alpha },{G}_{{\rm{int}}}^{\beta },{Z}_{\alpha },\,{\rm{and}}\,{Z}_{\beta }\) are the normalized differential conductance of the channel α, the normalized differential conductance of the channel β, the parameter Z in the eqn. (1) of the channel α and that of the channel β, respectively. Δ_{ α }, and Δ_{ β } are the proximity gap energy, and the bulk gap energy, respectively. Parameter P indicates the relative contribution of the two AR channels. Therefore, strong SOI can invoke more spinflips to make larger the value of P. We note that the appearance of two superconducting gaps are theoretically discussed in the case of coexistence of spinsinglet and triplet superconducting pair amplitude^{38,39}. We executed numerical calculations to fit the experimental data (see SI).
The best fitting result is shown in Fig. 3(b) by the solid lines plotted alongside the experimental data at 4.0 T. The obtained Δ_{ α } and Δ_{ β } are plotted as a function of dI/dV in Fig. 3(c). dI/dV for the xaxis is the differential conductance of the normal state measured at V_{sd} = 3.5 mV in units of e^{2}/h and indexed by g. Δ_{ β } is derived from the side peak positions and has a convex upward trend in each plateautransition regime between plateaus of g = 0 and 1, 1 and 2, and 2 and 3, respectively. These Δ_{ β } values are larger than the true bulk gap due to the dissipation in the QH bulk state (the equivalent circuit is the same as shown in Fig. 1(f)). We assume that the superconducting bulk gap Δ_{ bulk } = 0.35 meV which is derived in Fig. 1(c) is unchanged with V_{tg} and therefore Δ_{ β } in Fig. 3(c) should be equal to Δ_{ bulk }. This assumption is probably valid because the observed Δ_{ β } in the plateau regime where there is no dissipation is consistent with Δ_{ bulk } (see SI). Then we use the same equivalent circuit model as used for evaluating Δ_{ bulk } to calibrate the value of Δ_{ α } and finally obtain the true proximity gap of \({{\rm{\Delta }}}_{{\rm{triplet}}}\simeq 0.1\,{\rm{meV}}\) as 0.35 × Δ_{ α }/Δ_{ β } shown in Fig. 3(c) (see SI for details).
We also derived the parameters P and Z_{ α } and plot them as a function of change of g in Fig. 3(c), i.e. Δg = 0 to 1 between plateaus in Fig. 3(d) and (e), respectively. The pink rectangles, blue triangles, and orange circles represent the parameters derived from the right, center, and left panel of Fig. 3(b), respectively. Figure 3(d) shows that the estimated P in each transition regimes has similar results. If the SOI of InAs QW is assigned to the spinflip process, P can have the different value in different transition regime at the same magnetic field because top gate voltage can change not only the carrier density but also the Rashba SOI and the Zeeman energy (10 meV at 4 T) is large enough comparing to the SOI strength of InAs. Therefore, we think the strong SOI for the spinflip process comes from the SOI of NbTi or the interfacial SOI between InAs and NbTi^{40,41}. Indeed the spinflip process in NbN is mentioned in the experimental report on junctions of NbN and graphene in strong magnetic field^{42}. P indicating the proportion of AR in channel α has the maximum (\(\simeq 1\)) and Z_{ α } has a minimum at \({\rm{\Delta }}g\simeq 0.7\). Our experimental results are obtained by the twoterminal conductance measurement. Therefore the bulk contribution to the channel α becomes maximum at a position displaced from Δg = 0.5 and likely located between Δg = 0.5 and 1. Indeed we find that the bulk contribution is maximal at \({\rm{\Delta }}g\simeq 0.7\) which is consistent with measurement results on a Hallbar device (see SI). These results strongly and quantitatively support that channel α is comprised of the spinresolved QH bulk state and the conductance enhancement originates from the equalspin AR between the QH bulk state and the superconductor, while the channel β is assigned to conventional AR. These results imply that the equalspin AR can occur even with strong SOI instead of inhomogeneous magnetization in the SC junctions while previous studies for spintriplet superconducting proximity effect utilized the inhomogeneity. We note that the subgap feature and the side peaks have been theoretically predicted for the case of spinsinglet and spintriplet superconducting proximity effect between a topological insulator and a spinsinglet superconductor with magnetic field^{39}. There are a few theoretical works describing AR in the QH edge state^{10,43,44,45}, but none focus on the QH state in the plateautransition regime, and so further theoretical effort is necessary to reproduce the junction properties between superconductor and spinresolved QH bulk state. From the topological aspects, theory predicts that the chiral topological superconductor state can be realized in superconductorQH state junctions and therefore such junctions can be utilized to study nonAbelian statistics of the Majorana Fermions localized at the center of vortexes near the plateautransition regime^{21}. Our results indicate that it is possible to induce the proximity gap even in the spinresolved QH state via equalspin AR and so realize such chiral topological superconductivity.
In summary, we studied the transport properties of junctions between a NbTi superconductor and an InAs QW in the spinresolved QH regime. We observed subgap features indicating Andreev transport arising from two channels. One equal spin Andreev reflection channel which produces peaks at zero bias, and a conventional Andreev reflection channel producing side peaks. These results indicate that junctions of NbTi and the InAs QW are a promising candidate to experimentally study the spintriplet superconducting proximity effect in semiconductors and also topological superconductivity.
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Acknowledgements
We greatly thank Y. Tanaka, P. Burset, and R. S. Deacon for fruitful discussions. This work was partially supported by GrantinAid for Young Scientific Research (A) (No. JP15H05407), GrantinAid for Scientific Research (A) (No. JP16H02204), GrantinAid for Scientific Research (S) (No. JP26220710), JSPS Research Fellowship for Young Scientists (No. JP14J10600), JSPS Program for Leading Graduate Schools (MERIT) from JSPS, GrantinAid for Scientific Research on Innovative Area, “Nano Spin Conversion Science” (No.JP15H01012 and No. JP17H05177), GrantinAid for Scientific Research on Innovative Area, “Topological Materials Science” (Grant No. JP16H00984) from MEXT, CREST, ImPACT Program of Council for Science, Technology and Innovation (Cabinet Office, Government of Japan)and the Murata Science Foundation.
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S. M. and S. T. conceived the experiments. J.S. and C.J.P. grew the wafer. S.M., K.U., S.B., H.K., and M.T. contributed to the fabrication of the device. S.M., K.U. and S.B. carried out the measurements. S.M. and K.U. analyzed the data and wrote the paper. S.T. supervised the study.
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Matsuo, S., Ueda, K., Baba, S. et al. EqualSpin Andreev Reflection on Junctions of SpinResolved Quantum Hall Bulk State and SpinSinglet Superconductor. Sci Rep 8, 3454 (2018). https://doi.org/10.1038/s41598018217070
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DOI: https://doi.org/10.1038/s41598018217070
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