Abstract
Semiconductor nanowires are ideal for realizing various low-dimensional quantum devices. In particular, topological phases of matter hosting non-Abelian quasiparticles (such as anyons) can emerge when a semiconductor nanowire with strong spin–orbit coupling is brought into contact with a superconductor1,2. To exploit the potential of non-Abelian anyons—which are key elements of topological quantum computing—fully, they need to be exchanged in a well-controlled braiding operation3,4,5,6,7,8. Essential hardware for braiding is a network of crystalline nanowires coupled to superconducting islands. Here we demonstrate a technique for generic bottom-up synthesis of complex quantum devices with a special focus on nanowire networks with a predefined number of superconducting islands. Structural analysis confirms the high crystalline quality of the nanowire junctions, as well as an epitaxial superconductor–semiconductor interface. Quantum transport measurements of nanowire ‘hashtags’ reveal Aharonov–Bohm and weak-antilocalization effects, indicating a phase-coherent system with strong spin–orbit coupling. In addition, a proximity-induced hard superconducting gap (with vanishing sub-gap conductance) is demonstrated in these hybrid superconductor–semiconductor nanowires, highlighting the successful materials development necessary for a first braiding experiment. Our approach opens up new avenues for the realization of epitaxial three-dimensional quantum architectures which have the potential to become key components of various quantum devices.
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Change history
22 November 2021
Editor’s Note: The authors have alerted the editors of Nature to potential problems in the manner in which some of the raw data in this paper have been processed. While Nature is investigating the impact this will have on the conclusions of the paper, readers are cautioned against using results reported therein.
19 April 2022
A Correction to this paper has been published: https://doi.org/10.1038/s41586-022-04704-2
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Acknowledgements
We acknowledge N. Wilson for the assistance at University of California, Santa Barbara. This work has been supported by the European Research Council (ERC HELENA 617256 and Synergy), the Dutch Organization for Scientific Research (NWO-VICI 700.10.441), the Foundation for Fundamental Research on Matter (FOM) and Microsoft Corporation Station-Q. We acknowledge Solliance, a solar energy R&D initiative of ECN, TNO, Holst, TU/e, imec and Forschungszentrum Jülich, and the Dutch province of Noord-Brabant for funding the TEM facility. We thank the Office of Naval Research (ONR) for financial support. The work at University of California, Santa Barbara was supported in part by Microsoft Research. We also acknowledge the use of facilities within the National Science Foundation Materials Research and Science and Engineering Center (DMR 11–21053) at the University of California, Santa Barbara and the LeRoy Eyring Center for Solid State Science at Arizona State University.
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Contributions
S.G., D.C., J.A.L., C.J.P. and E.P.A.M.B. carried out the material synthesis. H.Z. and M.W.A.M. fabricated the devices and performed the transport measurements and data analysis. S.C.B., M.C.C. and R.S. carried out the substrate preparation. D.X. and G.W. fabricated the hard-gap devices and contributed to the measurement. S.G. and R.L.M.O.H.V. did the nanowire manipulation for the TEM analysis and transport measurements. M.A.V. performed TEM analysis. B.S., D.P. and J.S.L. contributed to the experiments at University of California, Santa Barbara. S.K. prepared the lamellae for TEM analysis. J.S. and D.B. contributed to the hard-gap device fabrication. K.Z. and Y.V. contributed to the Aharonov–Bohm device fabrication and data analysis. P.J.V.V. supported work with the MOVPE reactor. E.P.A.M.B., C.J.P. and P.K. provided key suggestions on the experiments. E.P.A.M.B., C.J.P. and L.P.K. supervised the projects. All authors contributed to the writing of the manuscript.
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Extended data figures and tables
Extended Data Figure 1 Fabrication of InP substrate with trenches.
1–8: Schematic illustration of the processing steps. 1, An out of the box wafer is etched in 7:1 buffered HF; an oxygen plasma step is performed to create a ‘sacrificial’ native oxide layer of 1.9 ± 0.1 nm (ref. 33); a 20 nm SiOx hard mask is deposited followed by another oxygen plasma treatment. 2, 3, 4, The electron-beam primer and resist layer is spun; rectangular windows of ~200 nm are written using EBL and subsequently developed. 5, 6, The hard mask is etched using reactive ion etching (RIE) with CHF3 and Ar. 7, 8, The wet etch in HCl (37%):H3PO4 (85%) with 5:1 ratio is performed to expose (111)B facets in InP (100) and the hard mask is removed using 7:1 buffered HF. A detailed fabrication recipe can be found in Methods.
Extended Data Figure 2 Catalyst deposition.
1–8: Schematic illustration of the processing steps. 1, 20 nm SixNy mask is deposited followed by an oxygen plasma treatment. 2–4, E-beam primer and resist layer is spun (nominal resist thickness needs to be half of the depth of the trenches); arrays of dots (10–50 nm) are written on inclined (111)B facets using e-beam lithography and the resist is then developed. 5, Openings in SixNy mask are defined using short 20:1 buffered HF etch. 6–8, 10 nm of gold is evaporated through the opening in SixNy mask followed by a lift-off. A detailed fabrication recipe can be found in Methods.
Extended Data Figure 3 Role of the SixNy mask in InSb nanowire growth.
a, b, A 30°-tilted SEM image of InP–InSb nanowires grown on a substrate without (a) and with (b) SixNy mask. A substantial amount of parasitic thin film growth is observed in a. Concave edges of the trenches act as a preferential nucleation site for InSb growth. Thin-film InSb growth is in direct competition with InSb nanowire growth, resulting in short nanowires and a very low yield of crossed junctions. By covering the substrate with a SixNy mask, the growth is restricted to areas where the InP substrate is exposed30. This, in combination with approximately 100 times lower molar fractions of TMIn and TMSb used for the growth of wires shown in b, eliminates the unwanted InSb layer growth and allows for growth of high-aspect-ratio InSb nanowires which merge into networks. Both scale bars are 1 μm.
Extended Data Figure 4 Lithographic control over the trench design layout enables growth of hashtags spanning different loop areas.
a, b, InSb nanowire networks grown on trenches with different spacing between the left–left (L1, L2) and right–right (R1, R2) trenches, labelled a and b in Fig. 1a, respectively. Control over the dimensions of the trenches allows us to tune the length of the hashtag parallelogram. The scale bars are 1 μm.
Extended Data Figure 5 Structural analysis of a hashtag taken from the substrate and deposited on a holey carbon film using a micromanipulator in the SEM.
a, High-angle annular dark field (HAADF) scanning TEM image of the hashtag. The red arrows indicate the positions of the gold catalyst particles. For one wire, the InP stem is present and recognizable. b, Corresponding bright field (BF) TEM image. c, BFTEM image displaying the central part of the hashtag as well as the 1.3 μm aperture inserted for the selected area electron diffraction (SAED) pattern displayed in d. The pattern represents a superposition of three twin-related 〈110〉 zone axis patterns. e, To reveal the orientation of the individual wires of the hashtag, SAED patterns for all the wires were acquired, using a smaller SAED aperture diameter of 0.25 μm. Three different 〈110〉 zone axis patterns were recorded. The colour coding of the apertures in e corresponds to the SAED patterns in f–h. i, Schematic representation of the formation of the hashtag presented in the TEM images. The blue and purple nanowires have two different orientations, related by a 180° rotation around their long axis. Thus, one of the wires has the same orientation as the substrate wafer, while the other one is twin related. The two yellow wires have identical orientations that differ from the orientations of the two other wires. Thus, these yellow wires are also twin-related to the substrate, though their rotation axis is different from that of the blue and purple wires.
Extended Data Figure 6 The number of superconducting islands, n + 1, is determined by the number of wires, n, directly in front of the shadowed nanowire.
a, A high-magnification top-down SEM image of the region indicated by a red rectangle in b. The three nanowires facing the Al flux cast shadows on the wire directly behind them, resulting in InSb nanowires with four superconducting islands. The shadowing offset is about 200 nm. The nanowires bend towards each other owing to the e-beam exposure during imaging.
Extended Data Figure 7 Aharonov–Bohm oscillations in four devices with different hashtag surface areas.
Device A has been studied in detail in the main text. For all devices, left upper panel shows the pseudo-coloured SEM image of the device, middle panels show the conductance measured in the out-of-plane (top) and in-plane (bottom) magnetic field and right panel shows the ensemble averaged FFT spectrum. Only the out-of-plane magnetic field, whose flux penetrates through the hashtag loop, gives Aharonov–Bohm oscillations which indicates that the Aharonov–Bohm oscillations indeed originate from the coherent interference of electron waves of the two separated conducting nanowire arms. A magnified view of the Aharonov–Bohm oscillations (a zoom-in on the region indicated by an orange rectangle in the upper middle panel) is shown in the lower left panel, while the right panel shows the averaged FFT spectrum. Plot of the peak frequency, assigned from the averaged FFT spectra, as a function of the measured loop area of the four devices is shown in the inset of Fig. 3b. Weak-antilocalization peak at B = 0 T is present for both field directions, and in three (A, B, D) out of four devices, suggesting the strong spin–orbit nature of the InSb nanowire network. The corresponding back gate voltages of the four devices are: 15 V, 9 V, 12 V and 9 V, respectively. Temperature is 300 mK. The scale bar is 1 μm.
Extended Data Figure 8 Ballistic transport, Andreev enhancement and hard gap in additional Al-InSb devices.
a, Above-gap (normal carriers) conductance of device Y as a function of Vgate. A conductance plateau near the quantized value (2e2/h) can clearly be seen, indicating ballistic transport. b, dI/dV versus bias voltage in the open and tunnelling regime, resolving strong Andreev enhancement (green) and a hard gap (red), respectively, with Vgate indicated by arrows in panel a. The coherence peaks are smeared out owing to thermal broadening (temperature of about 300 mK for this device). The Andreev enhancement is due to Andreev reflection: an incoming electron reflects as a hole at the N–S interface generating a Cooper pair. This process effectively doubles the transported charge from e to 2e, enhancing the sub-gap conductance. Our enhancement factor reaches 1.7 × 2e2/h, indicating the high Al–InSb interface transparency, with transmission larger than 0.96. The small dip in Andreev enhancement near zero bias is due to mode mixing induced by minimal residual disorder11. c, Sub-gap versus above-gap conductance of device Y (black dots), and a theoretical fit (red) based on the Beenakker formula, showing perfect agreement over three orders of magnitude conductance change. d, dI/dV of device Z as a function of Vgate. e, A line cut from panel d (black bar), plotted in linear (top) and logarithmic scale (bottom). The above-gap/sub-gap ratio is larger than 300. f, dI/dV of device M as a function of Vgate. g, A line cut from panel f (black bar), plotted on linear (left) and logarithmic scale (right). h, Sub-gap versus above-gap conductance of device M (black dots), and the Beenakker theoretical fit (red). Device shown in the main text (X), and devices Z and M are measured at around 20 mK.
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Gazibegovic, S., Car, D., Zhang, H. et al. RETRACTED ARTICLE: Epitaxy of advanced nanowire quantum devices. Nature 548, 434–438 (2017). https://doi.org/10.1038/nature23468
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DOI: https://doi.org/10.1038/nature23468
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