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Zero-bias peaks at zero magnetic field in ferromagnetic hybrid nanowires

Nature Physics volume 17, pages 43–47 (2021)Cite this article

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Abstract

Hybrid quantum materials allow for quantum phases that otherwise do not exist in nature1,2. For example, a one-dimensional topological superconductor with Majorana states bound to its ends can be realized by coupling a semiconductor nanowire to a superconductor in the presence of a strong magnetic field3,4,5. However, the applied magnetic fields are detrimental to superconductivity, and constrain device layout, components, materials, fabrication and operation6. Early on, an alternative source of Zeeman coupling that circumvents these constraints—using a ferromagnetic insulator instead of an applied field—was proposed theoretically7. Here, we report transport measurements in hybrid nanowires using epitaxial layers of superconducting Al and the ferromagnetic insulator EuS on semiconducting InAs nanowires. We infer a remanent effective Zeeman field exceeding 1 T and observe stable zero-bias conductance peaks in bias spectroscopy at zero applied field, consistent with topological superconductivity. Hysteretic spectral features in applied magnetic field support this picture.

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Fig. 1: Al/EuS shell characteristics.
Fig. 2: Bias spectroscopy at zero magnetic field.
Fig. 3: ZBP splittings at coercive fields.
Fig. 4: Axial versus off-axis applied field.

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Data availability

Source data are provided with this paper. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

We thank Z. Cui, K. Moler and I. Zhang for EuS magnetization studies, C. Sørensen for contributions to materials growth, S. Upadhyay for nanofabrication and K. Flensberg for valuable discussions. Research was supported by Microsoft, the Danish National Research Foundation and the European Commission.

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Authors and Affiliations

  1. Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

    S. Vaitiekėnas, Y. Liu, P. Krogstrup & C. M. Marcus

  2. Microsoft Quantum Lab—Copenhagen, Copenhagen, Denmark

    S. Vaitiekėnas & C. M. Marcus

  3. Microsoft Quantum Materials Lab—Copenhagen, Lyngby, Denmark

    Y. Liu & P. Krogstrup

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  1. S. Vaitiekėnas
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Contributions

Y.L. and P.K. developed the nanowire materials. S.V. fabricated the devices, performed measurements and analysed the data with input from C.M.M. All authors contributed to interpreting the data. The manuscript was written by S.V. and C.M.M. with input from all authors.

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Correspondence to C. M. Marcus.

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Peer review information Nature Physics thanks Peng Wei and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Non-overlapping Al/EuS shell characteristics.

a, Four-probe differential resistance of the Al shell adjacent to EuS, RS, measured for device 7 around zero bias as a function of temperature, T, shows a critical temperature TC0 ~ 1.5 K. Inset: Schematic wire cross section showing orientation of Al and EuS shells on adjacent pairs of facets. b,c, RS as a function of applied magnetic field along wire axis, H∥, and current bias, IS, sweeping H∥ from (b) negative to positive and (c) positive to negative.

Source data

Extended Data Fig. 2 Bias spectroscopy of wire with non-overlapping Al and EuS shells.

a, Colorized micrograph of device 8 with the measurement set-up. External axial magnetic field, H∥, is indicated by an arrow. b, Differential conductance, G, as a function of source-drain bias voltage, V, at H∥ = 0 shows a hard induced superconducting gap around Δ = 230μeV. Inset: Schematic wire cross section showing orientation of Al and EuS shells on adjacent pairs of facets. c, Evolution of the tunneling spectrum with H∥ swept from negative to positive. d, Difference of two conductance maps taken with H∥ swept to opposite directions illustrates a weak hysteresis. The data were taken at VC = − 6.65 V, VU = − 7 V and VL = 1.65 V.

Source data

Extended Data Fig. 3 Critical temperature and pair-breaking parameter.

a, Critical temperature, TC, for device 1 as a function of applied axial magnetic field, H∥, deduced from the critical current fits shown in Fig. 1b,c using Eq. (2). b, Pair-breaking parameter, α, estimated using Eq. (1) as described in Methods.

Source data

Extended Data Fig. 4 Zero-bias peak spectrum evolution with barrier-gate and back-gate voltages.

a, Differential conductance, G, measured for device 2 at zero bias as a function of barrier-gate voltage, VC, and back-gate voltage, VBG. b, Left: G as a function of source-drain bias voltage, V, and VC measured at VBG = − 3.15 V. Right: Line-cut plots of G with subtracted line resistance, \(\widetilde{G}\), (see Methods) taken from the right panel at various VC values. c–h, Similar to b measured within the white box in a at various VBG values ranging from − 3.05 V to − 2.55 V every 0.1 V. All the sweeps display a zero-bias peak that evolves into a zero-bias dip, with the crossover-conductance values varying from 0.2 e2/h to above e2/h depending on VBG. All the measurements were taken at VL = 0 V, VU = − 1 V, and zero applied magnetic field H∥ = 0.

Source data

Extended Data Fig. 5 Line-cut plots at various barrier-gate voltages.

Same data as in Extended Data Fig. 4c,e,g. a, Differential conductance with subtracted line resistance, \(\widetilde{G}\), (see Methods) measured for device 2 as a function of source-drain bias voltage, V, at various barrier-gate voltage VC values ranging from − 1.3 V to − 1.0 V every 2 mV and fixed back-gate voltage VBG = − 3.05 V. b,c, Same as (a) but measured at VBG = − 2.85 V and VBG = − 2.65 V, respectively.

Source data

Extended Data Fig. 6 Tunneling spectrum evolution with upper- and lower-gate voltages.

a–h, Differential conductance, G, measured for device 2 as a function of source-drain voltage bias, V, and upper-gate voltage, VU, taken at various lower-gate voltage, VL, values. A pair of faint subgap states is visible for VL close to zero. As VL is reduced, a stable zero-bias peak develops around VL = − 0.6 V, but then splits again for more negative voltages. i, G dependence on VU taken at VL = − 0.65 V while compensating with VC to maintain barrier iso-potential. j, Similar to i but as a function of VL taken at VU = − 0.7 V. The sharp resonances in i and j are due to charge motion in the junction and do not split the zero-bias peak. k, l, Zoom-ins on the end-state resonances visible in j. All the measurements were taken at back-gate voltage VBG = − 3 V and zero applied magnetic field H∥ = 0.

Source data

Extended Data Fig. 7 Spectrum evolution with different gate voltages.

a, Differential conductance, G, measured for device 2 as a function of source-drain bias voltage, V and back-gate voltage, VBG, measured along white dashed line in Fig. 2b, at VL = 0 V and VU = − 1 V. b, Line-cut plots of G with subtracted line resistance, \(\widetilde{G}\), (see Methods) taken from a at various VBG values. c,d, Similar to a,b but for device 3 as a function of upper-gate voltage, VU, measured at VBG = − 5 V, VL = − 0.5 V, and VC = − 1.705 V. e,f, Similar to a,b but for device 4 as a function of lower-gate voltage, VL, measured at VBG = 0.5 V, VU = − 0.8 V, and VC = − 0.89 V. All the measurements were taken at zero applied magnetic field H∥ = 0.

Source data

Extended Data Fig. 8 Robust zero-bias peak at coercive fields.

a, Differential conductance, G, as a function of source drain voltage bias, V, and applied axial magnetic field, H∥, for device 4 at VL = − 0.32 V in Fig. 2f, on the less negative gate voltage side of the zero-bias peak splitting. Sweep direction indicated by arrow. Zero-bias peak is continuous through magnetization reversal. b, Same as a with sweep direction from positive to negative. The data were taken at VBG = 0.5 V, VU = − 0.8 V, and VC = − 0.89 V.

Source data

Extended Data Fig. 9 Additional in-plane field angle measurements.

a, Differential conductance, G, measured for device 6 [lithographically equivalent to device 2 shown in Fig. 2a but with wire length of 1 μm] as a function of source-drain bias voltage, V and lower-gate voltage, VL. Top axis shows compensation gate voltages. The data were taken at VBG = − 1 V, VU = 0 V, and zero applied magnetic field H∥ = 0. b, G dependence on in-plane angle, φ [see Fig. 2a for orientation], taken at a fix external magnetic field amplitude, μ0Hφ = 30 mT and a gate configuration corresponding to VL = − 0.9 V in a shows a zero-bias peak robust for all φ.

Source data

Extended Data Fig. 10 Coercive field dependence on in-plane field angle.

a, Difference of two conductance maps measured for device 2 with axial magnetic field, H∥, swept to opposite directions, as a function of source-drain bias voltage, V, showing coercive field H∥,C = ± 49 mT. b–e, Similar to a but with field, Hφ, swept at in-plane angle, φ [see Fig. 2a for orientation]. The amplitude of coercive field, Hφ,C, increases with φ. See Supplementary Information for the corresponding conductance maps. f, Hφ,C measured from a-e as a function of φ increases as \(1/\cos (\varphi )\). g, Same data as in f multiplied by \(\cos (\varphi )\) does not depend on φ, indicating that the EuS magnetization is along the wire axis and that only the H∥ component controls magnetization. All the measurements were taken at VBG = − 3 V, VL = − 0.65 V, VU = − 0.6 V, and VC = − 1.1875 V.

Source data

Supplementary information

Supplementary Information

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Vaitiekėnas, S., Liu, Y., Krogstrup, P. et al. Zero-bias peaks at zero magnetic field in ferromagnetic hybrid nanowires. Nat. Phys. 17, 43–47 (2021). https://doi.org/10.1038/s41567-020-1017-3

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