Research ArticleSEMICONDUCTORS

Experimental phase diagram of zero-bias conductance peaks in superconductor/semiconductor nanowire devices

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Science Advances  08 Sep 2017:
Vol. 3, no. 9, e1701476
DOI: 10.1126/sciadv.1701476
  • Fig. 1 ZBP in a nanowire device controlled by gate voltages.

    (A) Topological phase diagram described by Eq. 1. Dashed lines indicate settings of μ in (E), (D), and (C). (B) Scanning electron micrograph of the device used in this work. An InSb nanowire is half-covered by a superconductor NbTiN and normal metal Pd contact. The nanowire is placed on FG and BG metal gates. (C to E) Differential conductance maps in bias voltage V versus magnetic field B at three different settings of BG1.

  • Fig. 2 The emergence of the ZBP.

    (A to I) Conductance maps in bias voltage V versus BG1 at different magnetic fields indicated in the lower right corner of each panel. The arrows in (F) mark the ZBP onset gate voltages plotted in Fig. 3. The dashed line in (H) is obtained by tracing the visible maximum in subgap conductance and flipping the resulting trace around V = 0 mV.

  • Fig. 3 Phase diagram of ZBPs.

    ZBP onset points are collected from the extended data set represented in Fig. 2 (black squares) and from fig. S4 (blue circles), with error bars judged by deviation of the peak from zero bias within one-half of the full width at half maximum of ZBPs. Data extracted from fig. S4 are offset by +0.02 V in BG1 to compensate for a systematic shift due to a charge switch. The top axis EZ is calculated from the magnetic field using g = 40. The right axis μ is calculated from BG1 according to 10 meV/V (see fig. S8A in the Supplementary Materials) and set to zero at the parabolic vertex, BG1 = −0.395 V. Equation 1 is plotted in solid line using Δ = 0.25 mV.

  • Fig. 4 Tight-binding model results reveal two weakly coupled MBSs.

    (A) Model schematics. A nanowire is contacted by a superconductor and a normal metal. The potential profile is shown as the black curve. A plane wave eikx coming from N can tunnel into the nanowire through the barrier above FG. The chemical potential above BG1, μBG1, is tunable, whereas potentials above BG2 and BG3 are fixed. The calculated wave function amplitudes for zero-energy states are shown in red and blue. (B) Conductance map taken at zero bias. The red curve corresponds to a plot of Eq. 1. (C) Conductance map in bias energy versus chemical potential at EZ = 1.7 Δ. (D) Conductance map in bias energy versus Zeeman energy splitting at μBG1 = 0 meV. In (B) to (D), thermal broadening is set to 50 μeV to match the experimental ZBP width.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/9/e1701476/DC1

    Supplementary Text

    fig. S1. Hard gap in a double full-cover superconducting device.

    fig. S2. Linecuts from Figs. 1 and 2 in the main text.

    fig. S3. Gates dependence of ZBP.

    fig. S4. ZBP evolution with BG1.

    fig. S5. ZBP evolution at a large range of magnetic field.

    fig. S6. Magnetic field orientation dependence of ZBP.

    fig. S7. ZBP evolution with BG1 at an angle of π/2.

    fig. S8. Expanded scan of BG1 and gates dependence of resonances.

    fig. S9. Comparing the first and second resonances in zero-bias conductance maps.

    fig. S10. Gate and field dependence of the second resonance.

    fig. S11. Schematic representation of the tight-binding Hamiltonian.

    fig. S12. Comparison between long and short wires on spatial and Zeeman-field dependence of the lowest-energy states.

    fig. S13. Low-energy spectrum and corresponding conductance map at different Zeeman fields.

    fig. S14. Low-energy spectrum and corresponding conductance map for a system with a step-like potential.

    fig. S15. Differential conductance at high values of μBG1.

    fig. S16. Conductance and local-density maps of particle states at zero field.

    fig. S17. Conductance maps for different potential profiles.

    fig. S18. Conductance map of bias versus μBG1 and corresponding potential profile for different BG2 settings.

    References (3437)

  • Supplementary Materials

    This PDF file includes:

    • Supplementary Text
    • fig. S1. Hard gap in a double full-cover superconducting device.
    • fig. S2. Linecuts from Figs. 1 and 2 in the main text.
    • fig. S3. Gates dependence of ZBP.
    • fig. S4. ZBP evolution with BG1.
    • fig. S5. ZBP evolution at a large range of magnetic field.
    • fig. S6. Magnetic field orientation dependence of ZBP.
    • fig. S7. ZBP evolution with BG1 at an angle of π/2.
    • fig. S8. Expanded scan of BG1 and gates dependence of resonances.
    • fig. S9. Comparing the first and second resonances in zero-bias conductance maps.
    • fig. S10. Gate and field dependence of the second resonance.
    • fig. S11. Schematic representation of the tight-binding Hamiltonian.
    • fig. S12. Comparison between long and short wires on spatial and Zeeman-field dependence of the lowest-energy states.
    • fig. S13. Low-energy spectrum and corresponding conductance map at different Zeeman fields.
    • fig. S14. Low-energy spectrum and corresponding conductance map for a system with a step-like potential.
    • fig. S15. Differential conductance at high values of μBG1.
    • fig. S16. Conductance and local-density maps of particle states at zero field.
    • fig. S17. Conductance maps for different potential profiles.
    • fig. S18. Conductance map of bias versus μBG1 and corresponding potential profile for different BG2 settings.
    • References (34–37)

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