Research ArticlePHYSICS

Toward tailoring Majorana bound states in artificially constructed magnetic atom chains on elemental superconductors

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Science Advances  11 May 2018:
Vol. 4, no. 5, eaar5251
DOI: 10.1126/sciadv.aar5251
  • Fig. 1 YSR states of individual magnetic Fe atoms and their interactions on Re(0001).

    (A and B) STM topographic images of isolated Fe atoms (A) and an Fe dimer (B) on Re(0001). Tunneling current, IT = 5.0 nA; sample bias voltage, VS = 3.0 mV; scan area, 7.0 × 4.0 nm2. The Fe dimer in (B) was created by placing an Fe atom next to another [white dotted arrow in (A)] at a distance of aRe = 0.274 nm. (C) Left: dI/dV spectra on a single Fe atom (red) and on the bare Re substrate (gray) measured with a superconducting Nb tip (IT = 1.0 nA, VS = 3.0 mV). Right: Same spectra plotted as a function of |V|. The green dotted line indicates the energy position of the superconducting gap edge of the Nb tip (Materials and Methods). A pair of YSR resonances are indicated by red and blue arrows at |ΔNb ± EB|, with ΔNb = 1.38 meV and EB = 0.020 meV, providing a signature for the localized magnetic moment of the Fe atom. (D) dI/dV spectra obtained at the positions marked by black dots in (A) and (B) for a single Fe atom (red), an Fe dimer (blue), and the bare Re(0001) (gray) measured with a nonsuperconducting tip (IT=5.0 nA, VS=1.5 mV). (E) Difference spectra for an Fe atom and a dimer after subtracting the spectrum obtained on the bare Re(0001) surface. Except for (C), a PtIr tip was used for taking topography images and spectra. All STM images and tunneling spectra were measured at T = 350 mK. a.u., arbitrary units.

  • Fig. 2 Artificially constructed atomic Fe chains on Re(0001) and SP-STM measurements for the magnetic structure.

    (A) Schematic view of the atom manipulation procedure applied to form a 1D atomic chain with an STM tip. (B) Stacked STM images for the artificially constructed Fe chains of various lengths along the close-packed [Embedded Image] direction (IT = 5.0 nA, VS = 3.0 mV; scale bar, 2.0 nm). (C) 3D-rendered STM image of a 40-atom-long Fe chain measured with a nonmagnetic PtIr tip. (D and E) SP-STM images recorded with Fe-coated PtIr tips sensitive to the (D) OP and the (E) IP component of the spins in the chain, with the magnetization directions schematically depicted in the inset. The same tunneling conditions of IT = 5.0 nA and VS = 3.0 mV were used for the measurements in (C) to (E). The magnetization directions of the Fe-coated tips were determined in situ directly before the SP-STM measurements on the atomic Fe chains (Materials and Methods) (28).

  • Fig. 3 Spatial and energy dependence of the LDOS in the 40-atom-long chain.

    (A) Top: Differential tunneling conductance (dI/dV) profiles at VS = 0.00 mV, +0.12 mV, −0.12 mV, and −0.65 mV along the 40-atom-long Fe chain, reflecting the spatial variation of the LDOS. All profiles were extracted from the spatially resolved dI/dV spectra after subtracting the spectrum on the bare Re substrate. The profile for V = −0.65 mV is vertically shifted for clarity (offset, 1.3 μS). Dark cyan arrows in the profile at −0.65 mV denote spatial locations for the confined states; the other colors show the spatial positions where the energy-resolved spectra in (B) were measured. Bottom: Constant-current STM profile (black, left vertical axis), which was recorded simultaneously with the dI/dV spectra and corresponding magnetic profile (blue, right vertical axis) obtained from the SP-STM image measured with the OP spin-sensitive tip. The gray shaded regions correspond to the Re substrate. The dotted lines in red are guides to the eye for the comparison of the spatial variation of the LDOS with the SP-STM profile. (B) dI/dV spectra obtained at the positions indicated by the arrows in (A) and the gray one for the Re substrate. The dotted vertical line shows the zero energy. (C) Spatial distribution of the LDOS at various energies for the two different ends of the 40-atom-long Fe chain. The white dotted lines indicate the boundary of the chain. The scan size of all images is 1.1 nm × 2.2 nm. The intensity scale at the right side is adjusted for each figure separately. Both ends show an identical and symmetric distribution of LDOS with respect to the center of the chain. The localized end states are visible in the LDOS maps at zero energy for both ends. The tunnel junctions were stabilized at IT = 5.0 nA and VS = 3.0 mV for all spectroscopic measurements.

  • Fig. 4 Development and stabilization of enhanced zero-energy LDOS at the ends with increasing chain length and the calculated topological phase diagram for the Fe chain.

    (A) Measured zero-energy dI/dV profiles along the chains for (from bottom to the top) 3 to 12, 20, 30, and 40 Fe atoms. For clarity, the profiles are shifted vertically. (B) Comparison of the variation of zero-energy tunneling conductance between the middle and the ends of the chains with increasing number of atoms. The conductance values at the end are averaged over the positions indicated by the two dotted lines in the profiles, whereas the ones for the middle are averaged values from the regions around the center of the chains. The tunneling junctions were stabilized at IT = 5.0 nA and VS = 3.0 mV for all spectroscopic measurements. (C) Calculated topological phase diagram for a straight monoatomic Fe chain with noncollinear magnetization as a function of the on-site energy μ and spin splitting parameter J (section S3 and Supplementary Materials). Blue and gray shaded regions correspond to the topologically nontrivial superconducting phase and the trivial phase, respectively. The two dotted lines represent the parameters determined from ab initio calculations for Fe on the Re(0001) surface, μ = −0.92 eV and J = 2.18 eV.

  • Fig. 5 Defect-induced zero-energy in-gap state for an Fe chain with a structural defect.

    (A to E) Sequential STM images for the demonstration of disassembling (A to C) and reassembling (C to E) the 8-atom-long Fe chain by continuous atom manipulations (scale bar, 2.0 nm). (F) Surface profiles along the dotted lines in (A) and (E) for the asymmetric and symmetric 8-atom-long chain, respectively. The 8- and 7-atom-long Fe chains in (A) and (B) show an asymmetric apparent height and are slightly bent from the chain axis because of the mislocated Fe atoms in the chains. After reassembling the 8-atom-long Fe chain, it becomes symmetric and straight. (G) Spatially resolved dI/dV spectra and the color-encoded spectroscopic maps for the asymmetric (top) and symmetric (bottom) 8-atom-long Fe chains. The black dotted lines indicate the boundary between the chains and the substrate. The white arrow indicates the defect-induced zero-energy bound state, which is absent at the other end and at the ends of the symmetric chain. We stabilized the tunneling junction at IT = 5.0 nA and VS = 3.0 mV for all STM images and the tunneling spectra.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/5/eaar5251/DC1

    section S1. Ab initio calculations

    section S2. Model parameters

    section S3. Tight-binding model

    fig. S1. Spatial distribution of the YSR states for a single Fe atom and an Fe dimer on the Re(0001) surface.

    fig. S2. The fast Fourier transformation analysis for the magnetic structure of the 40-atom-long Fe chain.

    fig. S3. Absence of the in-gap states on the 40-atom-long Fe chain above the superconducting critical temperature of Re.

    movie S1. Demonstration of subsequent atom manipulations to construct the close-packed chains of various lengths.

    movie S2. Spatially resolved 2D spectroscopic maps for two different ends of the 40-atom-long Fe chain below TC.

    movie S3. Spatially resolved 2D spectroscopic maps for the 40-atom-long Fe chain above TC.

    References (3746)

  • Supplementary Materials

    This PDF file includes:

    • section S1. Ab initio calculations
    • section S2. Model parameters
    • section S3. Tight-binding model
    • fig. S1. Spatial distribution of the YSR states for a single Fe atom and an Fe dimer on the Re(0001) surface.
    • fig. S2. The fast Fourier transformation analysis for the magnetic structure of the 40-atom-long Fe chain.
    • fig. S3. Absence of the in-gap states on the 40-atom-long Fe chain above the superconducting critical temperature of Re.
    • Legends for movies S1 to S3
    • References (37–46)

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    Other Supplementary Material for this manuscript includes the following:

    • movie S1 (.mp4 format). Demonstration of subsequent atom manipulations to construct the close-packed chains of various lengths.
    • movie S2 (.mp4 format). Spatially resolved 2D spectroscopic maps for two different ends of the 40-atom-long Fe chain below TC.
    • movie S3 (.mp4 format). Spatially resolved 2D spectroscopic maps for the 40-atom-long Fe chain above TC.

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