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Atomic-scale interface engineering of Majorana edge modes in a 2D magnet-superconductor hybrid system

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Science Advances  26 Jul 2019:
Vol. 5, no. 7, eaav6600
DOI: 10.1126/sciadv.aav6600
  • Fig. 1 Chiral Majorana edge modes and the structure of the nanoscale magnet-superconductor hybrid system Fe/Re(0001)-O(2 × 1).

    (A) Schematic picture of the Fe/Re(0001)-O(2 × 1) hybrid system, indicating the spatial structure of the Majorana edge modes and their spatial decay into the center of the island. Here, k is the mode’s momentum parallel to the edge. (B) Schematic picture of the edge mode’s dispersion, traversing the superconducting bulk gap. (C) Constant-current scanning tunneling microscope (STM) image of a small Fe island located on the O(2 × 1)-reconstructed surface of Re(0001). Scale bar, 5 nm. (D) Atomic model of the hybrid system, with the Re(0001) substrate (red spheres), p(2 × 1) oxide layer (blue spheres representing O atoms), and Fe adatoms (green spheres). O atoms are located above the Re hexagonal close-packed hollow sites, and Fe adatoms are located above the Re atoms. Lattice constant of the Re(0001) surface: aRe = 0.274 nm. (E) Experimentally measured dI/dU spectrum on the O(2 × 1) surface (black line), in the center (blue line), and at the edge (red line) of the Fe island. As all STS measurements were performed with a superconducting Nb tip whose gap size is ΔtipNb=1.41 meV (green dotted lines at ±ΔtipNb), the coherence peaks are located at ΔtipNb+ΔO(2×1) and ΔtipNb+ΔFe, respectively. This yields a measured superconducting gap of ΔO(2×1) ≈ 280 μeV in the O(2 × 1) layer and of ΔFe ≈ 240 μeV in the center of the Fe island. (F) Deconvoluted dI/dU spectrum on the O(2 × 1) surface (black line), in the center (blue line), and at the edge (red line) of the Fe island. Parameters for constant-current STM images and stabilization conditions for STS measurements: U = 2.5 mV, I = 1.0 nA, and T = 360 mK. LDOS, local density of states; a.u., arbitrary units.

  • Fig. 2 Evolution of the chiral edge states for the hybrid system Fe/Re(0001)-O(2 × 1) with increasing energy.

    (A to F) Experimentally measured differential tunneling conductance maps and (G to L) corresponding deconvoluted datasets (see section S3) for the Fe island shown in Fig. 1C from the Fermi level, EF=ΔtipNb to ΔFe = 240 μeV above EF. At low energies (A to C and G to I), the dI/dU map reveals states that are localized along the edges of the Fe island (edge modes). Once the localization length of the edge modes becomes of the size of the island (D and J), the dI/dU in the center of the island is comparable to that along the edges. (M to R) Theoretically computed spatially resolved LDOS for the same energies as in (G) to (L). The theoretical data have been spatially convoluted to reproduce the experimental spatial resolution (see section S4). STS measurement conditions: U = 2.5 mV, I = 1.0 nA, and T = 360 mK. The intensity scale is adjusted for each figure separately. Scale bars, 5 nm (A and M).

  • Fig. 3 Decay of the chiral edge states inside an Fe island.

    (A) Deconvoluted LDOS profiles obtained from the experimentally measured dI/dU spectra along the red dotted line in the inset for several different energies: EF, +40 μeV, +60 μeV, +80 μeV, and +100 μeV. (B) Theoretically computed LDOS along the red line in the inset for the same energies as in (A). The corresponding surface profiles of the island are depicted in the bottom panels of (A) and (B). The theoretical results have been spatially convoluted to reproduce the experimental spatial resolution (see section S4). Insets in (A) and (B): The STM topography image and theoretically considered model structure of an Fe island, respectively. All LDOS profiles in (A) and (B) are normalized by their maximum values at the island’s edge. (C) Theoretical phase diagram of the hybrid system. Chern number for an out-of-plane ferromagnetic structure of the Fe layer, as a function of VFeRe/VRe and μFe (see section S4). The phase diagram reveals an abundance of topological phases near the parameter set used to describe the Fe/Re(0001)-O(2 × 1) hybrid system (yellow dot with crossed dotted lines).

  • Fig. 4 Topological trivial Fe island on a bare Re(0001) surface.

    (A) The STM image of the Fe island being in direct contact with the superconducting Re substrate. Scale bar, 10 nm. (B) Experimentally measured dI/dU spectra on the clean Re(0001) surface (black), at the center (blue), and at the edge (red) of the Fe island using a superconducting Nb tip whose gap size is ΔtipNb=0.86meV (see section S3). Tunneling conditions for STM/STS measurements: U = 2.0 mV, I = 1.0 nA, and T= 360 mK. (C) The deconvoluted surface LDOS derived from the spectra shown in (B) taking into account the superconducting gap of the Nb tip used for the STS measurements (see section S3). (D) A zoomed-in STM image of the Fe island shown in (A) [yellow boxed area in (A)]. Scale bar, 5 nm. (E to G) Experimentally measured dI/dU maps for the Fe island shown in (D) at U = +0.86, +0.91, and +0.96 mV, which are corresponding to the energy of EF, 50 μeV, and 100 μeV, respectively. (H) Atomic model of the Fe island on the bare Re(0001) substrate. Fe adatoms are located at the hollow sites of the Re substrate. (I to K) The spatial distribution of the deconvoluted surface LDOS for the island shown in (D). (L) The zoomed-in image of the theoretically considered Fe island structure, reproducing the experimental Fe island in (D). (M to O) Calculated LDOS of the island shown in (L) at the same energies as the experimental results. The theoretical data have been spatially convoluted to reproduce the experimental spatial resolution (see section S4).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/7/eaav6600/DC1

    Section S1. Surface characterization of Fe/Re(0001)-O(2 × 1)

    Section S2. Universal topological nature of Fe islands/Re-O hybrid system

    Section S3. Deconvolution procedure of the tunneling spectra for the superconductor-superconductor tunnel junctions

    Section S4. Theoretical model

    Section S5. Magnetic structure of the Fe island and topological superconductivity

    Section S6. Evolution of topological Majorana modes in a generic topological superconductor

    Fig. S1. STM/STS characterization of the Re(0001)-O(2 × 1) surface.

    Fig. S2. Another example of a topological nontrivial Fe island on a Re(0001)-O(2 × 1) surface.

    Fig. S3. Deconvoluted tunneling spectra and LDOS maps depending on the parameter γ.

    Fig. S4. Theoretically computed LDOS.

    Fig. S5. Topological phase diagram.

    Fig. S6. Spatially resolved LDOS at EF of a magnetically disordered Fe island.

    Fig. S7. Energy evolution of the spatially resolved LDOS for a generic topological superconductor.

    Table S1. Tight binding parameters for the Fe/Re(0001)-O(2 × 1) hybrid system.

    References (3341)

  • Supplementary Materials

    This PDF file includes:

    • Section S1. Surface characterization of Fe/Re(0001)-O(2 × 1)
    • Section S2. Universal topological nature of Fe islands/Re-O hybrid system
    • Section S3. Deconvolution procedure of the tunneling spectra for the superconductor-superconductor tunnel junctions
    • Section S4. Theoretical model
    • Section S5. Magnetic structure of the Fe island and topological superconductivity
    • Section S6. Evolution of topological Majorana modes in a generic topological superconductor
    • Fig. S1. STM/STS characterization of the Re(0001)-O(2 × 1) surface.
    • Fig. S2. Another example of a topological nontrivial Fe island on a Re(0001)-O(2 × 1) surface.
    • Fig. S3. Deconvoluted tunneling spectra and LDOS maps depending on the parameter γ.
    • Fig. S4. Theoretically computed LDOS.
    • Fig. S5. Topological phase diagram.
    • Fig. S6. Spatially resolved LDOS at EF of a magnetically disordered Fe island.
    • Fig. S7. Energy evolution of the spatially resolved LDOS for a generic topological superconductor.
    • Table S1. Tight binding parameters for the Fe/Re(0001)-O(2 × 1) hybrid system.
    • References (3341)

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