Research ArticleCONDENSED MATTER PHYSICS

Topological bootstrap: Fractionalization from Kondo coupling

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Science Advances  06 Oct 2017:
Vol. 3, no. 10, e1700729
DOI: 10.1126/sciadv.1700729
  • Fig. 1 Example and phenomenology of topological bootstrap.

    (A) Two decoupled layers: a Chern insulator (blue, A) and a free layer of spins (white, B). e, electron. (B) After Kondo coupling, the Chern insulator induces a CSL (green) with the opposite chirality. The counterpropagating spin modes gap out, leaving a charge mode. (C) In a terrace construction, the induced and original edge modes are widely separated and coexist.

  • Fig. 2 Interpolation from global to local coupling.

    Systems A and B are each partitioned into regions. Corresponding regions r in A and B are coupled via a projection Pr onto the maximally entangled state of the two regions (dotted lines). If adjacent A regions are decoupled, as shown on the left, then each region of the Chern insulator induces a region of CSL via Eq. 8. Once the A regions are recoupled, adjacent edge states gap out, and the regions merge into a large Chern insulator. These interactions induce analogous interactions in B (inset), which fuse the B regions into a large CSL.

  • Fig. 3 Topological bootstrap in lattice models.

    (A) Free-fermion superconductor. Each site has four Majorana fermions, which form directed dimers (bold, with arrows) on the links with neighboring modes. (B) The superconductor induces the Wen plaquette/toric code via Kondo coupling. (C) Chern insulator on the kagome lattice realized from nearest-neighbor hopping of spin-up and spin-down electrons with a background π/2 flux per triangle. (D) The Chern insulator induces a CSL via Kondo coupling, with exchange and chirality parameters given in Eq. 15.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/10/e1700729/DC1

    Derivation of effective spin Hamiltonians for CSL

    fig. S1. Convergence in two-spin interaction coefficient as a function of mesh linear dimension.

    fig. S2. Convergence in spin chirality strength as a function of mesh linear dimension.

  • Supplementary Materials

    This PDF file includes:

    • Derivation of effective spin Hamiltonians for CSL
    • fig. S1. Convergence in two-spin interaction coefficient as a function of mesh linear dimension.
    • fig. S2. Convergence in spin chirality strength as a function of mesh linear dimension.

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