Research ArticlePHYSICAL SCIENCE

A novel artificial condensed matter lattice and a new platform for one-dimensional topological phases

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Science Advances  24 Mar 2017:
Vol. 3, no. 3, e1501692
DOI: 10.1126/sciadv.1501692
  • Fig. 1 Overview of the topological insulator heterostructure.

    (A) The heterostructure consists of a stack of alternating ℤ2 topological insulator layers and trivial insulator layers. We use Bi2Se3 as the topologically nontrivial layer and InxBi2−xSe3 as the topologically trivial layer. The ℤ2 invariant is denoted by ν0 = 1, 0. An amorphous Se capping layer protects the sample in atmosphere and is removed by heating the sample in situ. (B) Our system realizes an emergent version of a polyacetylene chain, well known as a toy model in the study of one-dimensional topological phases. The model has two carbon atoms per unit cell, with one orbital each and with hopping amplitudes t and t′ associated with the double and single carbon bonds. In the topological insulator heterostructure, the topological and trivial layers play the role of the double and single carbon bonds. (C) A conventional semiconductor heterostructure consists of an alternating pattern of materials with different band gaps. (D) In a topological insulator heterostructure, the band gaps in adjacent layers are inverted, giving rise to topologically protected Dirac cone interface states between layers. If the layers are thin, then adjacent Dirac cones may hybridize. This hybridization can be described by a hopping amplitude t across the topological layer and a hopping amplitude t′ across the trivial layer. (E) Illustration of the Dirac cone surface states at each interface in the heterostructure, assuming no hybridization. With a hybridization t, the topological interface states form a superlattice band structure. A standard low-energy electron diffraction pattern (F) and a core-level photoemission spectrum (G) show that the samples are of high quality and that the Se capping layer was successfully removed by in situ heating, exposing a clean sample surface in vacuum.

  • Fig. 2 Observation of an emergent superlattice band structure in trivial and topological phases.

    (A to D) The unit cells of the heterostructures studied, with different thicknesses and In doping of the InxBi2−xSe3 layer. (E to H) ARPES spectra of the heterostructures. (E) and (F) show gapped surface states, whereas (G) and (H) show gapless surface states. Note that in all samples measured, the top layer of the superlattice, which is the only layer directly measured by ARPES, is 4QL of Bi2Se3. Nonetheless, the spectra differ markedly. (I to L) The same spectra as in (E) to (H), but with additional hand-drawn lines showing the key features of the spectra. In the 4QL/4QL 20% and 4QL/2QL 25% samples, we observe gapped topological surface states, 1 and 2, along with a valence band quantum well state, 3. By contrast, in 4QL/2QL 15% and 4QL/1QL 20%, we observe a gapless Dirac cone surface state, 1, and two conduction band quantum well states, 2 and 3, and in 4QL/1QL 20%, we observe two valence quantum well states, 4 and 5. We emphasize that the gapless Dirac cone is observed although the top Bi2Se3 layer is only 4QL thick. (M to P) EDCs through the Embedded Image point of each spectrum in (E) to (H). The peaks corresponding to the bulk quantum well states and surface states are numbered on the basis of the correspondence with the full spectra (E to H).

  • Fig. 3 Realization of the Su-Schrieffer-Heeger (SSH) model.

    ARPES spectrum of 4QL/1QL 20% (A), with a second-derivative map of the same spectrum (B) and the same second-derivative map (C) with additional hand-drawn lines highlighting the gapless surface state and the two quantum well states in the conduction and valence bands. (D) A tight-binding calculation demonstrating a topological phase qualitatively consistent with our experimental result. (E) A cartoon of the band gap profile of the 4QL/1QL 20% heterostructure. The trivial layer is much thinner than the topological layer; thus, t < t′, and we are in the SSH topological phase. (F) The SSH topological phase can be understood as a phase where the surface states pair up with their nearest neighbors and gap out but where the pairing takes place in such a way that there is an unpaired lattice site at the end of the atomic chain. ARPES spectrum of 4QL/4QL 20% (G), with a second-derivative map of the same spectrum (H) and the same second-derivative map (I) with additional hand-drawn lines highlighting the gapped surface state and the quantum well state in the valence band. (J) A tight-binding calculation demonstrating a trivial phase qualitatively consistent with our experimental result. (K) A cartoon of the band gap profile of the 4QL/4QL 20% heterostructure. The trivial layer is as thick as the topological layer, with a larger band gap due to high In doping; thus, t > t′, and we are in the SSH trivial phase. (L) The SSH trivial phase can be understood as a phase where all lattice sites in the atomic chain have a pairing partner.

  • Fig. 4 Systematic study of the topological and trivial phases.

    (A to F) ARPES spectra of the 4QL/1QL samples at hν = 18 eV with varying concentrations of In, showing a robust topological phase. (G to I) EDCs through the Embedded Image point of each spectrum in (A) to (C). (J to O) ARPES spectra of the 3QL/3QL 20% and 4QL/4QL 20% samples at hν = 102 eV and of the 3QL/3QL 20% sample at hν = 111 eV, showing a robust trivial phase. (P to R) EDCs through the Embedded Image point of each spectrum in (G) to (I).

  • Fig. 5 Phase diagram of a tunable emergent superlattice band structure.

    (A) By varying the hopping t′ across the trivial layer, we realize a trivial phase and a topological phase in our superlattice band structure. (B) In the heterostructures demonstrated here, we expect that only nearest-neighbor hopping is relevant, giving rise to an emergent chiral symmetry along the stacking direction. By using thinner layers, we propose to introduce a next nearest-neighbor hopping, breaking this chiral symmetry. This may change the topological classification of our system. (C) By doubling the unit cell, we can break inversion symmetry. This will give rise to a spinful superlattice dispersion.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/3/e1501692/DC1

    Estimate of indium diffusion in the heterostructure

    Observation of a topological phase transition in numerics

    Fine dependence on indium doping

    Comparison with a single thin film of Bi2Se3

    Detailed analysis of bulk quantum well states

    fig. S1. Characterization of In diffusion in the heterostructures.

    fig. S2. Topological phase transition in numerics.

    fig. S3. Change in Fermi level with In doping.

    fig. S4. Dimerized-limit heterostructure and a single thin film of Bi2Se3.

    fig. S5. Bulk quantum well states of 4QL/2QL 15% and 4QL/1QL 20%.

    Reference (25)

  • Supplementary Materials

    This PDF file includes:

    • Estimate of indium diffusion in the heterostructure
    • Observation of a topological phase transition in numerics
    • Fine dependence on indium doping
    • Comparison with a single thin film of Bi2Se3
    • Detailed analysis of bulk quantum well states
    • fig. S1. Characterization of In diffusion in the heterostructures.
    • fig. S2. Topological phase transition in numerics.
    • fig. S3. Change in Fermi level with In doping.
    • fig. S4. Dimerized-limit heterostructure and a single thin film of Bi2Se3.
    • fig. S5. Bulk quantum well states of 4QL/2QL 15% and 4QL/1QL 20%.
    • Reference (25)

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