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

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Fig. 3 Realization of the Su-Schrieffer-Heeger (SSH) model. 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. Ilya Belopolski et al. Sci Adv 2017;3:e1501692 Published by AAAS