Abstract

Boundaries between distinct topological phases of matter support robust, yet exotic quantum states such as spin–momentum locked transport channels or Majorana fermions1,2,3. The idea of using such states in spintronic devices or as qubits in quantum information technology is a strong driver of current research in condensed matter physics4,5,6. The topological properties of quantum states have helped to explain the conductivity of doped trans-polyacetylene in terms of dispersionless soliton states7,8,9. In their seminal paper, Su, Schrieffer and Heeger (SSH) described these exotic quantum states using a one-dimensional tight-binding model10,11. Because the SSH model describes chiral topological insulators, charge fractionalization and spin–charge separation in one dimension, numerous efforts have been made to realize the SSH Hamiltonian in cold-atom, photonic and acoustic experimental configurations12,13,14. It is, however, desirable to rationally engineer topological electronic phases into stable and processable materials to exploit the corresponding quantum states. Here we present a flexible strategy based on atomically precise graphene nanoribbons to design robust nanomaterials exhibiting the valence electronic structures described by the SSH Hamiltonian15,16,17. We demonstrate the controlled periodic coupling of topological boundary states18 at junctions of graphene nanoribbons with armchair edges to create quasi-one-dimensional trivial and non-trivial electronic quantum phases. This strategy has the potential to tune the bandwidth of the topological electronic bands close to the energy scale of proximity-induced spin–orbit coupling19 or superconductivity20, and may allow the realization of Kitaev-like Hamiltonians3 and Majorana-type end states21.

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Acknowledgements

This work was supported by the Swiss National Science Foundation, the Office of Naval Research BRC Program, the European Union’s Horizon 2020 research and innovation programme (GrapheneCore1 696656), and the NCCR MARVEL. C.A.P. thanks the Swiss Supercomputing Center (CSCS) for computational support. X.Y. is grateful for a fellowship from the China Scholarship Council. O.G. thanks O. Yazyev, D. Rizzo and D. Bercioux for discussions.

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Nature thanks T. Heine, I. Swart and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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Author notes

  1. These authors contributed equally: Oliver Gröning, Shiyong Wang, Xuelin Yao

Affiliations

  1. Empa, Swiss Federal Laboratories for Materials Science and Technology, Dübendorf, Switzerland

    • Oliver Gröning
    • , Shiyong Wang
    • , Carlo A. Pignedoli
    • , Gabriela Borin Barin
    • , Pascal Ruffieux
    •  & Roman Fasel
  2. School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, China

    • Shiyong Wang
  3. Max Planck Institute for Polymer Research, Mainz, Germany

    • Xuelin Yao
    • , Akimitsu Narita
    •  & Klaus Müllen
  4. Department of Physics, Applied Physics and Astronomy, Rensselaer Polytechnic Institute, Troy, NY, USA

    • Colin Daniels
    • , Andrew Cupo
    •  & Vincent Meunier
  5. Department of Chemistry and Food Chemistry, Technische Universität Dresden, Dresden, Germany

    • Xinliang Feng
  6. Department of Chemistry and Biochemistry, University of Bern, Bern, Switzerland

    • Roman Fasel

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Contributions

O.G., P.R. and R.F. conceived and supervised this work. A.N., X.Y., X.F. and K.M. designed and synthesized the molecular precursors. S.W. performed the on-surface synthesis and scanning probe microscopy characterization. G.B.B. did the Raman analysis, C.D., A.C. and V.M. performed the corresponding simulations. C.A.P. did the DFT calculations. O.G. developed the conceptual framework, performed the tight-binding calculations and wrote the manuscript, with contributions from all co-authors. P.R., S.W. and O.G. designed the figures, with contributions from other co-authors.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to Oliver Gröning.

Supplementary information

  1. Supplementary Information

    This file contains Supplementary Text and Data, Supplementary Figures 1-38 and Supplementary References.

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https://doi.org/10.1038/s41586-018-0375-9

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