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Engineering of robust topological quantum phases in graphene nanoribbons


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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Fig. 1: The SSH model and its realization in edge-extended graphene nanoribbons.
Fig. 2: Electronic structure of the staggered edge-extended 7-AGNR-S(1,3) nanoribbon.
Fig. 3: Bulk–boundary correspondence for the staggered edge-extended 7-AGNR-S(n,m) nanoribbon family.
Fig. 4: Non-trivial topological (\({{\mathbb{Z}}}_{2}\) = 1) phase of the inline edge-extended 7-AGNR-I(1,3) structure.

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  1. Hasan, M. Z. & Kane, C. L. Topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).

    Article  ADS  CAS  Google Scholar 

  2. König, M. et al. Quantum spin Hall insulator state in HgTe quantum wells. Science 318, 766–770 (2007).

    Article  ADS  PubMed  CAS  Google Scholar 

  3. Kitaev, G. Unpaired Majorana fermions in quantum wires. Phys. Usp. 44, 131–136 (2001).

    Article  ADS  Google Scholar 

  4. Bradlyn, B. et al. Topological quantum chemistry. Nature 547, 298–305 (2017).

    Article  ADS  PubMed  CAS  Google Scholar 

  5. de Vries, E. K. et al. Towards the understanding of the origin of charge-current-induced spin voltage signals in the topological insulator Bi2Se3. Phys. Rev. B 92, 201102 (2015).

    Article  ADS  CAS  Google Scholar 

  6. Mourik, V. et al. Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices. Science 336, 1003–1007 (2012).

    Article  ADS  PubMed  CAS  Google Scholar 

  7. Chiang, C. K. et al. Electrical conductivity in doped polyacetylene. Phys. Rev. Lett. 39, 1098 (1977).

    Article  ADS  CAS  Google Scholar 

  8. Su, W.-P., Schrieffer, J. R. & Heeger, A. J. Soliton excitations in polyacetylene. Phys. Rev. B 22, 2099–2111 (1980).

    Article  ADS  CAS  Google Scholar 

  9. Longuet-Higgins, H. C. & Salem, F. R. S. L. The alternation of bond lengths in long conjugated chain molecules. Proc. R. Soc. Lond. A 251, 172–183 (1959).

    Article  Google Scholar 

  10. Su, W., Schrieffer, J. R. & Heeger, A. J. Solitons in polyacetylene. Phys. Rev. Lett. 42, 1698 (1979).

    Article  ADS  CAS  Google Scholar 

  11. Asbóth, J. K., Oroszlány, L. & Pályi, O. A short course on topological insulators: band-structure topology and edge states in one and two dimensions Lecture Notes in Physics Vol. 919 (Springer, Cham, 2016).

  12. Meier, E. J., An, F. A. & Gadway, B. Observation of the topological soliton state in the Su–Schrieffer–Heeger model. Nat. Commun. 7, 13986 (2016).

    Article  ADS  PubMed  PubMed Central  CAS  Google Scholar 

  13. Tan, W., Sun, Y., Chen, H. & Shen, S.-Q. Photonic simulation of topological excitations in metamaterials. Sci. Rep. 4, 3842 (2015).

    Article  CAS  Google Scholar 

  14. Chen, B. G.-g., Upadhyaya, N. & Vitelli, V. Nonlinear conduction via solitons in a topological mechanical insulator. Proc. Natl Acad. Sci. USA 111, 13004–13009 (2014).

    Article  ADS  MathSciNet  PubMed  MATH  CAS  Google Scholar 

  15. Cai, J. et al. Atomically precise bottom-up fabrication of graphene nanoribbons. Nature 466, 470–473 (2010).

    Article  ADS  PubMed  CAS  Google Scholar 

  16. Nguyen, G. D. et al. Atomically precise graphene nanoribbon heterojunctions from a single molecular precursor. Nat. Nanotechnol. 12, 1077–1082 (2017).

    Article  ADS  PubMed  CAS  Google Scholar 

  17. Talirz, L., Ruffieux, P. & Fasel, R. On-surface synthesis of atomically precise graphene nanoribbons. Adv. Mater. 28, 6222–6231 (2016).

    Article  PubMed  CAS  Google Scholar 

  18. Cao, T., Zhao, F. & Louie, S. G. Topological phases in graphene nanoribbons: junction states, spin centers, and quantum spin chains. Phys. Rev. Lett. 119, 076401 (2017).

    Article  ADS  PubMed  Google Scholar 

  19. Wang, Z. et al. Strong interface-induced spin–orbit interaction in graphene on WS2. Nat. Commun. 6, 8339 (2015).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  20. Feigel’man, M. V., Skvortsov, M. A. & Tikhonov, K. S. Theory of proximity-induced superconductivity in graphene. Solid State Commun. 149, 1101–1105 (2009).

    Article  ADS  CAS  Google Scholar 

  21. Nadj-Perge, S. et al. Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor. Science 346, 602–607 (2014).

    Article  ADS  PubMed  CAS  Google Scholar 

  22. Shen, Q., Gao, H.-Y. & Fuchs, H. Frontiers of on-surface synthesis: from principles to applications. Nano Today 13, 77–96 (2017).

    Article  CAS  Google Scholar 

  23. Fairbrother, A. et al. High vacuum synthesis and ambient stability of bottom-up graphene nanoribbons. Nanoscale 9, 2785–2792 (2017).

    Article  PubMed  CAS  Google Scholar 

  24. Llinas, J. P. et al. Short-channel field-effect transistors with 9-atom and 13-atom wide graphene nanoribbons. Nat. Commun. 8, 633 (2017).

    Article  ADS  PubMed  PubMed Central  CAS  Google Scholar 

  25. Wakabayashi, K., Sasaki, K., Nakanishi, T. & Enoki, T. Electronic states of graphene nanoribbons and analytical solutions. Sci. Technol. Adv. Mater. 11, 054504 (2010).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  26. Söde, H. et al. Electronic band dispersion of graphene nanoribbons via Fourier-transformed scanning tunneling spectroscopy. Phys. Rev. B 91, 045429 (2015).

    Article  ADS  CAS  Google Scholar 

  27. Deniz, O. et al. Revealing the electronic structure of silicon intercalated armchair graphene nanoribbons by scanning tunneling spectroscopy. Nano Lett. 17, 2197–2203 (2017).

    Article  ADS  PubMed  CAS  Google Scholar 

  28. Wang, S. et al. Giant edge state splitting at atomically precise graphene zigzag edges. Nat. Commun. 7, 11507 (2016).

    Article  ADS  PubMed  PubMed Central  CAS  Google Scholar 

  29. Kimouche, A. et al. Ultra-narrow metallic armchair graphene nanoribbons. Nat. Commun. 6, 10177 (2015).

    Article  ADS  PubMed  PubMed Central  CAS  Google Scholar 

  30. Merino-Díez, N. et al. Width-dependent band gap in armchair graphene nanoribbons reveals Fermi level pinning on Au(111). ACS Nano 11, 11661–11668 (2017).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  31. Kharche, N. & Meunier, V. Width and crystal orientation dependent band gap renormalization in substrate-supported graphene nanoribbons. J. Phys. Chem. Lett. 7, 1526–1533 (2016).

    Article  PubMed  CAS  Google Scholar 

  32. Fujita, M., Wakabayashi, K., Nakada, K. & Kusakabe, K. Peculiar localized state at zigzag graphite edge. J. Phys. Soc. Jpn 65, 1920–1923 (1996).

    Article  ADS  CAS  Google Scholar 

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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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Authors and Affiliations



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.

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Correspondence to Oliver Gröning.

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

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Gröning, O., Wang, S., Yao, X. et al. Engineering of robust topological quantum phases in graphene nanoribbons. Nature 560, 209–213 (2018).

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