Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Tailoring topological order and π-conjugation to engineer quasi-metallic polymers


Topological band theory predicts that a topological electronic phase transition between two insulators must proceed via closure of the electronic gap. Here, we use this transition to circumvent the instability of metallic phases in π-conjugated one-dimensional (1D) polymers. By means of density functional theory, tight-binding and GW calculations, we predict polymers near the topological transition from a trivial to a non-trivial quantum phase. We then use on-surface synthesis with custom-designed precursors to make polymers consisting of 1D linearly bridged acene moieties, which feature narrow bandgaps and in-gap zero-energy edge states when in the topologically non-trivial phase close to the topological transition point. We also reveal the fundamental connection between topological classes and resonant forms of 1D π-conjugated polymers.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type



Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Topological quantum phase transition in the acene polymer family.
Fig. 2: Experimental and theoretical results for anthracene (n = 3) polymer.
Fig. 3: Experimental and theoretical results for pentacene (n = 5) polymer.
Fig. 4: Experimental and theoretical results for topologically non-trivial bisanthene polymers.

Similar content being viewed by others

Data availability

The data for the tight-binding calculation as presented in Fig. 1, as well as STS and DFT DOS data as presented in Figs. 2, 3 and 4 are available as source data. Other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Code availability

The tight-binding calculations have been performed using a custom-made code on the Wave Metrics IGOR Pro platform. Details of this tight-binding code can be obtained from the corresponding author upon reasonable request.


  1. Chiang, C. K. et al. Electrical conductivity in doped polyacetylene. Phys. Rev. Lett. 39, 1098–1101 (1977).

    Article  CAS  Google Scholar 

  2. Farchioni, R. & Grosso, G. Organic electronic Materials: Conjugated Polymers and Low Molecular Weight Organic Solids (Springer, 2001).

  3. Heeger, A. J. Semiconducting and metallic polymers: the fourth generation of polymeric materials (Nobel Lecture). Angew. Chem. Int. Ed. 40, 2591–2611 (2001).

    Article  CAS  Google Scholar 

  4. Heeger, A. J., Kivelson, S., Schrieffer, J. R. & Su, W. P. Solitons in conducting polymers. Rev. Mod. Phys. 60, 781–850 (1988).

    Article  CAS  Google Scholar 

  5. Facchetti, A. π-Conjugated polymers for organic electronics and photovoltaic cell applications. Chem. Mater. 23, 733–758 (2011).

    Article  CAS  Google Scholar 

  6. Roncali, J. Synthetic principles for bandgap control in linear π-conjugated systems. Chem. Rev. 97, 173–206 (1997).

    Article  CAS  Google Scholar 

  7. Roncali, J. Molecular engineering of the band gap of π-conjugated systems: facing technological applications. Macromol. Rapid Commun. 28, 1761–1775 (2007).

    Article  CAS  Google Scholar 

  8. Chujo, Y. Conjugated Polymer Synthesis: Methods and Reactions (Wiley-VCH, 2010).

  9. Steckler, T. T. et al. Very low band gap thiadiazoloquinoxaline donor–acceptor polymers as multi-tool conjugated polymers. J. Am. Chem. Soc. 136, 1190–1193 (2014).

    Article  CAS  Google Scholar 

  10. Dou, L., Liu, Y., Hong, Z., Li, G. & Yang, Y. Low-bandgap near-IR conjugated polymers/molecules for organic electronics. Chem. Rev. 115, 12633–12665 (2015).

    Article  CAS  Google Scholar 

  11. Kawabata, K., Saito, M., Osaka, I. & Takimiya, K. Very small bandgap π-conjugated polymers with extended thienoquinoids. J. Am. Chem. Soc. 138, 7725–7732 (2016).

    Article  CAS  Google Scholar 

  12. Scherf, U. & Müllen, K. Design and synthesis of extended pi-systems: monomers, oligomers, polymers. Synthesis 1–2, 23–38 (1992).

    Article  Google Scholar 

  13. Garay, R. O., Naarmann, H. & Muellen, K. Synthesis and characterization of poly(1,4-anthrylenevinylene). Macromolecules 27, 1922–1927 (1994).

    Article  CAS  Google Scholar 

  14. Taylor, P. N., Wylie, A. P., Huuskonen, J. & Anderson, H. L. Enhanced electronic conjugation in anthracene-linked porphyrins. Angew. Chem. Int. Ed. 37, 986–989 (1998).

    Article  CAS  Google Scholar 

  15. Susumu, K., Duncan, T. V. & Therien, M. J. Potentiometric, electronic structural, and ground- and excited-state optical properties of conjugated bis[(porphinato)zinc(II)] compounds featuring proquinoidal spacer units. J. Am. Chem. Soc. 127, 5186–5195 (2005).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  17. 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 

  18. Gross, L. et al. Atomic force microscopy for molecular structure elucidation. Angew. Chem. Int. Ed. 57, 3888–3908 (2018).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  20. Rizzo, D. J. et al. Topological band engineering of graphene nanoribbons. Nature 560, 204–208 (2018).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  22. Bennett, P. B. et al. Bottom-up graphene nanoribbon field-effect transistors. Appl. Phys. Lett. 103, 253114 (2013).

    Article  CAS  Google Scholar 

  23. 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  CAS  Google Scholar 

  24. Moreno, C. et al. Bottom-up synthesis of multifunctional nanoporous graphene. Science 360, 199–203 (2018).

    Article  CAS  Google Scholar 

  25. Borin Barin, G. et al. Surface-synthesized graphene nanoribbons for room temperature switching devices: substrate transfer and ex situ characterization. ACS Appl. Nano Mater. 2, 2184–2192 (2019).

    Article  CAS  Google Scholar 

  26. Sánchez-Grande, A. et al. On-surface synthesis of ethynylene bridged anthracene polymers. Angew. Chem. Int. Ed. 58, 6559–6563 (2019).

    Article  CAS  Google Scholar 

  27. Bettanin, F. et al. Singlet La and Lb bands for N-acenes (N = 2–7): a CASSCF/CASPT2 study. J. Chem. Theory Comput. 13, 4297–4306 (2017).

    Article  CAS  Google Scholar 

  28. Asbóth, J. K., Oroszlány, L. & Pályi, A. in A Short Course on Topological Insulators: Band Structure and Edge States in One and Two Dimensions 1–22 (Springer International Publishing, 2016).

  29. Pavliček, N. et al. Polyyne formation via skeletal rearrangement induced by atomic manipulation. Nat. Chem. 10, 853–858 (2018).

    Article  CAS  Google Scholar 

  30. Sun, Q. et al. On-surface formation of cumulene by dehalogenative homocoupling of alkenyl gem-dibromides. Angew. Chem. Int. Ed. 56, 12165–12169 (2017).

    Article  CAS  Google Scholar 

  31. Gross, L., Mohn, F., Moll, N., Liljeroth, P. & Meyer, G. The chemical structure of a molecule resolved by atomic force microscopy. Science 325, 1110–1114 (2009).

    Google Scholar 

  32. Neaton, J. B., Hybertsen, M. S. & Louie, S. G. Renormalization of molecular electronic levels at metal-molecule interfaces. Phys. Rev. Lett. 97, 216405 (2006).

    Article  CAS  Google Scholar 

  33. Amy, F., Chan, C. & Kahn, A. Polarization at the gold/pentacene interface. Org. Electron. 6, 85–91 (2005).

    Article  CAS  Google Scholar 

  34. Cohen, A. J., Mori-Sánchez, P. & Yang, W. Insights into current limitations of density functional theory. Science 321, 792 (2008).

    Article  CAS  Google Scholar 

  35. Kertesz, M., Choi, C. H. & Yang, S. Conjugated polymers and aromaticity. Chem. Rev. 105, 3448–3481 (2005).

    Article  CAS  Google Scholar 

  36. Jelínek, P. High resolution SPM imaging of organic molecules with functionalized tips. J. Phys.-Condens. Mat. 29, 343002 (2017).

    Article  Google Scholar 

  37. Kawai, S. et al. Diacetylene linked anthracene oligomers synthesized by one-shot homocoupling of trimethylsilyl on Cu(111). ACS Nano 12, 8791–8797 (2018).

    Article  CAS  Google Scholar 

  38. Karpfen, A. Ab initio studies on polymers. IV. Polydiacetylenes. J. Phys. C 13, 5673–5689 (1980).

    Article  CAS  Google Scholar 

  39. Hernandez, V., Castiglioni, C., del Zoppo, M. & Zerbi, G. Confinement potential and pi-electron delocalization in polyconjugated organic materials. Phys. Rev. B 50, 9815–9823 (1994).

    Article  CAS  Google Scholar 

  40. Estarellas, M. P., D’Amico, I. & Spiller, T. P. Topologically protected localised states in spin chains. Sci. Rep. 7, 42904 (2017).

    Article  CAS  Google Scholar 

  41. Heeger, A. J. Semiconducting and metallic polymers: the fourth generation of polymeric materials. J. Phys. Chem. B 105, 8475–8491 (2001).

    Article  CAS  Google Scholar 

  42. Little, W. A. Possibility of synthesizing an organic superconductor. Phys. Rev. 134, A1416–A1424 (1964).

    Article  Google Scholar 

  43. Gorodetsky, A. A. et al. Reticulated heterojunctions for photovoltaic devices. Angew. Chem. Int. Ed. 49, 7909–7912 (2010).

    Article  CAS  Google Scholar 

  44. Zeng, Z. et al. Stable tetrabenzo-Chichibabin’s hydrocarbons: tunable ground state and unusual transition between their closed-shell and open-shell resonance forms. J. Am. Chem. Soc. 134, 14513–14525 (2012).

    Article  CAS  Google Scholar 

  45. Blum, V. et al. Ab initio molecular simulations with numeric atom-centered orbitals. Comput. Phys. Commun. 180, 2175–2196 (2009).

    Article  CAS  Google Scholar 

  46. Perdew, J. P., Burke, W. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996).

    Article  CAS  Google Scholar 

  47. Becke, A. D. Density-functional thermochemistry. III. The role of exact exchange. J. Chem. Phys. 98, 5648 (1993).

    Article  CAS  Google Scholar 

  48. Lewis, J. P. et al. Advances and applications in the FIREBALL ab initio tight-binding molecular-dynamics formalism. Phys. Status Solidi B Basic Res. 248, 1989–2007 (2011).

    CAS  Google Scholar 

  49. Hapala, P. et al. Mechanism of high-resolution STM/AFM imaging with functionalized tips. Phys. Rev. B 90, 085421 (2014).

    Article  CAS  Google Scholar 

  50. Krejčí, O., Hapala, P., Ondráček, M. & Jelínek, P. Principles and simulations of high-resolution STM imaging with a flexible tip apex. Phys. Rev. B 95, 045407 (2017).

    Article  Google Scholar 

Download references


This work was supported by the ERC Consolidator Grant ELECNANO (no. 766555), the EC FP7-PEOPLE-2011-COFUND AMAROUT II, the Spanish Ramón y Cajal programme (no. RYC-2012-11133), the Spanish Ministerio de Economía y Competitividad (projects FIS 2013-40667-P and FIS 2015-67287-P) and the Comunidad de Madrid (projects QUIMTRONIC-CM (Y2018/NMT-4783), MAD2D (S2013/MIT-3007), NANOFRONTMAG (S2013/MT-2850) and PHOTOCARBON (S2013/MIT-2841)). We also acknowledge support from the European Research Council (ERC-320441-Chirallcarbon) and the MINECO of Spain (projects CTQ2017-83531-R and CTQ2016-81911-REDT). IMDEA Nanociencia thanks support from the Severo Ochoa Programme for Centers of Excellence in R&D (MINECO, grant SEV-2016-0686). We also acknowledge support of MEYS CR LM2018110, GACR 18-09914S and Operational Programme Research, Development and Education financed by European Structural and Investment Funds and the Czech Ministry of Education, Youth and Sports (project no. CZ.02.1.01/0.0/0.0/16_019/0000754). P.J. acknowledges support from Praemium Academie of the Academy of Science of the Czech Republic. S.E. and B.M. are grateful for support from the Internal Student Grant of Palacký University Olomouc in Olomouc, Czech Republic (project no. IGA_PrF_2019_026). P.J. and S.E. acknowledge access to computing and storage facilities owned by parties and projects contributing to the Czech National Grid Infrastructure MetaCentrum provided under the programme Projects of Large Research, Development, and Innovations Infrastructures (CESNET LM2015042).

Author information

Authors and Affiliations



P.J., N.M. and D.E. conceived and designed the experiments. O.G., P.J., N.M. and D.E. supervised the project and led the collaboration efforts. B.C., A.S.-G., B.T. and D.E. carried out the experiments and obtained the data. J.S., E.R.-S. and N.M. synthesized the precursors. The experimental data were analysed by B.C., A.S.-G., B.T., B.M., R.Z., R.M., O.G., P.J. and D.E., and discussed by all the authors. S.E. and P.J. performed the DFT and GW calculations. O.G. carried out the tight-binding calculations. The manuscript was written by B.C., O.G., P.J., N.M. and D.E., with contributions from all the authors.

Corresponding authors

Correspondence to Oliver Gröning, Pavel Jelínek, Nazario Martín or David Ecija.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Nanotechnology thanks Martina Corso, Giovanni Costantini and Oleg Yazyev for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Tables 1–3, Figs. 1–23, Notes 1–9 and refs. 1–9.

Source data

Source Data Fig. 1

This file contains the data of the tight-binding calculations in panel b

Source Data Fig. 2

This file contains unprocessed STS graphs and DFT density of states plots related to anthracene polymers

Source Data Fig. 3

This file contains unprocessed STS graphs and DFT density of states plots related to pentacene polymers

Source Data Fig. 4

This file contains unprocessed STS graphs and DFT density of states plots related to bisanthracene polymers

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cirera, B., Sánchez-Grande, A., de la Torre, B. et al. Tailoring topological order and π-conjugation to engineer quasi-metallic polymers. Nat. Nanotechnol. 15, 437–443 (2020).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Find nanotechnology articles, nanomaterial data and patents all in one place. Visit Nano by Nature Research