Robust zero-energy modes in an electronic higher-order topological insulator


Quantum simulators are essential tools for understanding complex quantum materials. Platforms based on ultracold atoms in optical lattices and photonic devices have led the field so far, but the basis for electronic quantum simulators is now being developed. Here, we experimentally realize an electronic higher-order topological insulator (HOTI). We create a breathing kagome lattice by manipulating carbon monoxide molecules on a Cu(111) surface using a scanning tunnelling microscope. We engineer alternating weak and strong bonds to show that a topological state emerges at the corner of the non-trivial configuration, but is absent in the trivial one. Different from conventional topological insulators, the topological state has two dimensions less than the bulk, denoting a HOTI. The corner mode is protected by a generalized chiral symmetry, which leads to a particular robustness against perturbations. Our versatile approach to designing artificial lattices holds promise for revealing unexpected quantum phases of matter.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Design of the breathing kagome lattice.
Fig. 2: Wave function mapping.
Fig. 3: Robustness of the zero mode.
Fig. 4: Boundary defects in the kagome lattice.

Data availability

All data are available from the corresponding authors on reasonable request. The experimental data can be accessed using open-source tools.


  1. 1.

    Feynman, R. P. There’s plenty of room at the bottom. Eng. Sci. 23, 22–36 (1960).

    Google Scholar 

  2. 2.

    Georgescu, I. M., Ashhab, S. & Nori, F. Quantum simulation. Rev. Mod. Phys. 86, 153–185 (2014).

    Article  Google Scholar 

  3. 3.

    Greiner, M., Mandel, O., Esslinger, T., Hänsch, T. W. & Bloch, I. Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature 415, 39–44 (2002).

    CAS  Article  Google Scholar 

  4. 4.

    Bloch, I., Dalibard, J. & Nascimbene, S. Quantum simulations with ultracold quantum gases. Nat. Phys. 8, 267–276 (2012).

    CAS  Article  Google Scholar 

  5. 5.

    Blatt, R. & Roos, C. F. Quantum simulations with trapped ions. Nat. Phys. 8, 277–284 (2012).

    CAS  Article  Google Scholar 

  6. 6.

    Aspuru-Guzik, A. & Walther, P. Photonic quantum simulators. Nat. Phys. 8, 285–291 (2012).

    CAS  Article  Google Scholar 

  7. 7.

    Gomes, K. K., Mar, W., Ko, W., Guinea, F. & Manoharan, H. C. Designer Dirac fermions and topological phases in molecular graphene. Nature 483, 306–310 (2012).

    CAS  Article  Google Scholar 

  8. 8.

    Crommie, M. F., Lutz, C. P. & Eigler, D. M. Confinement of electrons to quantum corrals on a metal surface. Science 262, 218–220 (1993).

    CAS  Article  Google Scholar 

  9. 9.

    Hirjibehedin, C. F., Lutz, C. P. & Heinrich, A. J. Spin coupling in engineered atomic structures. Science 312, 1021–1024 (2006).

    CAS  Article  Google Scholar 

  10. 10.

    Khajetoorians, A. A., Wiebe, J., Chilian, B. & Wiesendanger, R. Realizing all-spin–based logic operations atom by atom. Science 332, 1062–1064 (2011).

    CAS  Article  Google Scholar 

  11. 11.

    Slot, M. R. et al. Experimental realization and characterization of an electronic Lieb lattice. Nat. Phys. 13, 672–676 (2017).

    CAS  Article  Google Scholar 

  12. 12.

    Drost, R., Ojanen, T., Harju, A. & Liljeroth, P. Topological states in engineered atomic lattices. Nat. Phys. 13, 668–671 (2017).

    CAS  Article  Google Scholar 

  13. 13.

    Slot, M. R. et al. p-band engineering in artificial electronic lattices. Phys. Rev. X 9, 011009 (2019).

    CAS  Google Scholar 

  14. 14.

    Collins, L. C., Witte, T. G., Silverman, R., Green, D. B. & Gomes, K. K. Imaging quasiperiodic electronic states in a synthetic penrose tiling. Nat. Commun. 8, 15961 (2017).

    CAS  Article  Google Scholar 

  15. 15.

    Kempkes, S. N. et al. Design and characterization of electrons in a fractal geometry. Nat. Phys. 15, 127–131 (2019).

    CAS  Article  Google Scholar 

  16. 16.

    Moore, J. E. The birth of topological insulators. Nature 464, 194–198 (2010).

    CAS  Article  Google Scholar 

  17. 17.

    Haldane, F. D. M. Nobel lecture: topological quantum matter. Rev. Mod. Phys. 89, 040502 (2017).

    Article  Google Scholar 

  18. 18.

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

    CAS  Article  Google Scholar 

  19. 19.

    Benalcazar, W. A., Bernevig, B. A. & Hughes, T. L. Quantized electric multipole insulators. Science 357, 61–66 (2017).

    CAS  Article  Google Scholar 

  20. 20.

    Noh, J. et al. Topological protection of photonic mid-gap defect modes. Nat. Photon. 12, 408–415 (2018).

    CAS  Article  Google Scholar 

  21. 21.

    Schindler, F. et al. Higher-order topology in bismuth. Nat. Phys. 14, 918–924 (2018).

    CAS  Article  Google Scholar 

  22. 22.

    Mittal, S. et al. Photonic quadrupole topological phases. Nat. Photon. (2019).

    CAS  Article  Google Scholar 

  23. 23.

    El Hassan, A. et al. Corner states of light in photonic waveguides. Preprint at (2018).

  24. 24.

    Serra-Garcia, M. et al. Observation of a phononic quadrupole topological insulator. Nature 555, 342–345 (2018).

    CAS  Article  Google Scholar 

  25. 25.

    Imhof, S. et al. Topolectrical-circuit realization of topological corner modes. Nat. Phys. 14, 925–929 (2018).

    CAS  Article  Google Scholar 

  26. 26.

    Peterson, C. W., Benalcazar, W. A., Hughes, T. L. & Bahl, G. A quantized microwave quadrupole insulator with topologically protected corner states. Nature 555, 346–350 (2018).

    CAS  Article  Google Scholar 

  27. 27.

    Xue, H., Yang, Y., Gao, F., Chong, Y. & Zhang, B. Acoustic higher-order topological insulator on a kagome lattice. Nat. Mater. 18, 108–112 (2019).

    CAS  Article  Google Scholar 

  28. 28.

    Ni, X., Weiner, M., Alú, A. & Khanikaev, A. B. Observation of higher-order topological acoustic states protected by generalized chiral symmetry. Nat. Mater. 18, 113–120 (2019).

    CAS  Article  Google Scholar 

  29. 29.

    Ezawa, M. Higher-order topological insulators and semimetals on the breathing kagome and pyrochlore lattices. Phys. Rev. Lett. 120, 026801 (2018).

    Article  Google Scholar 

  30. 30.

    Benalcazar, W. A., Li, T. & Hughes, T. L. Quantization of fractional corner charge in C n-symmetric higher-order topological crystalline insulators. Phys. Rev. B 99, 245151 (2019).

    CAS  Article  Google Scholar 

  31. 31.

    Bartels, L., Meyer, G. & Rieder, K.-H. Basic steps of lateral manipulation of single atoms and diatomic clusters with a scanning tunneling microscope tip. Phys. Rev. Lett. 79, 697–700 (1997).

    CAS  Article  Google Scholar 

  32. 32.

    Meyer, G. et al. Controlled manipulation of atoms and small molecules with a low temperature scanning tunneling microscope. Single Mol. 1, 79–86 (2000).

    CAS  Article  Google Scholar 

  33. 33.

    Celotta, R. J. et al. Invited article: autonomous assembly of atomically perfect nanostructures using a scanning tunneling microscope. Rev. Sci. Instrum. 85, 121301 (2014).

    Article  Google Scholar 

Download references


We acknowledge H. Hansson, D. Haldane and M. Franz for fruitful discussions. W.A.B. thanks the Eberly Postdoctoral Fellowship at The Pennsylvania State University for support. The work of D.B. is supported by Spanish Ministerio de Ciencia, Innovation y Universidades (MICINN) under project FIS2017-82804-P and by the Transnational Common Laboratory Quantum–ChemPhys. D.V., I.S. and C.M.S. acknowledge funding from the Nederlandse Organisatie voor Wetenschappelijk Onderzoek via grants 16PR3245 and DDC13, and D.V. acknowledges the European Research Council Advanced Grant FIRSTSTEP 692691.

Author information




S.N.K. and J.J.v.d.B. performed the theoretical calculations under the supervision of C.M.S., W.A.B. and D.B. M.R.S., S.N.K. and I.S. planned the experiment. M.R.S. performed the experiment and data analysis with contributions from P.C. under the supervision of I.S. and D.V. C.M.S., S.N.K. and M.R.S. wrote the manuscript with input from all authors.

Corresponding authors

Correspondence to I. Swart or C. Morais Smith.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

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

Supplementary information

Supplementary Information

Supplementary Figs. 1–15, Notes 1–4 and refs. 1–13.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kempkes, S.N., Slot, M.R., van den Broeke, J.J. et al. Robust zero-energy modes in an electronic higher-order topological insulator. Nat. Mater. 18, 1292–1297 (2019).

Download citation

Further reading


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing