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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.

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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.

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


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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.

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Authors and Affiliations



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.

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Correspondence to I. Swart or C. Morais Smith.

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

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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).

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