# Topological band engineering of graphene nanoribbons

## Abstract

Topological insulators are an emerging class of materials that host highly robust in-gap surface or interface states while maintaining an insulating bulk1,2. Most advances in this field have focused on topological insulators and related topological crystalline insulators3 in two dimensions4,5,6 and three dimensions7,8,9,10, but more recent theoretical work has predicted the existence of one-dimensional symmetry-protected topological phases in graphene nanoribbons (GNRs)11. The topological phase of these laterally confined, semiconducting strips of graphene is determined by their width, edge shape and terminating crystallographic unit cell and is characterized by a $${{\mathbb{Z}}}_{2}$$ invariant12 (that is, an index of either 0 or 1, indicating two topological classes—similar to quasi-one-dimensional solitonic systems13,14,15,16). Interfaces between topologically distinct GNRs characterized by different values of $${{\mathbb{Z}}}_{2}$$ are predicted to support half-filled, in-gap localized electronic states that could, in principle, be used as a tool for material engineering11. Here we present the rational design and experimental realization of a topologically engineered GNR superlattice that hosts a one-dimensional array of such states, thus generating otherwise inaccessible electronic structures. This strategy also enables new end states to be engineered directly into the termini of the one-dimensional GNR superlattice. Atomically precise topological GNR superlattices were synthesized from molecular precursors on a gold surface, Au(111), under ultrahigh-vacuum conditions and characterized by low-temperature scanning tunnelling microscopy and spectroscopy. Our experimental results and first-principles calculations reveal that the frontier band structure (the bands bracketing filled and empty states) of these GNR superlattices is defined purely by the coupling between adjacent topological interface states. This manifestation of non-trivial one-dimensional topological phases presents a route to band engineering in one-dimensional materials based on precise control of their electronic topology, and is a promising platform for studies of one-dimensional quantum spin physics.

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## Acknowledgements

Research supported by the Office of Naval Research MURI Program N00014-16-1-2921 (precursor design, STM spectroscopy, band structure), by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under award number DE-SC0010409 (precursor synthesis and characterization) and the Nanomachine Program award number DE-AC02-05CH11231 (surface growth, heterojunction analysis), by the Center for Energy Efficient Electronics Science NSF Award 0939514 (end state modelling), and by the National Science Foundation under grant DMR-1508412 (development of theory formalism). Computational resources have been provided by the DOE at Lawrence Berkeley National Laboratory's NERSC facility and by the NSF through XSEDE resources at NICS. We acknowledge useful discussions with O. Gröning from EMPA Federal Laboratories for Materials Testing and Research.

### Reviewer information

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

## Author information

Authors

### Contributions

D.J.R., G.V., T. Cao, S.G.L., M.F.C. and F.R.F. initiated and conceived the research, G.V. and F.R.F. designed, synthesized and characterized the molecular precursors, D.J.R., C.B., H.R., T. Chen and M.F.C. performed on-surface synthesis and STM characterization and analysis, T.Cao., F.Z. and S.G.L. performed the DFT calculations and the theoretical analysis that predicted and interpreted the STM data. D.J.R., T. Cao, G.V., S.G.L., M.F.C. and F.R.F. wrote the manuscript. All authors contributed to the scientific discussion.

### Corresponding authors

Correspondence to Steven G. Louie or Michael F. Crommie or Felix R. Fischer.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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## Extended data figures and tables

### Extended Data Fig. 1 Sterically enforced site-selective polymerization.

a, Molecular precursor 1. b, Sterically distinct reaction sites during radical chain growth polymerization of poly-1 (anthracene versus biphenyl). c, The corresponding edge structures in the fully formed GNR (armchair and zigzag termination, respectively).

### Extended Data Fig. 2 Electronic structure of two different 7/9-AGNR superlattices.

a, c, The unit cell of structure a (a) and the DFT-calculated band structure for the 7/9-AGNR superlattice composed of topologically nontrivial interfaces (c) show two new topologically induced bands. b, d, The unit cell of structure b (b) and the DFT-calculated band structure of the 7/9-AGNR superlattice composed of topologically trivial interfaces (d) show no topologically induced bands in the energy gap region.

### Extended Data Fig. 3 Electronic structure of finite nontrivial 7/9-AGNR superlattice.

a, Fully relaxed finite (8-supercell) 7/9-AGNR superlattice with end (green) and bulk (red) unit cells indicated. b, DFT-calculated projected DOS of the finite (8-supercell) 7/9-AGNR superlattice obtained from the end unit cell (green) and a bulk unit cell (red) (Gaussian broadening of 0.05 eV was used here). Three end states are seen that closely correspond to the experimental end states shown in Fig. 3b. c, DFT-calculated band structure of 7/9-AGNR showing the overall value of $${{\mathbb{Z}}}_{2}$$ for occupation up to all three energy gaps around EF based on the edge structure shown in Fig. 3a. d, Chart of frontier band parity eigenvalues and corresponding $${{\mathbb{Z}}}_{2}$$ invariants for electron filling up to and including a given frontier band. This superlattice end-state behaviour is different from the behaviour of a ‘straight-edge’ topologically nontrivial AGNR owing to the presence of multiple energy gaps that can accommodate topologically protected end states rather than only a single gap.

### Extended Data Fig. 4 Topologically nontrivial 7/9-AGNR with different end structure.

a, The red (green) curve shows dI/dV point spectroscopy data collected on the 7/9-AGNR superlattice bulk (end) region. The dashed black curve shows the spectrum collected on bare Au(111). Only one end state is observed that lies in the energy gap between the OTB and UTB. The spectroscopy parameters are Vac = 20 mV and f = 581 Hz. b, The DFT-calculated band structure of 7/9-AGNR shows an overall topologically nontrivial phase for the edge structure shown in c only for bands filled up to and including the OTB. c, Sketch of GNR structure and STM topographic image of additional 7/9-AGNR end terminus that is seen for <10% of all 7/9 AGNR superlattices in the experiment. Experimental topography and dI/dV maps are shown for the OTB, the end state and the UTB (topography Vs = –0.10 V, It = 50 pA; dI/dV maps It = 50 pA, f = 581 Hz, Vac = 20 mV). d, Unit cell commensurate with uncommon end terminus shown in c, along with chart of frontier band parity eigenvalues and corresponding $${{\mathbb{Z}}}_{2}$$ invariants for electron filling up to and including a given frontier band. For this edge structure only the OTB/UTB gap is topologically nontrivial and supports a topologically protected end state. The UTB/CB and VB/OTB gaps are topologically trivial and do not support end states, unlike the behaviour seen for the other, more common, termination shown in Fig. 3a.

### Extended Data Fig. 5 Comparison of bond-resolved STM measurements conducted with CO-functionalized and spontaneously functionalized STM tips.

a, Bond-resolved STM image of 7/9-AGNR, obtained with a tip that was spontaneously functionalized via an unknown molecule from the surface (Vs = 0.02 V, It = 80 pA, f = 581 Hz, Vac = 12 mV). b, Bond-resolved STM image of 7/9-AGNR, obtained with a tip deliberately functionalized with CO (Vs = 0.02 V, It = 180 pA, f = 581 Hz, Vac = 12 mV).

## Supplementary information

### Supplementary Information

This file contains supplementary materials and general methods, and supplementary figures S1-S13.

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Rizzo, D.J., Veber, G., Cao, T. et al. Topological band engineering of graphene nanoribbons. Nature 560, 204–208 (2018). https://doi.org/10.1038/s41586-018-0376-8

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