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Topological states engineered in narrow strips of graphene

In materials known as graphene nanoribbons, topological states can be precisely engineered and probed, providing an experimental platform for studying electronic topology.
Katharina J. Franke is in the Department of Physics, Freie Universität Berlin, 14195 Berlin, Germany.
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Felix von Oppen is in the Department of Physics, Freie Universität Berlin, 14195 Berlin, Germany.
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For more than a decade, two-dimensional sheets of carbon atoms known as graphene have captured researchers’ imaginations. Last year, it was predicted that electronic states in narrow strips of graphene — dubbed graphene nanoribbons — could have different topologies depending on the width of the strip1. In two papers in Nature, Rizzo et al.2 and Gröning et al.3 report experiments that confirm this prediction. Their results show that graphene nanoribbons provide a flexible and highly precise platform for designing and fabricating materials that have what is known as a non-trivial topology. The authors suggest that such materials could be used to realize desired exotic topological states for quantum technologies.

We learn in school that materials can differ starkly in their electrical properties. The difference between conductors and insulators is rooted in the states that are available to the electrons in these materials. In conductors, such as metals, electrons can move freely because available states exist at arbitrarily low energies. By contrast, the electrons in insulators are effectively localized, and do not conduct electricity unless they are provided with sufficient energy to overcome an energy gap.

This understanding of conductors and insulators was an early triumph for the application of quantum theory to materials. However, over the past decade or so, researchers have learnt that this picture needs to be amended in fundamental ways. This realization has led to the discovery of materials known as topological insulators, which are insulating in their interior but robustly conducting on their boundaries4. Correspondingly, these materials have an energy gap in their interior, but are gapless on their boundaries. This behaviour reflects beautiful, albeit somewhat abstract, topological properties of the materials’ electronic states.

Rizzo et al. and Gröning et al. have experimentally demonstrated that graphene nanoribbons can be used to produce such topological states. Defect-free graphene nanoribbons can be grown on metallic substrates in a remarkably flexible manner5. Starting with cleverly designed precursor molecules, the nanoribbons’ terminations and widths can be controlled with single-atom precision. The authors used this synthesis technique to grow nanoribbons that alternate in width (Fig. 1a).

Figure 1 | A graphene nanoribbon. a, Rizzo et al.2 and Gröning et al.3 synthesized strips of graphene (a two-dimensional form of carbon) known as graphene nanoribbons (black). The nanoribbons alternated in width such that the topologies of electronic states in the narrow sections (white) and wide sections (blue) were trivial and non-trivial, respectively. The authors report localized topological electronic states at the junctions (blue lines) between narrow and wide sections, and at the ends (red lines) of the nanoribbons. b, This micrograph shows one end of a nanoribbon studied by Rizzo and colleagues. Scale bar, 1 nanometre.Image: D. J. Rizzo et al./Nature

The widths were chosen such that the nanoribbons consist of alternating topologically trivial and non-trivial segments. Whenever two materials of different topology are brought into contact, gapless states must form at the interface. Consequently, such states are produced at the junctions between the nanoribbon segments. Because nanoribbons are essentially one-dimensional, each of these gapless junction states is simply an individual electron orbital localized in the vicinity of the intersection.

But the topology of the nanoribbons does not stop here. Rizzo et al. and Gröning et al. used the junction states as building blocks to engineer yet another system. This system is closely related to an archetypal model of electronic topology known as the Su–Schrieffer–Heeger (SSH) model, which emerged in the late 1970s from the study of organic conductors such as polyacetylene6.

Although the SSH model is simple, it has remarkable properties. In particular, a finite chain of electronic orbitals described by the SSH model can have gapless topological states localized at its ends. The crucial ingredient in the model is an alternation of weak and strong bonds between neighbouring electron orbitals.

In the authors’ nanoribbons, adjacent gapless junction states straddle narrow or wide regions of the material. The coupling of these states is stronger across the wide regions than across the narrow regions, producing exactly the bond alternation that underlies the SSH model. Such a coupling is therefore expected to generate topological states at the ends of the nanoribbons, assuming that these materials are suitably designed1.

Rizzo et al. and Gröning et al. confirmed this theoretical prediction to an impressive degree. The authors used a combination of scanning tunnelling microscopy and spectroscopy to probe and visualize the electronic properties of the nanoribbons with atomic-scale spatial resolution (Fig. 1b). They observed the junction states — which formed broadened energy bands as a result of their coupling — and the end states associated with the bond alternation. Of note is the fact that the authors grew and probed their nanoribbons on a highly conducting gold substrate, which effectively weakens the electric forces between the electrons in the nanoribbons. Without such a conducting substrate, these forces could be substantial, and might produce additional interesting physics1.

Beyond fabricating these specific nanoribbons and exploring their electronic topologies, the two studies reveal several key insights. For instance, the production of topological electronic materials is often hampered by sample imperfections. Frequently, defects induce a large internal conductivity, even if the material is nominally a topological insulator. This problem is particularly severe in 1D systems, in which the electrons cannot circumvent defects. Such systems are often fabricated using a top-down approach, in which the materials are patterned from larger structures. A promising avenue for alleviating the issue of sample imperfections is to produce the systems by means of a bottom-up method, such as that used by the authors, in which the materials are made by chemical processes.

These studies also highlight the potential of using topological boundary states for materials engineering. This idea can be extended to higher dimensions than the authors’ 1D system, for instance to periodic ‘superlattices’ made of alternating topologically trivial and non-trivial layers. Finally, the authors suggest that, when in contact with a superconductor, the nanoribbons could act as a topological superconductor — another fascinating class of topological electronic state that might have applications in quantum computing.

Nature 560, 175-176 (2018)

doi: 10.1038/d41586-018-05851-1
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References

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    Cao, T., Zhao, F. & Louie, S. G. Phys. Rev. Lett. 119, 076401 (2017).

  2. 2.

    Rizzo, D. J. et al. Nature 560, 204–208 (2018).

  3. 3.

    Gröning, O. et al. Nature 560, 209–213 (2018).

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

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    Cai, J. et al. Nature 466, 470–473 (2010).

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    Su, W. P., Schrieffer, J. R. & Heeger, A. J. Phys. Rev. Lett. 42, 1698–1701 (1979).

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