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Topological mosaics in moiré superlattices of van der Waals heterobilayers

Nature Physics volume 13, pages 356–362 (2017)Cite this article

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Abstract

Van der Waals (vdW) heterostructures formed by two-dimensional atomic crystals provide a powerful approach towards designer condensed matter systems1,2,3,4,5,6,7,8,9,10,11,12,13,14,15. Incommensurate heterobilayers with small twisting and/or lattice mismatch lead to the interesting concept of moiré superlattices2,3,4,5,6,7, where the atomic registry is locally indistinguishable from commensurate bilayers but has local-to-local variation over long range. Here we show that such moiré superlattices can lead to periodic modulation of local topological order in vdW heterobilayers formed by two massive Dirac materials. By tuning the vdW heterojunction from normal to the inverted type-II regime via an interlayer bias, the commensurate heterobilayer can become a topological insulator (TI), depending on the interlayer hybridization controlled by the atomic registry between the vdW layers. This results in a mosaic pattern of TI regions and normal insulator (NI) regions in moiré superlattices, where topologically protected helical modes exist at the TI/NI phase boundaries. By using symmetry-based k ⋅p and tight-binding models, we predict that this topological phenomenon can be present in inverted transition metal dichalcogenides heterobilayers. Our work points to a new means of realizing programmable and electrically switchable topological superstructures from two-dimensional arrays of TI nano-dots to one-dimensional arrays of TI nano-stripes.

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Figure 1: Electrically controlled band inversion in heterobilayer of massive Dirac materials.
Figure 2: Topological phase diagrams for commensurate TMD bilayers.
Figure 3: Bulk-edge correspondence in the topological phase diagram.
Figure 4: Topological mosaic in long-period moiré pattern.
Figure 5: Topologically protected helical modes at the boundaries of TI nano-stripes in 1D moiré superlattices.

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Acknowledgements

The work is mainly supported by the Croucher Foundation (Croucher Innovation Award), the Research Grants Council and University Grants Committee of Hong Kong (HKU17312916, AoE/P-04/08), and the University of Hong Kong (ORA). Y.W. is partly supported by the NSFC with Grant No. 11604162 and Grant No. 61674083. X.X. is supported by the Department of Energy, Basic Energy Sciences, Materials Sciences and Engineering Division (DE-SC0008145 and SC0012509), and the Cottrell Scholar Award.

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Authors and Affiliations

  1. Department of Physics and Center of Theoretical and Computational Physics, University of Hong Kong, Hong Kong, China

    Qingjun Tong, Hongyi Yu, Qizhong Zhu, Yong Wang & Wang Yao

  2. School of Physics, Nankai University, Tianjin 300071, China

    Yong Wang

  3. Department of Physics, University of Washington, Seattle, Washington 98195, USA

    Xiaodong Xu

  4. Department of Materials Science and Engineering, University of Washington, Seattle, Washington 98195, USA

    Xiaodong Xu

Authors
  1. Qingjun Tong
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  3. Qizhong Zhu
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Contributions

W.Y. conceived and designed the research. Q.T. and H.Y. performed the calculations. Q.T., H.Y. and W.Y. analysed the results with input from Q.Z. and X.X. Y.W. provided support with first-principles calculations. W.Y., Q.T., H.Y. and X.X. prepared the manuscript.

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Correspondence to Wang Yao.

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Tong, Q., Yu, H., Zhu, Q. et al. Topological mosaics in moiré superlattices of van der Waals heterobilayers. Nature Phys 13, 356–362 (2017). https://doi.org/10.1038/nphys3968

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