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Electronic-structure methods for twisted moiré layers

Nature Reviews Materials volume 5, pages 748–763 (2020)Cite this article

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Abstract

When single layers of 2D materials are stacked on top of one another with a small twist in orientation, the resulting structure often involves incommensurate moiré patterns. In these patterns, the loss of angstrom-scale periodicity poses a significant theoretical challenge, and the new moiré length scale leads to emergent physical phenomena. The range of physics arising from twisted bilayers has led to significant advances that are shaping into a new field, twistronics. At the moiré scale, the large number of atoms in these systems can make their accurate simulation daunting, necessitating the development of efficient multiscale methods. In this Review, we summarize and compare such modelling methods — focusing in particular on density functional theory, tight-binding Hamiltonians and continuum models — and provide examples spanning a broad range of materials and geometries.

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Fig. 1: An introduction to twistronics.
Fig. 2: Examples of 2D materials.
Fig. 3: Local stacking order in twisted bilayers.
Fig. 4: Examples of atomic relaxations in moiré materials.
Fig. 5: Comparison of electronic band structures for 1.08° twisted bilayer graphene generated by different methods.
Fig. 6: Twist-induced electronic properties in 2D moiré heterostructures.

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Acknowledgements

The authors thank Z. Zhu, D. Larson and E. Kucukbenli for helpful discussions and reference recommendations. This work was supported in part by ARO MURI award no. W911NF-14-0247 and by the STC Center for Integrated Quantum Materials, NSF grant no. DMR-1231319. The tight-binding calculation shown in Fig. 5 was run on the Odyssey cluster supported by the FAS Division of Science, Research Computing Group at Harvard University.

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Carr, S., Fang, S. & Kaxiras, E. Electronic-structure methods for twisted moiré layers. Nat Rev Mater 5, 748–763 (2020). https://doi.org/10.1038/s41578-020-0214-0

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