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Magic-angle lasers in nanostructured moiré superlattice


Conventional laser cavities require discontinuity of material property or disorder to localize a light field for feedback. Recently, an emerging class of materials, twisted van der Waals materials, have been explored for applications in electronics and photonics. Here we propose and develop magic-angle lasers, where the localization is realized in periodic twisted photonic graphene superlattices. We reveal that the confinement mechanism of magic-angle lasers does not rely on a full bandgap but on the mode coupling between two twisted layers of photonic graphene lattice. Without any fine-tuning in structure parameters, a simple twist can result in nanocavities with strong field confinement and a high quality factor. Furthermore, the emissions of magic-angle lasers allow direct imaging of the wavefunctions of magic-angle states. Our work provides a robust platform to construct high-quality nanocavities for nanolasers, nano light-emitting diodes, nonlinear optics and cavity quantum electrodynamics at the nanoscale.

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Fig. 1: Design and operation principle of a magic-angle laser.
Fig. 2: Band diagram and mode localization without a photonic bandgap.
Fig. 3: Lasing and wavefunctions of flatband and delocalized modes in the magic-angle laser.
Fig. 4: Field confinement mechanism without a bandgap.
Fig. 5: Localization features of the magic-angle laser.
Fig. 6: Magic-angle lasers at twisted angles of 4.41°, 6.01° and 9.43°.

Data availability

The authors declare that the main data supporting the findings of this study are available within the article and its Supplementary Information. Extra data are available from the corresponding author upon reasonable request.


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This work is supported by the Beijing Natural Science Foundation (grant no. Z180011), the National Natural Science Foundation of China (grant nos. 91950115, 11774014 and 61521004) and the National Key R&D Program of China (grant no. 2018YFA0704401).

Author information




R.-M.M. conceived and supervised the project. X.-R.M., Z.-K.S. and R.-M.M. performed the optical characterization. Z.-K.S. fabricated the devices. H.-Y.L. and S.-L.W. carried out the numerical simulations. R.-M.M., X.-R.M. and H.-Y.L. did the data analysis. R.-M.M. wrote the manuscript with input from all authors.

Corresponding author

Correspondence to Ren-Min Ma.

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The authors declare no competing interests.

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Peer review information Nature Nanotechnology thanks the anonymous reviewers for their contribution to the peer review of this work.

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Supplementary Information

Supplementary Sections 1–15 and Figs. 1–24.

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Mao, XR., Shao, ZK., Luan, HY. et al. Magic-angle lasers in nanostructured moiré superlattice. Nat. Nanotechnol. 16, 1099–1105 (2021).

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