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Magic-angle lasers in nanostructured moiré superlattice

Nature Nanotechnology volume 16, pages 1099–1105 (2021)Cite this article

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Abstract

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°.

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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.

References

  1. Geim, A. & Grigorieva, I. Van der Waals heterostructures. Nature 499, 419–425 (2013).

    Article  CAS  Google Scholar 

  2. Liu, Y. et al. Van der Waals heterostructures and devices. Nat. Rev. Mater. 1, 16042 (2016).

    Article  CAS  Google Scholar 

  3. Novoselov, K. S., Mishchenko, A., Carvalho, A. & Castro Neto, A. H. 2D materials and van der Waals heterostructures. Science 461, aac9439 (2016).

    Article  Google Scholar 

  4. Lopes dos Santos, J. L., Peres, N. M. R. & Castro Neto, A. C. Graphene bilayer with a twist: electronic structure. Phys. Rev. Lett. 99, 256802 (2007).

    Article  CAS  Google Scholar 

  5. Suárez Morell, E., Correa, J. D., Vargas, P., Pacheco, M. & Barticevic, Z. Flat bands in slightly twisted bilayer graphene: tight-binding calculations. Phys. Rev. B 82, 121407(R) (2010).

    Article  Google Scholar 

  6. Li, G. et al. Observation of Van Hove singularities in twisted graphene layers. Nat. Phys. 6, 109–113 (2010).

    Article  Google Scholar 

  7. Bistritzer, R. & MacDonald, A. H. Moiré bands in twisted double-layer graphene. Proc. Natl Acad. Sci. USA 108, 12233–12237 (2011).

    Article  CAS  Google Scholar 

  8. Carr, S. et al. Twistronics: manipulating the electronic properties of two-dimensional layered structures through their twist angle. Phys. Rev. B 95, 075420 (2017).

    Article  Google Scholar 

  9. Kim, K. et al. Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene. Proc. Natl Acad. Sci. USA 114, 3364–3369 (2017).

    Article  CAS  Google Scholar 

  10. Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).

    Article  CAS  Google Scholar 

  11. Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).

    Article  CAS  Google Scholar 

  12. Ribeiro-Palau, R. et al. Twistable electronics with dynamically rotatable heterostructures. Science 361, 690–693 (2018).

    Article  CAS  Google Scholar 

  13. Alexeev, E. M. et al. Resonantly hybridized excitons in moiré superlattices in van der Waals heterostructures. Nature 567, 81–86 (2019).

    Article  CAS  Google Scholar 

  14. Tran, K. et al. Evidence for moiré excitons in van der Waals heterostructures. Nature 567, 71–75 (2019).

    Article  CAS  Google Scholar 

  15. Jin, C. et al. Observation of moiré excitons in WSe2/WS2 heterostructure superlattices. Nature 567, 76–80 (2019).

    Article  CAS  Google Scholar 

  16. Seyler, K. L. et al. Signatures of moiré-trapped valley excitons in MoSe2/WSe2 heterobilayers. Nature 567, 66–70 (2019).

    Article  CAS  Google Scholar 

  17. Ciarrocchi, A. et al. Polarization switching and electrical control of interlayer excitons in two-dimensional van der Waals heterostructures. Nat. Photon. 13, 131–136 (2019).

    Article  CAS  Google Scholar 

  18. Shimazaki, Y. et al. Strongly correlated electrons and hybrid excitons in a moiré heterostructure. Nature 580, 472–477 (2020).

    Article  CAS  Google Scholar 

  19. Brotons-Gisbert, M. A. et al. Spin–layer locking of interlayer excitons trapped in moiré potentials. Nat. Mater. 19, 630–636 (2020).

    Article  CAS  Google Scholar 

  20. Li, W. et al. Dipolar interactions between localized interlayer excitons in van der Waals heterostructures. Nat. Mater. 19, 624–629 (2020).

    Article  CAS  Google Scholar 

  21. Regan, E. C. et al. Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices. Nature 579, 359–363 (2020).

    Article  CAS  Google Scholar 

  22. Kennes, D. M. et al. Moiré heterostructures as a condensed-matter quantum simulator. Nat. Phys. 17, 155–163 (2021).

    Article  CAS  Google Scholar 

  23. MacDonald, A. H. Trend: bilayer graphene’s wicked, twisted road. Physics 12, 12 (2019).

    Article  Google Scholar 

  24. Yankowitz, M. et al. Tuning superconductivity in twisted bilayer graphene. Science 363, 1059–1064 (2019).

    Article  CAS  Google Scholar 

  25. Lu, X. et al. Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene. Nature 574, 653–657 (2019).

    Article  CAS  Google Scholar 

  26. Jiang, Y. et al. Charge order and broken rotational symmetry in magic-angle twisted bilayer graphene. Nature 573, 91–95 (2019).

    Article  CAS  Google Scholar 

  27. Kerelsky, A. et al. Maximized electron interactions at the magic angle in twisted bilayer graphene. Nature 572, 95–100 (2019).

    Article  CAS  Google Scholar 

  28. Xie, Y. et al. Spectroscopic signatures of many-body correlations in magic-angle twisted bilayer graphene. Nature 572, 101–105 (2019).

    Article  CAS  Google Scholar 

  29. Choi, Y. et al. Electronic correlations in twisted bilayer graphene near the magic angle. Nat. Phys. 15, 1174–1180 (2019).

    Article  CAS  Google Scholar 

  30. Stepanov, P. et al. Untying the insulating and superconducting orders in magic-angle graphene. Nature 583, 375–378 (2020).

    Article  CAS  Google Scholar 

  31. Sunku, S. S. et al. Photonic crystals for nano-light in moiré graphene superlattices. Science 362, 1153–1156 (2018).

    Article  CAS  Google Scholar 

  32. Wang, P. et al. Localization and delocalization of light in photonic moiré lattices. Nature 577, 42–46 (2020).

    Article  CAS  Google Scholar 

  33. Lassaline, N. et al. Optical Fourier surfaces. Nature 582, 506–510 (2020).

    Article  CAS  Google Scholar 

  34. Fu, Q. et al. Optical soliton formation controlled by angle twisting in photonic moiré lattices. Nat. Photon. 14, 663–668 (2020).

    Article  CAS  Google Scholar 

  35. Wang, W. et al. Moiré fringe induced gauge field in photonics. Phys. Rev. Lett. 125, 203901 (2020).

    Article  CAS  Google Scholar 

  36. Hu, G. et al. Moiré hyperbolic metasurfaces. Nano Lett. 20, 3217–3224 (2020).

    Article  CAS  Google Scholar 

  37. Hu, G. et al. Topological polaritons and photonic magic angles in twisted α-MoO3 bilayers. Nature 582, 209–213 (2020).

    Article  CAS  Google Scholar 

  38. Chen, M. et al. Configurable phonon polaritons in twisted α-MoO3. Nat. Mater. 19, 1307–1311 (2020).

    Article  CAS  Google Scholar 

  39. Duan, J. et al. Twisted nano-optics: manipulating light at the nanoscale with twisted phonon polaritonic slabs. Nano Lett. 20, 5323–5329 (2020).

    Article  CAS  Google Scholar 

  40. Zheng, Z. et al. Phonon polaritons in twisted double-layers of hyperbolic van der Waals crystals. Nano Lett. 20, 5301–5308 (2020).

    Article  CAS  Google Scholar 

  41. Vahala, K. J. Optical microcavities. Nature 424, 839–846 (2003).

    Article  CAS  Google Scholar 

  42. Ma, R. M. & Oulton, R. F. Applications of nanolasers. Nat. Nanotechnol. 14, 12–22 (2019).

    Article  CAS  Google Scholar 

  43. Carr, S., Fang, S., Jarillo-Herrero, P. & Kaxiras, E. Pressure dependence of the magic twist angle in graphene superlattices. Phys. Rev. B 98, 085144 (2018).

    Article  CAS  Google Scholar 

  44. Yankowitz, M. et al. Dynamic band-structure tuning of graphene moiré superlattices with pressure. Nature 557, 404–408 (2018).

    Article  CAS  Google Scholar 

  45. Björk, G., Karlsson, A. & Yamamoto, Y. Definition of a laser threshold. Phys. Rev. A 50, 1675–1680 (1994).

    Article  Google Scholar 

  46. Ma, R. M. Lasing under ultralow pumping. Nat. Mater. 18, 1152–1153 (2019).

    Article  CAS  Google Scholar 

  47. Painter, O. et al. Two-dimensional photonic band-gap defect mode laser. Science 284, 1819–1821 (1999).

    Article  CAS  Google Scholar 

  48. Asano, T. & Noda, S. Photonic crystal devices in silicon photonics. Proc. IEEE 106, 2183–2195 (2018).

    Article  CAS  Google Scholar 

  49. Tsakmakidis, K. L., Hess, O., Boyd, R. W. & Zhang, X. Ultraslow waves on the nanoscale. Science 358, eaan5196 (2017).

    Article  Google Scholar 

  50. DeGiorgio, V. & Scully, M. O. Analogy between the laser threshold region and a second-order phase transition. Phys. Rev. A 2, 1170–1177 (1970).

    Article  Google Scholar 

  51. Haken, H. in Synergetics (eds. Pacault, A. & Vidal, C.) 22–33 (Springer, 1979).

  52. Tsakmakidis, K. L., Jha, P. K., Wang, Y. & Zhang, X. Quantum coherence-driven self-organized criticality and nonequilibrium light localization. Sci. Adv. 4, eaaq0465 (2018).

    Article  Google Scholar 

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Acknowledgements

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).

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Author notes

  1. These authors contributed equally: Xin-Rui Mao, Zeng-Kai Shao, Hong-Yi Luan, Shao-Lei Wang.

Authors and Affiliations

  1. State Key Lab for Mesoscopic Physics and School of Physics, Peking University, Beijing, China

    Xin-Rui Mao, Zeng-Kai Shao, Hong-Yi Luan, Shao-Lei Wang & Ren-Min Ma

  2. Frontiers Science Center for Nano-optoelectronics and Collaborative Innovation Center of Quantum Matter, Peking University, Beijing, China

    Xin-Rui Mao, Zeng-Kai Shao, Hong-Yi Luan, Shao-Lei Wang & Ren-Min Ma

  3. Peking University Yangtze Delta Institute of Optoelectronics, Nantong, China

    Ren-Min Ma

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Contributions

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.

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Correspondence to Ren-Min Ma.

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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 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). https://doi.org/10.1038/s41565-021-00956-7

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