Abstract
The study of van der Waals heterostructures with an interlayer twist, known as twistronics, has been instrumental in advancing the understanding of many strongly correlated phases, many of which derive from the topology of the physical system. Here we explore the application of the twistronics paradigm in plasmonic systems with a non-trivial topology by creating a moiré skyrmion superlattice using two superimposed plasmonic skyrmion lattices with a relative twist. We measure the complex electric field distribution of the moiré skyrmion superlattice using time-resolved polarimetric photoemission electron microscopy. Our results show that each supercell has very large topological invariants and harbours a skyrmion bag, the size of which is controllable by the twist angle and centre of rotation. Our work indicates how twistronics can enable the creation of various topological features in optical fields and provides a route for locally manipulating electromagnetic field distributions.
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Data availability
The data supporting the findings of this study are available from the corresponding author upon reasonable request. Reconstructed electric field distributions of the PEEM measurements and PEEM simulations are available via Figshare at https://doi.org/10.6084/m9.figshare.28541801 (ref. 56). Source data are provided with this paper.
Code availability
The code used to produce the results are available from the corresponding author upon reasonable request.
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Acknowledgements
We acknowledge support from the ERC (Complexplas, 3DPrintedoptics) (J.S., F.M., A.M., B.F. and H.G.), DFG (grant no. SPP1391 Ultrafast Nanooptics (J.S., F.M., A.M., B.F., H.G., A.N., P.D. and F.-J.M.z.H.), CRC 1242 Non-Equilibrium Dynamics of Condensed Matter in the Time Domain (project no. 278162697-SFB 1242 to A.N., P.D. and F.-J.M.z.H.), BMBF (Printoptics) (J.S., F.M., A.M., B.F. and H.G.), BW Stiftung (Spitzenforschung, Opterial) (J.S., F.M., A.M., B.F. and H.G.) and Carl-Zeiss Stiftung (J.S., F.M., A.M., B.F. and H.G.). T.J.D. acknowledges support from the MPI Guest Professorship Program and from the DFG (grant no. GRK2642) through a Photonic Quantum Engineers for a Mercator Fellowship. S.T. acknowledges support from the Adams fellowship programme of the Israel Academy of Science and Humanities, the Rothschild fellowship of the Yad Hanadiv Foundation, the VATAT-Quantum fellowship of the Israel Council for Higher Education, the Helen Diller Quantum Center postdoctoral fellowship and the Viterbi fellowship of the Technion – Israel Institute of Technology.
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Contributions
G.B and S.T. conceived the idea of twisted skyrmion lattices and skyrmion bags. J.S., F.M. and H.G. conceived the idea of the commensurate angles. J.S. and T.J.D. carried out the simulations, analytical calculations and skyrmion number analysis. A.N., P.D. and F.-J.M.z.H. carried out the PEEM experiment and vectorial retrieval. B.F., A.M. and H.G. grew the single-crystal gold flakes and carried out the ion-beam structuring. K.C., S.T. and G.B carried out the scanning near-field optical microscopy experiment. J.S., T.J.D., S.T., B.F. and H.G. wrote the paper. All authors contributed to the discussions and the final editing.
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Extended data
Extended Data Fig. 1 Temporal analysis of PEEM measurement results.
The experimental skyrmion number of the skyrmion bag and the cluster within in the bag are displayed as a function of the time delay between the pump and probe pulse in the PEEM experiment. The data is plotted together with the results obtained from the PEEM simulation (solid lines).
Extended Data Fig. 2 Analysis of PEEM simulation results of a skyrmion bag comprising (a-c) N=1 skyrmion (skyrmionium) and (d-f) N=19 skyrmions.
a, d, Electric field distribution exemplary for structures with twist angle φ\(=\)30° (\(N=1\)) and φ\(=\)9.4° (\(N=19\)). The out-of-plane component is illustrated using the color plot and the in-plane component of the electric field is depicted using the vector plot. b, e, Distributions of the out-of-plane amplitude (brightness) and in-plane orientation (color) of the normalized electric field. Colorful areas indicate closed-loop lines, along which the electric field vectors only have an in-plane component. The in-plane orientation of the field vectors rotates by \(2\pi\) along these lines of all skyrmions. c, f, Skyrmion number density of the electric field. Integration of the skyrmion number density yields the total skyrmion number. For the total bag the integrated area is given by the enclosed space inside the dashed green line. The skyrmion cluster only counts the skyrmions inside the bag which means that in this case the skyrmion number density is integrated within the area surrounded by the dashed red line.
Extended Data Fig. 3 Skyrmion number of the skyrmion bag and the skyrmion cluster inside the bag as a function of the twist angle for the skyrmion bags with 19 (a), 7 (b) and 1 (c) skyrmions in the bag.
The skyrmion numbers are calculated by integrating the skyrmion number density. For the total bag, the integrated area is given by the enclosed space inside the green dashed line of Fig. 4c, f. The skyrmion cluster only counts the skyrmions inside the bag which means that the skyrmion number density is integrated within the area surrounded by the orange line of Fig. 4c, f. For the three different skyrmion bags, both skyrmion numbers remain constant over a wide range of twist angles.
Extended Data Fig. 4 Analysis of (a-c) PEEM simulation, (d-f) PEEM measurement results of a skyrmion bag with 7 skyrmions at twist angle of 13.2°.
a, d, Electric field distribution. The out-of-plane component is illustrated using the color plot and the in-plane component of the electric field is depicted using the vector plot. b, e, Distributions of the out-of-plane amplitude (brightness) and in-plane orientation (color) of the normalized electric field. Colorful areas indicate closed-loop lines, along which the electric field vectors only have an in-plane component. The in-plane orientation of the field vectors rotates by \(2\pi\) along these lines of all skyrmions. c, f, Skyrmion number density of the electric field. Integration of the skyrmion number density yields the total skyrmion number. For the total bag the integrated area is given by the enclosed space inside the green dashed line. The skyrmion cluster only counts the skyrmions inside the bag which means that the skyrmion number density is integrated within the area surrounded by the dashed red line.
Extended Data Fig. 5 Further analysis of PEEM measurement results of skyrmion bags with 7 skyrmions in a commensurate superlattice at 13.2° twist angle.
a, Electric field distribution. The out-of-plane component is illustrated using the color plot. b, Skyrmion number density of the electric field. Integration of the skyrmion number density yields the total skyrmion number. For the total bags the integrated area is given by the enclosed space inside the green dashed lines. The skyrmion cluster only counts the skyrmions inside the bag, which means that the skyrmion number density is integrated within the area surrounded by the dashed red lines. In this measurement, three out of seven skyrmion bags of the observed superlattice have the correct skyrmion numbers of \({S}_{\mathrm{bag}}=6\) and \({S}_{\mathrm{cluster}}=7\). The center super-cell is surrounded by black dashed lines.
Supplementary information
Supplementary Information
Supplementary Notes 1–10, Figs. 1–12 and Table 1.
Supplementary Video 1
Electric field vector from the PEEM simulation of the 16.4° structure.
Supplementary Video 2
Skyrmion number density from the PEEM simulation of the 16.4° structure.
Supplementary Video 3
Reconstructed electric field vector from the PEEM measurements of the 16.4° structure.
Supplementary Video 4
Skyrmion number density from the PEEM measurements of the 16.4° structure.
Supplementary Video 5
Reconstructed electric field vector from the PEEM measurements of the 13.2° structure.
Source data
Source Data Fig. 2
Source data for electric field distributions.
Source Data Fig. 3
Source data for electric field distributions and scanning electron microscopy images.
Source Data Fig. 4
Source data for electric field distributions.
Source Data Fig. 5
Source data for electric field distributions.
Source Data Extended Data Fig. 2
Source data for electric field distributions.
Source Data Extended Data Fig. 4
Source data for electric field distributions.
Source Data Extended Data Fig. 5
Source data for electric field distributions.
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Schwab, J., Neuhaus, A., Dreher, P. et al. Skyrmion bags of light in plasmonic moiré superlattices. Nat. Phys. 21, 988–994 (2025). https://doi.org/10.1038/s41567-025-02873-1
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DOI: https://doi.org/10.1038/s41567-025-02873-1
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