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Mesoscale atomic engineering in a crystal lattice

Nature (2026) Cite this article

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Abstract

Controlling individual atoms using lasers1, ion traps2 and scanning probe tips3 has transformed our understanding of matter and enabled breakthroughs in quantum science4,5,6. Extending this control into three-dimensional (3D) solids and across mesoscopic scales, however, remains a foundational challenge. Electron irradiation in electron microscopes is known to induce atomic displacements7, and atomic manipulation has been proposed8 and demonstrated9,10. Yet repeated and deterministic control has remained elusive9,10,11,12,13,14,15,16,17. Here we demonstrate deterministic atomic engineering in a 3D crystal, creating ordered arrangements of more than 40,000 user-defined defects within minutes across a 150 nm × 100 nm × 13 nm volume. By steering individual Cr atoms in the magnetic semiconductor CrSBr into selected interstitial sites using an electron beam directed with sub-20-pm-scale accuracy, we create vacancy–interstitial complexes. The resulting impurity array forms a mesoscale crystal embedded within the host lattice, a new form of engineered artificial matter that remains stable at room temperature and outside the microscope. By tracking Cr atom displacements, we identify conditions under which the defect structures are predictable. Our calculations suggest that these defects form correlated impurity states with intra-defect optical transitions and inter-defect kinetic and Coulomb interactions. This establishes a generalizable platform for atomic defect engineering at mesoscopic, and potentially macroscopic, scales, opening opportunities for scalable quantum technologies, including deterministic colour-centre placement, quantum simulation of many-body lattice models and atomic-scale manufacturing.

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Fig. 1: Atomic engineering of artificial matter in 16L-thick (12.7 nm) CrSBr.
The alternative text for this image may have been generated using AI.
Fig. 2: Multi-directional Cr atom steering.
The alternative text for this image may have been generated using AI.
Fig. 3: Picometre-scale positioning defines the limits of engineered atomic matter.
The alternative text for this image may have been generated using AI.
Fig. 4: Mesoscale atomic engineering of 3D defect superlattices with intra-impurity and tunable inter-impurity Coulomb interactions.
The alternative text for this image may have been generated using AI.
Fig. 5: Three-dimensional mesoscopic defect crystal.
The alternative text for this image may have been generated using AI.
Fig. 6: Capturing atom dynamics by atom streaking imaging.
The alternative text for this image may have been generated using AI.

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Data availability

The microscopy data underlying the figures in this study are available at Zenodo76 (https://doi.org/10.5281/zenodo.17944979). Additional data supporting the findings of this study are available from the corresponding author upon request.

Code availability

The electron beam propagation (channelling) simulation, HAADF-STEM image simulation, dose rate calculation scripts and plotting scripts used for data analysis are publicly available at GitHub (https://github.com/KleinAtomLab/Mesoscale-atomic-engineering). The DFT and GW calculations were performed using established community software packages that are not publicly redistributable in their modified form. All relevant computational parameters, input settings and methodological details required to reproduce these calculations are provided in the Methods and the Supplementary Information. The quantitative analysis procedures for the ALO approach are described in detail in the Supplementary Information and ref. 53. A comprehensive discussion of the SLO algorithm and its positioning precision will be presented in a dedicated follow-up study. At the time of publication, the code underlying this work, specifically the custom software developed by the authors for beam positioning, lattice walking without lattice jumps, directional scanning and the automated experimental workflow used in this study, is not available for peer review or public release because of ongoing intellectual property protection and provisional patent filings. The algorithms and implementations are considered proprietary and are subject to confidentiality constraints at this stage.

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Acknowledgements

J.K. and F.M.R. acknowledge support from the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award No. DE-SC0025387 (algorithm development, data acquisition and analysis) and by the National Science Foundation (NSF) under Trailblazer Engineering Impact Award No. 2421694 (defect calculations). The STEM experiments were supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division and by the Center for Nanophase Materials Sciences (CNMS) at Oak Ridge National Laboratory, a US Department of Energy Office of Science User Facility. M.R. acknowledges support from the Vidi ENW research programme of the Dutch Research Council (NWO) under grant DOI: 10.61686/YDRHT18202 (file no. VI.Vidi.233.077). The ab initio DFT and DFT+U computations were performed on the Dutch national supercomputer Snellius under project no. EINF-4184. This work was authored in part by the National Laboratory of the Rockies for the US Department of Energy under contract no. DE-AC36-08GO28308. S.A., D.P. and M.v.S. were supported by the Computational Chemical Sciences program within the US Department of Energy Office of Basic Energy Sciences. S.A., D.P. and M.v.S. acknowledge the use of the National Energy Research Scientific Computing Center (NERSC), supported by the US Department of Energy under contract no. DE-AC02-05CH11231, through NERSC award BES-ERCAP0021783, as well as computational resources sponsored by the US Department of Energy Office of Energy Efficiency and Renewable Energy and located at the National Laboratory of the Rockies. M.W. acknowledges support from the Center for Visualizing Catalytic Processes (VISION), funded by the Danish National Research Foundation (DNRF146). Z.S. was supported by project LUAUS25268 from the Ministry of Education, Youth and Sports (MEYS) and by the project Advanced Functional Nanorobots (reg. no. CZ.02.1.01/0.0/0.0/15_003/0000444, financed by the EFRR). We acknowledge the MIT SuperCloud and Lincoln Laboratory Supercomputing Center for providing HPC and database resources. This manuscript has been authored by UT-Battelle, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US Government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. The DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (https://www.energy.gov/doe-public-access-plan).

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Author notes

  1. These authors contributed equally: Julian Klein, Kevin M. Roccapriore

Authors and Affiliations

  1. Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

    Julian Klein, Mads Weile & Frances M. Ross

  2. Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN, USA

    Kevin M. Roccapriore & Andrew R. Lupini

  3. AtomQ, Knoxville, TN, USA

    Kevin M. Roccapriore

  4. Center for Visualizing Catalytic Processes (VISION), Department of Physics, Technical University of Denmark, Kongens Lyngby, Denmark

    Mads Weile

  5. Institute for Molecules and Materials, Radboud University, Nijmegen, The Netherlands

    Sergii Grytsiuk & Malte Rösner

  6. Department of Inorganic Chemistry, University of Chemistry and Technology Prague, Prague, Czech Republic

    Zdenek Sofer

  7. Theory and Simulation of Condensed Matter, King’s College London, London, UK

    Dimitar Pashov

  8. National Laboratory of the Rockies, Golden, CO, USA

    Mark van Schilfgaarde & Swagata Acharya

  9. Faculty of Physics, Bielefeld University, Bielefeld, Germany

    Malte Rösner

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Contributions

J.K. conceptualized and supervised the project and together with K.M.R and F.M.R. designed the experiments. Z.S. synthesized bulk crystals of CrSBr. J.K. prepared STEM samples. J.K. and K.M.R. developed electron beam control algorithms and microscopy workflows. K.M.R and J.K. collected STEM data with the help of A.R.L.; M.W. and J.K. performed STEM simulations. S.G. and M.R. provided ab initio DFT and DFT+U calculations, including optimized defect supercell; performed wannierization of the impurity states; and derived estimates for the impurity model parameters. S.A., D.P. and M.v.S. computed and analysed electronic and excitonic spectra within \(\mathrm{QS}G\hat{W}\) framework. All authors discussed the results. The manuscript was written by J.K. with input from all co-authors.

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Correspondence to Julian Klein, Kevin M. Roccapriore or Frances M. Ross.

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Competing interests

J.K., K.M.R. and F.M.R. are inventors on two filed patent applications55,56.

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Nature thanks Ute Kaiser, Jani Kotakoski and Toma Susi for their contribution to the peer review of this work. Peer reviewer reports are available.

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Supplementary Information (download PDF )

This file contains Supplementary Information sections 1–9, Supplementary Figs. 1–31, Supplementary Tables 1 and 2, and additional references. It contains additional methodological details, theoretical analysis, extended experimental results, and supporting figures and tables related to the main paper. The sections include discussions of vacancy–interstitial defect complexes in CrSBr, the automated workflow for deterministic atomic engineering, including positioning algorithms; simulations of the electron beam intensity distribution, including electron beam channelling; theoretical calculations of defect complexes, including Coulomb interactions; additional examples of engineered impurity superlattices and corresponding electron diffraction; displacement mechanisms of Cr atoms, including stability; and experimental observations of Cr atom dynamics under the electron beam using the atom streaking technique.

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Klein, J., Roccapriore, K.M., Weile, M. et al. Mesoscale atomic engineering in a crystal lattice. Nature (2026). https://doi.org/10.1038/s41586-026-10431-9

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