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Gibertini, M., Tomadin, A., Polini, M., Fasolino, A. & Katsnelson, M. I. Electron density distribution and screening in rippled graphene sheets. Phys. Rev. B 81, 125437 (2010). 39. Gibertini, M., Tomadin, A., Guinea, F., Katsnelson, M. I. & Polini, M. Electron-hole puddles in the absence of charge impurities. Phys. Rev. B 85, 201405 (2012). Acknowledgements We acknowledge technical support from Y. Lechaux and J. Quereda. This work has been supported by Ministerio de Ciencia e Innovación (Grant PID2019-106820RB-C2-2) and Junta de Castilla y León (Grants SA256P18 and SA121P20, including EU/FEDER funds). This work was supported by HFML-RU/NWO-I, member of the European Magnetic Field Laboratory (EMFL). This work was also supported by CENTERA Labora- tories in the frame of the International Research Agendas Program for the Foundation for Polish Sciences co-financed by the European Union under the European Regional Development Fund (no. MAB/2018/9). D.V. acknowledges financial support from the Ministry of Universities (Spain) (Ph.D. contract FPU19/04224). J.A.D-N thanks the support from the Universidad de Salamanca for the María Zambrano postdoctoral grant funded by the Next Generation EU Funding for the Requalification of the Spanish University System 2021–23, Spanish Ministry of Universities. K.W. and T.T. acknowledge support from the Elemental Strategy Initia- tive conducted by the MEXT, Japan (Grant Number JPMXP0112101001) and JSPS KAKENHI (Grant Numbers 19H05790, 20H00354 and 21H05233). Author contributions U.Z., S.W. and S.P. conceived the experiment and coordinated the col- laboration. D.V., V.C. and M.S. fabricated the graphene devices and performed the transport measurements. J.A.D.-N., A.M.-R. and J.S.-S. provided technical assistance in the cleanroom processing. C.S.A.M. and K.R. provided technical assistance during the high-field experi- ments. K.W. and T.T. provided single crystals of hBN. B.B., C.S. and E.D. supervised the experimental work. D.V., V.C., M.S., and S.P. performed the data analysis. M.I.K. provided theoretical input for the interpretation of the results. S.P. wrote the manuscript with input from all the co- authors. Competing interests The authors declare no competing interests. Additional information Supplementary information The online version contains supplementary material available at https://doi.org/10.1038/s41467-023-35986-3. Correspondence and requests for materials should be addressed to Sergio Pezzini. Peer review information Nature Communications thanks Mikhail Portnoi and the anonymous reviewers for their contribution to the peer review of this work. Reprints and permissions information is available at http://www.nature.com/reprints Publisher’s note Springer Nature remains neutral with regard to jur- isdictional claims in published maps and institutional affiliations. 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