Observation of giant nonlinear valley Hall effect

Nature Physics (2026)Cite this article Valleytronic applications utilize the valley degree of freedom—that is, the location of a state’s wavefunction within the Brillouin zone—to store and process information. In this context, the valley Hall effect is important for reading and writing the valley state. So far, research on this effect has focused on its linear response to an applied current and has not considered nonlinear responses. Here we report the observation of a nonlinear valley Hall effect in a graphene moiré superlattice, indicated by the generation of second-harmonic non-local voltages under a.c. currents. The nonlinear effect we observe has a magnitude surpassing the linear version and is highly tunable with a gate voltage. The nonlinear signal shows quadratic scaling with driving current and quartic scaling with local resistance, setting it apart from its linear counterpart. We further reveal a nonlinear inverse valley Hall effect by observing the third- and fourth-harmonic non-local voltages. This effect provides a mechanism for valley manipulation and may enable a valley rectifier device that converts a.c. charge current into d.c. valley current.This is a preview of subscription content, access via your institution Access Nature and 54 other Nature Portfolio journals Get Nature+, our best-value online-access subscription $32.99 / 30 days cancel any timeSubscribe to this journal Receive 12 print issues and online access $259.00 per yearonly $21.58 per issueBuy this articleUSD 39.95Prices may be subject to local taxes which are calculated during checkoutThe data that support the findings of this study are available within the Article and its Supplementary Information. Other relevant data are available from the corresponding authors upon reasonable request. 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Nano Lett. 13, 5242–5246 (2013).Article ADS Google Scholar Download referencesP.H. was sponsored by National Key Research and Development Program of China (2022YFA1403300), National Natural Science Foundation of China (U23A2071), Natural Science Foundation of Shanghai (23ZR1403600) and the start-up funding from Fudan University. This work was supported by Quantum Science and Technology-National Science and Technology Major Project (2024ZD0300103), Shanghai Municipal Science and Technology Major Project (2019SHZDZX01), Fundamental and Interdisciplinary Disciplines Breakthrough Plan of the Ministry of Education of China (JYB2025XDXM120). C.X. was sponsored by National Natural Science Foundation of China (12574114) and the start-up funding from Fudan University. S.A.Y. was supported by The HK PolyU Start-up (P0057929).These authors contributed equally: Pan He, Min Zhang, Jin Cao.State Key Laboratory of Surface Physics, Institute for Nanoelectronic Devices and Quantum Computing, Fudan University, Shanghai, ChinaPan He, Min Zhang, Jingru Li, Hao Liu, Jinfeng Zhai, Ruibo Wang & Jian ShenHefei National Laboratory, Hefei, ChinaPan He & Jian ShenResearch Laboratory for Quantum Materials, Department of Applied Physics, The Hong Kong Polytechnic University, Hong Kong, ChinaJin Cao & Shengyuan A. YangInterdisciplinary Center for Theoretical Physics and Information Sciences, Fudan University, Shanghai, ChinaCong XiaoDepartment of Physics, Fudan University, Shanghai, ChinaJian ShenShanghai Research Center for Quantum Sciences, Shanghai, ChinaJian ShenZhangjiang Fudan International Innovation Center, Fudan University, Shanghai, ChinaJian ShenCollaborative Innovation Center of Advanced Microstructures, Nanjing, ChinaJian ShenSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarP.H. and J.S. planned the study. P.H. and M.Z. performed the transport measurements and the data analysis. M.Z., J.L., H.L., J.Z. and R.W. fabricated devices. J.C., C.X. and S.A.Y. performed theoretical studies. P.H., M.Z., J.C., C.X., S.A.Y. and J.S. wrote the manuscript. All authors commented the manuscript.Correspondence to Pan He, Cong Xiao, Shengyuan A. Yang or Jian Shen.The authors declare no competing interests.Nature Physics thanks Su-Yang Xu and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.Supplementary Notes 1–6 and Supplementary Figs. 1–16.Statistical source data.Statistical source data.Statistical source data.Statistical source data.Statistical source data.Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.Reprints and permissionsHe, P., Zhang, M., Cao, J. et al. Observation of giant nonlinear valley Hall effect. Nat. Phys. (2026). https://doi.org/10.1038/s41567-026-03221-7Download citationReceived: 23 March 2025Accepted: 19 February 2026Published: 31 March 2026Version of record: 31 March 2026DOI: https://doi.org/10.1038/s41567-026-03221-7Anyone you share the following link with will be able to read this content:Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative