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. 2021 Dec 10;12:7201. doi: 10.1038/s41467-021-26414-5

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© The Author(s) 2021

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 3 — a, b The photograph of the fabricated electric circuit for the hybrid second-order ST effect (a) and SS effect (b). The values of the capacitors and inductors are the same as theoretical design. Arrows with different colors are the same as INICs labeled in Fig. 1d. The inset presents the enlarged view of the unit cell. c, d The measured voltage distribution at the resonance frequency for the hybrid second-order ST effect and SS effect in (c) and (d), respectively. Each unit cell contains four sublattices (a, b, c, d). Big arrows in (c) show the directions of skin and topological pumping. Big arrows in (d) show the directions of skin pumping.