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. 2021 May 11;12:2703. doi: 10.1038/s41467-021-23077-0

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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. 2 — a Simulated AC current dependence of the rectification DC voltage at various magnetic fields. b Calculated time-dependent voltage (top panel) and order parameter (bottom panel) over a period of a sine wave AC current. Unit t₀ is the period of the sine wave. c, d Color maps of the superconducting Cooper-pair density (screenshots of Supplementary Movie 1) at 0.45 and 0.95 of the sine-wave period, respectively. Black dots indicate nanoholes. The red spots in d show flux-carrying flux-quanta. The gray arrows indicate the direction of the driven flux-quanta.