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. 2020 Mar 3;11:1161. doi: 10.1038/s41467-020-14900-1

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© The Author(s) 2020

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 licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence 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 licence, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 6 — Filled symbols represent data for a 200-nm-thick film analyzed by the 3D localization formula, whereas open symbols represent those for a 50-nm-thick film analyzed by the 3D formula and 2D formula (HLN formula). Error bars are estimated at the lowest temperature for each data using standard deviation. For the 50-nm film, the error was comparable or smaller than the size of the open symbols. Theory predicts dephasing from electron–electron interaction to follow l_ϕ = T^−0.75 in 3D systems (upper dashed line), while l_ϕ = T^−0.5 in 2D systems (lower dashed line). Source Data are provided as a Source Data file.