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. 2019 Jun 19;9:8811. doi: 10.1038/s41598-019-45338-1

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© The Author(s) 2019

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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Current-voltage characteristics (IVCs) of Nb/Si₃N₄ samples measured under zero-field condition. IVC isotherms for (a) B1, (b) B2 and (c) B3. (d) The IVCs for B3 are shifted in voltage for clarity. The steps in the IVCs are extended by the dotted lines to show their convergence at a current, known as excess current I_s which is lower than the critical current. The existence of the excess current and the increasing slopes for the intermediate steps for increasing current direction (up sweep) are the signature of phase slip lines. Critical currents are defined as shown by the dotted arrows. The line arrows indicate the current sweeping direction.