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. 2019 Jun 24;10:2774. doi: 10.1038/s41467-019-10672-5

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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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Fig. 1 — Demonstration of the sensitivity of s-SNOM to the presence of the 2DES at room temperature. a, b Sample description and images of the AFM height, near-field amplitude and near-field phase for the two samples with different thickness of LAO (2 and 8 u.c. respectively). The conducting 2DES is present only in (b), as the LAO thickness exceeds 4 u.c. c Line profiles along the dashed lines in (a) and (b). The near-field signal s₃exp(iϕ₃) at the third harmonic is normalized to the signal s_3,refexp(iϕ_3,ref) in the reference region with an additional layer of a-STO. The laser wavelength is 10.7 μm. The scale bars are 1 μm