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. 2021 Feb 19;12:938. doi: 10.1038/s41467-021-21193-5

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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. 1 — a The AFM tip couples to the AGP inside the layered structure via the evanescent field above graphene. b The exponentially decaying z-component of the AGP electric field E_z penetrates into the free space above graphene by distance D_e and couples to the AFM tip that acts as a z-oriented electric dipole p_z. c Penetration depth of |E_z | as a function of excitation frequency and spacer thickness calculated for graphene E_F = −0.5 eV.