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. 2025 Feb 25;16:1959. doi: 10.1038/s41467-025-57235-5

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© The Author(s) 2025

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. 4 — a–d Top: Spectrally integrated optical reflection contrast (RC) of the sensor 2 s exciton as a function of moiré lattice filling factor $ν$ and out-of-plane magnetic field $B$ under zero electric field at 1.6 K. The dashed lines show the expected dispersion for states with Chern number C = −1, 0 and 1 near $ν$ = 1. The arrows denote the saturation field and emergence of the Chern insulator(s). Bottom: filling dependence of the spontaneous magnetic circular dichroism (MCD) at representative temperatures. The twist angle in WSe₂ bilayers is 1.8 (a), 2.1 (b), 2.3 (c) and 2.5 degrees (d). The saturation field $B_{s}$ (denoted by white arrows) decreases with twist angle. In 1.8° twisted WSe₂, spontaneous MCD is not observed down to 1.6 K and a weak C = −1 Chern insulator coexists with a C = 1 Chern insulator.