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. 2020 Sep 15;11:4619. doi: 10.1038/s41467-020-18470-0

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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 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. 3 — Experimental (a) longitudinal optical conductivity spectra σ_xx(ω) and (c) optical Hall conductivity spectra σ_xy(ω). The red circle at zero energy in c represents the DC value of the σ_xy of the bulk single crystal. The inset of c shows the optical Hall conductivity spectra including the terahertz spectra on the logarithmic energy scale. The red square at zero energy in the inset of c represents the DC value of the σ_xy of the thin film. The dashed lines in c for a photon energy region of 8–80 meV, where the MO measurements could not be done, represent the anticipated connections between the experimental σ_xy(ω) values in THz/DC and infrared regions, assuming that no sharp resonance structure is present in this narrow energy window. Theoretical (b) longitudinal optical conductivity spectra σ_xx(ω) and (d) Hall conductivity spectra σ_xy(ω) (see Method). In d, the red and blue curves represent the σ_xy(ω) spectra which take into account all band structures, while the pink and light blue ones show the σ_xy(ω) arising from the topological bands indicated by bold lines in e. These theoretical calculations include only the interband transition, so that the response from the intraband transition or Drude response of conduction electrons is omitted. e The band structure obtained from the calculation considering the renormalization factor. The two bands indicated by bold curves compose the anti-crossing lines and Weyl points. f Optical Hall conductivity σ_xy(ω) calculated for a single anti-crossing point in the two-dimensional electronic structure with mass gap m = 0.02 eV and chemical potential μ = 0.03 eV (red), 0.05 eV (orange), 0.07 eV (green), 0.09 eV (blue). The dotted line illustrates the schematic curve of the integrated sum of these resonances arising from the dispersive nodal ring. (Inset) Schematic illustration of the optical transitions on the cross-sections of the dispersive anti-crossing lines.