Fig. 3: Comparing the low-energy dispersions between Cr- and Mn-intercalated NbS₂.

a Intensity plots along the Γ − M and Γ − K directions of Cr_1/3NbS₂. b The same as (a) but for Mn_1/3NbS₂. c EDCs along Cut1 and Cut2 in (a) and (b). Different colors represent cuts in different materials: black for Cr_1/3NbS₂ and red for Mn_1/3NbS₂. The horizontal blue dashed lines that run through (a–c) are guides for comparing energy positions. d k_z dispersion of the ω band at the M₀ point. e The crossing bands along Γ − K in (a, b) are fitted by parabolic curves and the Fermi velocities are fitted by lines, respectively [see details in Supplementary Fig. 1] (Supplementary Information for the first-principles electronic structure calculations). The size of each marker reflects the measurement uncertainty (~15 meV and  ±0.01 Å⁻¹), while the black (±20 meV and 0.01 Å⁻¹) and red (±40 meV and 0.01 Å⁻¹) bars at the bottom represent the maximum fitting errors in the energy and momentum directions, respectively. f Electron configurations of TM in D_3d and Nb in D_3h crystal fields. In the upper panel, the black solid arrows represent the electron filling of Cr d³ in the t_2g orbitals, while the additional electron in Mn d⁴ occupies one of the e_g orbitals. In the lower panel, the black dashed arrow represents an electron transferring from the TM to the NbS₂ layer.