Fig. 5. DFT band structure of MnBi₈Te₁₃ calculated using the experimental lattice parameters with relaxed atomic positions.

(A to D) Bulk band structure. Bulk Brillouin zone (BZ) and the (001) surface BZ of MnBi₈Te₁₃ with the high symmetry points marked (A). Bulk band structure of MnBi₈Te₁₃ in the out-of-plane FM configuration, with spin-orbit coupling and correlation parameter U included (B). Spin-resolved band structure zoom in around the Γ point (C). Orbital-resolved band structure zoom in around the Γ point (D). The red and blue dots indicate Te p_z and Bi p_z orbitals, respectively. There are clear band inversions between the Te p_z and Bi p_z states at the Γ point. (E and F) DFT calculation of a seven-layered finite-sized slab model corresponding to the QL₁ surface arrangement, i.e., with vacuum-[QL-SL-QL-QL-QL-SL-QL]-vacuum. (E) Band structure of this slab model. The sizes of the blue and red dots represent the fraction of electronic charge residing in the topmost QL and the nearest-neighboring SL, respectively. (F) Evolution of the sum of Wannier charge centers (WCCs) along k_y in the k_z = 0 plane. The trajectory of WCC is an open curve traversing the whole BZ once, indicating the Chern number C = 1 in the k_z = 0 plane.