Fig. 1. Magnetic reSM.

(A) Example tight-binding model for reSM. There are two sublattices per unit cell (shaded) due to an antiferromagnetic order m_x, producing a total of four bands. On-site potential J stands for the exchange coupling $-\mathit{J}{\mathit{m}}_{\mathit{x}}\cdot {\mathit{c}}_{\mathit{x}}^{†}\mathrm{\sigma }{\mathit{c}}_{\mathit{x}}$. In addition to the standard nearest-neighbor hopping t, a spin-dependent hopping ± t_Jσ_x is included, which can be viewed as originating from an exchange coupling to a magnetic moment in the middle of the nearest-neighbor bonds (section S8). (B) Dispersion relation at J/t = 1 and t_J/t = 1/4. In this case, η in Eq. 4 is +1, and the dispersion is gapped between the second and the third bands. (C) Dispersion relation at J/t = 1 and t_J/t = 3/4. Now, η = −1, and a pair of Dirac nodes exist as predicted. (D) Fermi surface of the 3D version of the reSM. The two Weyl points on the k₃ = 0 (k₃ = π) plane have the chirality +1 (–1), indicating a huge Fermi arc on some 2D surfaces. The signs on the TRIMs indicate the product of the C_2z rotation eigenvalues of occupied bands in this model.