Fig. 4: Effect of the Fe(1) site ordering on inversion-symmetry and quantum destructive interference.

a Illustration of one vdW slab of the Fe(1) site-disordered phase, in which the Fe(1) sites are randomly distributed such that global inversion symmetry is preserved. b, c The schematic view of the lattice showing the C_2y and C_3z symmetries in the Fe(1) site-disordered phase, respectively. d The tight-binding model showing Dirac crossings at K (K′) protected by the above symmetries and the associated twofold topological crossing due to the ferromagnetic order and the gap by SOC. e The helical topological nodal lines induced by the ABC stacking of the vdW slabs that results in winding of the nodal lines with opposite chiralities around \(\bar{K}\) and \(\bar{{K}^{{\prime} }}\). f Illustration of one vdW slab of the Fe(1) ordered-site phase, in which the Fe(1) is DUU-ordered, forming a bipartite crystalline lattice. g The Fe(1) and the nearest neighbor Fe(3) sites form a clover lattice as shown in the red dashed box in (f). h Single clover unit showing the destructive interference of the hopping amplitude at the Fe(1) and Fe(3) sites due to the alternating sign of the Wannier phase, leading to a localization of the electronic wavefunction. The sites and wavefunction amplitudes are labeled on the corresponding atoms. i The original (blue) and the \(\sqrt{3}\,\times\,\sqrt{3}\) superstructure (red) BZ. j, k Tight-binding model for the clover lattice without and with spin-orbital coupling (SOC), respectively. With SOC, the flat band is gapped with a Chern number of 1, and is hence topologically nontrivial.