Fig. 3: DyB4, a Type-III TMDI candidate.
From: Magnetic wallpaper Dirac fermions and topological magnetic Dirac insulators
a Tetragonal crystal structure of DyB4. b, c Magnetic spin structures in the b Γ2 and c Γ4 states. The Γ4 state corresponds to Type-III MSG 127.392 \(P{4}^{{\prime} }/{m}^{{\prime} }{b}^{{\prime} }m\) with (001)-surface MWG \(p{4}^{{\prime} }{g}^{{\prime} }m\). d Density functional theory (DFT) total energy differences between the Γ4 and Γ2 states. The absolute values are adjusted to be in the range between 0 eV and 1 eV. The magnetic phase transition is indicated by the brown solid line. The Γ4 state has lower energy than the Γ2 state when U≤ 6.5 eV. e, f Bulk band structure from DFT+U calculations (U = 6.5 eV and J = 1 eV) for the Γ4 state. The band gap near the Fermi level is indicated by the red dashed lines. g, h Wilson loop spectra below the red dashed line along \(\overline{\Gamma }\)-\(\overline{M}\)-\(\overline{{\Gamma }^{{\prime} }}\). The winding structure exhibits g \({{{{\mathcal{C}}}}}_{m}^{x\overline{y}}=-2\) at U = 6.5 eV and h \({{{{\mathcal{C}}}}}_{m}^{x\overline{y}}=-1\) at U = 6.0 eV. i, j (001)-surface spectra for the i top (B-terminated) and j bottom (Dy-terminated) surfaces obtained using the surface Green’s function method. The white arrows guide where surface states appear. k, l (001)-surface band structures from a 60-layer slab calculation, which are drawn to show surface states indicated by the white arrows in i, j. Bulk and surface bands are represented by gray and black, respectively. Surface Dirac fermions are moved inside the gap by applying a surface potential of −0.2 eV on the top. i–l are calculated using the Wannierized tight-binding model from the DFT+U calculation (U = 6.5 eV).
