Fig. 1: Magic band structure and localization at the TB level.
TB band structures of TBG lattices with geometric parameters: (a) θ31 = 1.050°-d31 = 3.349 Å (representing the MA condition), (b) θ9 = 3.481°-d9 = 2.7329 Å (green dashed lines), and θ11 = 2.876°-d11 = 2.8304 Å (blue lines). c Compressed band structures from (b), scaled by factors of \({s}_{9}^{31}=0.3017\) (green dashed lines) and \({s}_{11}^{31}=0.3652\) (blue lines), superimposed onto the MATBG bands (red lines) from (a). The three plots coincide in the ± 20 meV energy range, highlighted by the shaded region. All band dispersions are plotted along the \(\tilde{\Gamma }\tilde{K}\tilde{M}\tilde{\Gamma }\) path with the Fermi energy set to zero. d–f Projected local density near the Fermi level for (d) MATBG (red spots), (e) TBG with θ9-d9 (green spots), and (f) TBG with θ11-d11 (blue spots). The in-plane coordinates are given in both nm and moiré lattice units (mlu). The black parallelogram represents the moiré unit cell of the respective TBG system.
