Origin of the magic angle in twisted bilayer graphene from hybridization of valence and conduction bands

The magic-angle phenomenon of twisted bilayer graphene (tBG), i.e, the nontrivial topological flat bands with vanishing Fermi velocity at half filling, has aroused prominent attention on superconductivity, correlated insulators, orbital magnetism, etc. Several efforts have been made to unravel the generation mechanism of the magic-angle phenomenon in tBG. Herein, we show that the hybridizations between the conduction band (CB) and valence band (VB) from different monolayers are critically responsible for the flat bands with band inversion as a signature of the magic-angle phenomenon. The proposed new mechanism for the magic-angle phenomenon is verified by the reversion of irreducible representations of energy bands at $\mathrm{\ensuremath{\Gamma}}$ point. We also discuss the effects of VB-VB and CB-CB hybridizations on the band structures of tBG. The tight-binding results indicate that the VB-VB and CB-CB hybridizations from different layers play the role of the moir\'e potential in real space and reduce the bandwidth in the framework of nearly-free electron model. Our conclusions can also give the explanation on the absence of the magic-angle phenomenon even with bandwidth reductions in twisted bilayer ${\mathrm{MoS}}_{2}$ and BN.