Moiré polar vortex, flat bands, and Lieb lattice in twisted bilayer BaTiO3

Through first-principles calculations based on density functional theory, we investigate the crystal and electronic structures of twisted bilayer BaTiO3. Our findings reveal that large stacking fault energy leads to a chiral in-plane vortex pattern that was recently observed in experiments. We also found nonzero out-of-plane local dipole moments, indicating that the strong interlayer interaction might offer a promising strategy to stabilize ferroelectric order in the two-dimensional limit. The vortex pattern in the twisted BaTiO3 bilayer supports localized electronic states with quasi-flat bands, associated with the interlayer hybridization of oxygen pz orbitals. We found that the associated bandwidth reaches a minimum at similar to 19 degrees twisting, configuring the largest magic angle in moir & eacute; systems reported so far. Further, the moir & eacute; vortex pattern bears a notable resemblance to two interpenetrating Lieb lattices and the corresponding tight-binding model provides a comprehensive description of the evolution the moir & eacute; bands with twist angle and reveals the topological nature.