Moiré polar vortex, flat bands and Lieb lattice in twisted bilayer BaTiO${}_3$

Abstract

Advances in material fabrication techniques and growth methods have opened up a new chapter for twistronics, in the form of twisted freestanding three-dimensional material membranes. Through first-principles calculations based on density functional theory, we investigate the crystal and electronic structures of twisted bilayer BaTiO${}_3$. Our findings reveal that large stacking fault energy leads to chiral in-plane vortex pattern that was recently observed in experiments. Moreover, we also found non-zero out-of-plane local dipole moments, indicating that the strong interlayer interaction might offer promising strategy to stabilize ferroelectric order in the two-dimensional limit. Remarkably, the vortex pattern in the twisted BaTiO${}_3$ bilayer support localized electronic states with quasi-flat bands, associated with the interlayer hybridization of oxygen $p_z$ orbitals. We found that the associated band width reaches a minimum at $\sim$19${}^{\circ }$ twisting, configuring the largest magic angle in moiré systems reported so far. Further, the moiré vortex pattern bears a striking resemblance to two interpenetrating Lieb lattices and corresponding tight-binding model provides a comprehensive description of the evolution the moiré bands with twist angle and reveals the topological nature of these states.

arXiv comment8 pages, 5 figures

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• On the origin of the unusual strain morphologies and polar Moiré patterns in twisted ferroelectrics
• Switchable Topological Polar Textures in Freestanding Ultrathin Ferroelectric Oxides
• Sliding and superlubric moiré twisting ferroelectric transition in HfO2