Moir\'e polar vortex, flat bands and Lieb lattice in twisted bilayer BaTiO$_3$

TL;DR

This study uses first-principles calculations to explore twisted bilayer BaTiO₃, revealing vortex patterns, flat bands, and Lieb lattice structures that could influence ferroelectricity and topological states in moiré materials.

Contribution

It uncovers the electronic and structural properties of twisted bilayer BaTiO₃, including vortex patterns, flat bands at a specific twist angle, and the Lieb lattice analogy, advancing moiré system understanding.

Findings

Large stacking fault energy induces chiral vortex patterns.

Flat bands occur at approximately 19° twist angle, the largest known magic angle.

Moiré vortex pattern resembles two interpenetrating Lieb lattices.

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 moir\'e systems reported so far. Further, the moir\'e vortex pattern bears a striking resemblance to two interpenetrating Lieb lattices and corresponding tight-binding model provides a comprehensive description of the evolution the moir\'e bands with twist angle and reveals the topological nature of these states.