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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 ~19° twisting, configuring the largest magic angle in moiré systems reported so far. Further, the moiré 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 moiré bands with twist angle and reveals the topological nature. [ABSTRACT FROM AUTHOR]

We investigate the electronic properties of N-layer black phosphorus by means of an analytical method based on a recently proposed tight-binding Hamiltonian involving 14 hopping parameters. The method provides simple and accurate general expressions for the Hamiltonian of N-layer phosphorene, which are suitable for the study of electronic transport and optical properties of such systems, and the results show the features that emerge as the number of layers increases. In addition, we show that the N-layer problem can be translated into N effective monolayer problems in the long wavelength approximation and, within this analytical picture, we obtain expressions for the energy gap and the effective masses for electrons and holes along the N-layer black phosphorus plane directions as a function of the number of layers, as well as for the Landau levels as a function of perpendicular magnetic field. [ABSTRACT FROM AUTHOR]

We investigate the energy spectrum of single-layer black phosphorene nanoribbons (BPNs) by means of a low-energy expansion of a recently proposed tight-binding model that describes electron and hole bands close to the Fermi energy level. Using the continuum approach, we propose boundary conditions based on sublattice symmetries for BPNs with zigzag and armchair edges and show that our results for the energy spectra exhibit good agreement with those obtained by using the five-parameter tight-binding model. We also explore the behavior of the energy gap versus the nanoribbon width W. Our findings demonstrate that band gaps of armchair BPNs scale as 1/W², while zigzag BPNs exhibit a 1/W tendency. We analyze the different possible combinations of the zigzag edges that result in twofold degenerate and nondegenerate edge states. Furthermore, we obtain expressions for the wave functions and discuss the limit of validity of such an analytical model. [ABSTRACT FROM AUTHOR]