Electronic properties of multilayered Lieb, transition, and Kagome lattices

Based on the interconvertibility feature shared between monolayer Lieb and Kagome lattices, which allows mapping transition lattice's stages between these two limits ($\pi/2 \leq\theta \leq 2\pi/3$), in this work we extend the recently proposed one-control ($\theta$) parameter tight-binding model for the case of a multilayer Lieb-Kagome system, by considering the two most-common stacks: AA and AB (Bernal). We systematically study the band transformations between the two lattices by adjusting the interlayer hopping and distance, with or without considering the influence of the nearest interlayer neighbors, for different numbers of stacked layers, and under the application of an external perpendicular electric field. The energetic changes are understood from the perspective of the layer dependence of the pseudospin components and the total probability density distributions. The present framework provides an appropriate and straightforward theoretical approach to continuously investigate the evolution of electronic properties in the multilayer Lieb-Kagome system under various external effects.