Electronic properties of multilayered Lieb, transition, and Kagome lattices

TL;DR

This paper extends a tight-binding model to multilayer Lieb, transition, and Kagome lattices, systematically analyzing their electronic band transformations under various stacking configurations, interlayer couplings, and external electric fields.

Contribution

It introduces a unified theoretical framework for studying multilayer Lieb-Kagome systems, considering different stacking orders and external influences, advancing understanding of their electronic properties.

Findings

Band structures depend on stacking and interlayer coupling.

External electric fields modify electronic properties.

Layer-dependent pseudospin influences energy distributions.

Abstract

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.