Stacking-dependent topological electronic structures in honeycomb-kagome heterolayers

Heterostructures of stacked two-dimensional lattices have shown great promise for engineering novel material properties. As an archetypal example of such a system, the hexagon-shared honeycomb-kagome lattice has been experimentally synthesized in various material platforms. In this work, we explore three rotationally symmetric variants of the honeycomb-kagome lattice: the hexagonal, triagonal, and biaxial phases. While the triagonal and biaxial phases exhibit trivial insulating and Dirac semimetal band structures, respectively, the hexagonal phase hosts a higher-order topological phase driven by band inversion near the Γ-point. This highlights a key distinction from the conventional band inversions at the K-point observed in hexagonal homobilayer systems. Furthermore, we demonstrate how the distinct topological properties of these phases result in network band structures within moiré heterostructures formed by twisted or lattice-mismatched HK systems. These network band structures can be experimentally observed through extrinsic twisting or intrinsic lattice mismatch between the honeycomb and kagome systems.