We investigate both first-order topology, as realized through Haldane's model, and second-order topology, implemented through an additional Kekul\'e-distortion, on the honeycomb lattice. The interplay and competition of both terms result in a phase diagram at half-filling which contains twelve distinct phases. All phases can be characterized by the first Chern number or by a quantized ZQ Berry phase. Highlights include phases with high Chern numbers, a novel Z6 topological phase, but also coupled kagome-lattice Chern insulators. Furthermore, we explore the insulating phases at lower fillings, and find again first-order and second-order topological phases. Finally, we identify real-space structures which feature corner states not only at half but also at third and sixth fillings, in agreement with the quantized ZQ Berry phases.
@article{arxiv.2110.15549,
title = {Competition of First-Order and Second-Order Topology on the Honeycomb Lattice},
author = {Matthew Bunney and Tomonari Mizoguchi and Yasuhiro Hatsugai and Stephan Rachel},
journal= {arXiv preprint arXiv:2110.15549},
year = {2022}
}