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arXiv · 2110.15549

Competition of First-Order and Second-Order Topology on the Honeycomb Lattice

Matthew Bunney·Tomonari Mizoguchi·Yasuhiro Hatsugai·Stephan Rachel
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Abstract

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 $\mathbb{Z}_Q$ Berry phase. Highlights include phases with high Chern numbers, a novel $\mathbb{Z}_6$ 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 $\mathbb{Z}_Q$ Berry phases.

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Matthew Bunney, Tomonari Mizoguchi, Yasuhiro Hatsugai, Stephan Rachel. 2021-10-29. Competition of First-Order and Second-Order Topology on the Honeycomb Lattice. https://doi.org/10.1103/physrevb.105.045113

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