Topological phases, including the conventional first-order and higher-order topological insulators and semimetals, have emerged as a thriving topic in the fields of condensed-matter physics and material science. Usually, a topological insulator is characterized by a fixed order topological invariant and exhibits associated bulk-boundary correspondence. Here, we realize a new type of topological insulator in a bilayer phononic crystal, which hosts simultaneously the first-order and second-order topologies, referred here as the hybrid-order topological insulator. The one-dimensional gapless helical edge states, and zero-dimensional corner states coexist in the same system. The new hybrid-order topological phase may produce novel applications in topological acoustic devices.
@article{arxiv.2012.14616,
title = {Hybrid-order topological insulators in a phononic crystal},
author = {Yating Yang and Jiuyang Lu and Mou Yan and Xueqin Huang and Weiyin Deng and Zhengyou Liu},
journal= {arXiv preprint arXiv:2012.14616},
year = {2021}
}