Three dimensional (3D) third-order topological insulators (TIs) have zero-dimensional (0D) corner states, which are three dimensions lower than bulk. Here we investigate the third-order TIs on breathing pyrochlore lattices with p-orbital freedom. The tight-binding Hamiltonian is derived for the p-orbital model, in which we find that the two orthogonal π-type (transverse) hoppings are the key to open a band gap and obtain higher-order topological corner states. We introduce the Z4 berry phase to characterize the bulk topology and analysis the phase diagram. The corner states, demonstrated in a finite structure of a regular tetrahedron, exhibit rich 3D orbital configurations. Furthermore, we design an acoustic system to introduce the necessary π-type hopping and successfully observe the orbital corner states. Our work extends topological orbital corner states to third-order, which enriches the contents of orbital physics and may lead to applications in novel topological acoustic devices.
@article{arxiv.2411.13128,
title = {Third-order Orbital Corner State and its Realization in Acoustic Crystals},
author = {Jiyu Wang and Ying Chen and Xiancong Lu},
journal= {arXiv preprint arXiv:2411.13128},
year = {2025}
}