Nondegenerate chiral phonons in the Brillouin-zone center of root 3 x root 3 honeycomb superlattices

The theoretical finding on chiral phonons at Brillouin-zone corners (valleys) of two-dimensional honeycomb lattices and its experimental verification in monolayer tungsten diselenide [H. Zhu, J. Yi, M. Li, J. Xiao, L. Zhang, C. Yang, R. A. Kaindl, L. Li, Y. Wang, and X. Zhang, Science 359, 579 (2018)], have attracted wide attention in the study of phonon chirality very recently. In this paper, to make chiral phonons more measurable, the valley phonons were folded to Brillouin-zone center in root 3 x root 3 honeycomb superlattices, and near the center topological chiral phonons can be observed. The chiral phonons which are not the superposition of linear modes are nondegenerate and can be optically excited in helicity-resolved Raman scattering. Moreover, by adjusting the doping mass, the topological chiral phonons can be engineered in specific branches. Finally, in deformed root 3 x root 3 honeycomb superlattices, topological chiral phonons can also be found near the Brillouin-zone center. We believe that the findings of nondegenerate topological chiral phonons in the Brillouin-zone center help to enrich our understanding of chiral phonons and promote future applications in phononics.