Chiral phonons in the honeycomb sublattice of layered CoSn-like compounds

Honeycomb and kagome lattices exhibit extraordinary electronic properties. It is a natural consequence of additional discrete degree of freedom associated with a valley or the occurrence of electronic flat bands. The combination of both types of lattices, observed in CoSn-like compounds, leads not only to the topological electronic behavior, but also to the emergence of chiral phonon modes. We study CoSn-like compounds and show that chiral phonons are realized here. Previous theoretical studies demonstrated that the chiral phonons can be found in ideal two-dimensional honeycomb or kagome lattices. Recent experimental results support such a prediction as the chiral phonons were observed in the transition metal dichalcogenide ${\mathrm{WSe}}_{2}$. It turns out that in the case of CoSn-like systems with the $P6/mmm$ symmetry, the kagome lattice formed by $d$-block element is decorated by the additional $p$-block atom. As a result one finds a two-dimensional triangular lattice of atoms with nonequal masses and the absence of chiral phonons in the kagome plane. Contrary to this, the interlayer honeycomb lattice of $p$-block atoms is preserved and allows for the realization of chiral phonons. In this paper we discuss the properties of such chiral phonons in seven CoSn-like compounds and demonstrate that they do not depend on the atomic mass ratio or the presence of intrinsic magnetic order. The chiral phonons of $d$-block atoms can be restored by removing the inversion symmetry. The latter is possible in the crystal structure of CoGe and RhPb with the reduced symmetry ($P\overline{6}2m$) and in distorted-kagome-like lattice.