Chiral phonons in the honeycomb sublattice of layered CoSn-like compounds
Andrzej Ptok, Aksel Kobiałka, M. Sternik, Jan Łażewski, Paweł T. Jochym, Andrzej M. Oleś, S. Stankov, Przemysław Piekarz
Abstract
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.