Systems containing the ideal kagome lattice can exhibit several distinct and novel exotic states of matter. One example of such systems is a recently discovered $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A=\mathrm{K}$, Rb, and Cs) family of compounds. Here the coexistence of the charge density wave (CDW) and superconductivity is observed. In this paper, we study the dynamic properties of the $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ systems in context of origin of the CDW phase. We show and discuss the structural phase transition from $P6/mmm$ to $C2/m$ symmetry that is induced by the presence of phonon soft modes. We conclude that the CDW observed in this family of compounds is a consequence of the atom displacement, from the high-symmetry position of the kagome net, in the low-temperature phase. Additionally, using the numerical ab initio methods, we discuss the charge distribution on the $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ surface. We show that the observed experimental stripelike modulation of the surface can be related to surface reconstruction and manifestation of the three-dimensional $2\times 2\times 2$ bulk CDW. Finally, the consequence of realization of the $C2/m$ structure on the electronic properties is discussed. We show that the electronic band structure reconstruction and the accompanying modification of density of states correspond well to the experimental data.

• Received 12 October 2021
• Accepted 8 June 2022

DOI:https://doi.org/10.1103/PhysRevB.105.235134