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.

中文翻译：

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AV3Sb5(A=K, Rb, Cs) 化合物中电荷密度波起源的动力学研究

包含理想 kagome 晶格的系统可以表现出几种不同且新颖的奇异物质状态。这种系统的一个例子是最近发现的$\mathrm{一个}{\mathrm{五}}_3{锑}_5$($\mathrm{一个}=\mathrm{ķ}$、Rb 和 Cs) 化合物家族。这里观察到电荷密度波（CDW）和超导性的共存。在本文中，我们研究的动态特性$\mathrm{一个}{\mathrm{五}}_3{锑}_5$CDW 阶段起源背景下的系统。我们展示并讨论了结构相变$磷6/米米米$至$C2/米$由声子软模式的存在引起的对称性。我们得出结论，在这一系列化合物中观察到的 CDW 是原子位移的结果，从 kagome 网的高对称位置，在低温阶段。此外，使用数值从头算方法，我们讨论了电荷分布$\mathrm{一个}{\mathrm{五}}_3{锑}_5$表面。我们表明，观察到的表面的实验条纹状调制可能与表面重建和三维的表现有关$2\times 2\times 2$散装 CDW。最后，实现的结果$C2/米$结构上的电子特性进行了讨论。我们表明电子能带结构重建和伴随的状态密度修改与实验数据很好地对应。