Dynamical Study of the Origin of the Charge Density Wave in $A$V$_{3}$Sb$_{5}$ ($A=$K, Rb, Cs) Compounds

TL;DR

This study investigates the origin of charge density waves in $A$V$_{3}$Sb$_{5}$ compounds, revealing structural phase transitions driven by phonon soft modes and surface reconstructions that influence electronic properties.

Contribution

It provides a detailed dynamical analysis of the CDW formation, linking structural transitions and surface effects to electronic structure modifications in $A$V$_{3}$Sb$_{5}$ compounds.

Findings

Structural phase transition from P6/mmm to C2/m symmetry due to phonon soft modes.

Charge density wave results from atom displacement in the low-temperature phase.

Surface reconstruction explains the observed surface modulation and its relation to bulk CDW.

Abstract

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 $A$V$_{3}$Sb$_{5}$ ($A$ = 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 $A$V$_{3}$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 are 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 low-temperature phase. Additionally, using the numerical {\it ab initio} methods, we discuss the charge distribution on the $A$V$_{3}$Sb$_{5}$ surface. We show that the observed experimental %$4\times 1$ stripe-like 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 are discussed. We show that the electronic band structure reconstruction and the accompanying modification of density of states correspond well to the experimental data.