Structural instability and charge modulations in the Kagome superconductor $A$V$_3$Sb$_5$

Recently, both charge density wave (CDW) and superconductivity have been observed in Kagome compounds $A$V$_3$Sb$_5$. However, the nature of CDW that results in many novel charge modulations is still under hot debate. By means of the first-principles calculations, we discover two kinds of CDW states, the trimerized and hexamerized 2$\times$2 phase and dimerized 4$\times$1 phase existing in $A$V$_3$Sb$_5$. Our phonon excitation spectrum and electronic Lindhard function calculations reveal that the most intensive structural instability in $A$V$_3$Sb$_5$ originates from a combined in-plane vibration mode of V atoms through the electron-phonon coupling, rather than the Fermi surface nesting effect. Crucially, a metastable 4$\times$1 phase with V-V dimer pattern and twofold symmetric bowtie shaped charge modulation is revealed in CsV$_3$Sb$_5$, implying that both dimerization and trimerization exist in the V Kagome layers. These results provide essential understanding of CDW instability and new thoughts for the novel charge modulation patterns.