Condensation of preformed charge density waves in kagome metals

Abstract: Charge density wave (CDW) is a spontaneous spatial modulation of electric charges in solids whose general microscopic descriptions are yet to be completed. Layered kagome metals of $A$V$_3$Sb$_5$ ($A$ = K, Rb, Cs) provide a unique chance to realize its emergence intertwined with dimensional effects as well as their special lattice. Here, based on a state-of-the-art molecular dynamics simulation, we uncover that the phase transition to charge ordered states in kagome metals is a condensation process of incoherently preformed CDWs. We demonstrate that charge modulation first preforms on each kagome layer at a well defined temperature but its phase fluctuation proliferates across the entire layers with a $10^5$ times slower frequency than typical phonon vibrations until reaching its freezing temperature. We find that the fluctuation is not random but confined to a limited number of states as a consequence of unavoidable degeneracy in stacking layered charge orders. As the size of interfacial alkali atom increases, the fluctuating phases are shown to counterbalance the condensation of orderings, resulting in a maximized transition temperature for RbV$_3$Sb$_5$. Our results resolve several controversial observations on their CDW formations and highlight a crucial role of interlayer interactions for the charge ordering in kagome metals.