Nature of order-disorder charge-density-wave phase transition in kagome metal RbV3Sb5

Using first-principles density-functional theory calculations and free energy analysis, we demonstrate that for ${\mathrm{RbV}}_{3}{\mathrm{Sb}}_{5}$, the long-range $2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}2$ charge density wave (CDW) is condensed from the disordered $2\ifmmode\times\else\texttimes\fi{}2$ charge orders at ${T}_{\mathrm{CDW}}$, indicating an order-disorder nature of CDW phase transition. It is revealed that the dynamic fluctuations of four degenerate $2\ifmmode\times\else\texttimes\fi{}2$ charge orders exist above ${T}_{\mathrm{CDW}}$, giving rise to a configurational entropy. Our free energy analysis predicts the first-order transition with a release of entropy at ${T}_{\mathrm{CDW}}\phantom{\rule{4pt}{0ex}}\ensuremath{\approx}$ 95 K, consistent with the measured specific heat data showing the presence of a sharp peak across the phase transition. Furthermore, we identify that the CDW fluctuations above ${T}_{\mathrm{CDW}}$ occur through a thermal reaction with the concerted V-V bond breakages and formations of V trimers and hexamers, corroborated by the experimental evidence of strong CDW fluctuations extending to higher than $\ensuremath{\sim}1.7\phantom{\rule{4pt}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{4pt}{0ex}}{T}_{\mathrm{CDW}}$. The present results not only shed light on the nature of the first-order, order-disorder CDW phase transition in ${\mathrm{AV}}_{3}{\mathrm{Sb}}_{5}$ but also have broader implications for understanding the disorder-induced collapse of long-range CDW order in other kagome metals such as ${\mathrm{ScV}}_{6}{\mathrm{Sn}}_{6}$ and FeGe.