In contrast to the ${\mathrm{AV}}_3{\mathrm{Sb}}_5$ (A = K, Rb, Cs) family exhibiting the ubiquitous $2\times 2\times 2$ charge density wave (CDW) order, only ${\mathrm{ScV}}_6{\mathrm{Sn}}_6$ in the ${\mathrm{RV}}_6{\mathrm{Sn}}_6$ (R = Sc, Y, La) family displays the unusual CDW with a $\sqrt{3}\times \sqrt{3}$ in-plane ordering and a tripling of the unit cell along the $c$ axis. Here, using first-principles density-functional theory calculations, we show that both the $\sqrt{3}\times \sqrt{3}\times 2$ and $\sqrt{3}\times \sqrt{3}\times 3$ CDW orderings can be driven by a Jahn-Teller-like effect where the Sn atoms residing in the kagome bilayers partially undergo delicately different schemes of interlayer dimerization, accompanied by charge redistribution between such Sn atoms and band-gap opening. Counterintuitively, whereas the $\sqrt{3}\times \sqrt{3}\times 2$ phase is energetically more stable than $\sqrt{3}\times \sqrt{3}\times 3$, the latter is thermodynamically stabilized above the CDW transition temperature $T_{\mathrm{CDW}}$ by its higher configurational entropy contributed by degenerate fluctuating phases, and is kinetically selected below $T_{\mathrm{CDW}}$, as corroborated by experimental observation of the accompanying first-order phase transition. Our findings reveal the order-disorder nature of the $\sqrt{3}\times \sqrt{3}\times 3$ CDW phase transition in ${\mathrm{ScV}}_6{\mathrm{Sn}}_6$, with broader implications for understanding charge orderings and CDW fluctuations in other kagome metals.

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• Charge density waves
• First-principles calculations
• Phase transitions