Driving mechanism and dynamic fluctuations of charge density waves in the kagome metal <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>ScV</mml:mi><mml:mn>6</mml:mn></mml:msub><mml:msub><mml:mi>Sn</mml:mi><mml:mn>6</mml:mn></mml:msub></mml:mrow></mml:math>

Abstract

In contrast to the ${\mathrm{AV}}_{3}{\mathrm{Sb}}_{5}$ (A = K, Rb, Cs) family exhibiting the ubiquitous $2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}2$ 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 $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ 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 $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}\ifmmode\times\else\texttimes\fi{}2$ and $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}\ifmmode\times\else\texttimes\fi{}3$ 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 $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}\ifmmode\times\else\texttimes\fi{}2$ phase is energetically more stable than $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}\ifmmode\times\else\texttimes\fi{}3$, 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 $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}\ifmmode\times\else\texttimes\fi{}3$ CDW phase transition in ${\mathrm{ScV}}_{6}{\mathrm{Sn}}_{6}$, with broader implications for understanding charge orderings and CDW fluctuations in other kagome metals.

Topics & Concepts