Abundant Lattice Instability in Kagome Metal ScV6Sn6

Kagome materials are emerging platforms for studying charge and spin orders. In this Letter, we have revealed a rich lattice instability in a ${\mathbb{Z}}_{2}$ kagome metal ${\mathrm{ScV}}_{6}{\mathrm{Sn}}_{6}$ by first-principles calculations. Beyond verifying the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}\ifmmode\times\else\texttimes\fi{}3$ charge density wave (CDW) order observed by the recent experiment, we further identified three more possible CDW structures, i.e., $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}\ifmmode\times\else\texttimes\fi{}2$ CDW with $P6/mmm$ symmetry, $2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}2$ CDW with $Immm$ symmetry, and $2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}2$ CDW with $P6/mmm$ symmetry. The former two are more energetically favored than the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}\ifmmode\times\else\texttimes\fi{}3$ phase, while the third one is comparable in energy. These CDW distortions involve mainly out-of-plane motions of Sc and Sn atoms, while V atoms constituting the kagome net are almost unchanged. We attribute the lattice instability to the smallness of Sc atomic radius. In contrast, such instability disappears in its sister compounds $R{\mathrm{V}}_{6}{\mathrm{Sn}}_{6}$ ($R$ is Y, or a rare-earth element), which exhibit quite similar electronic band structures to the Sc compound, because $R$ has a larger atomic radius. Our work indicates that ${\mathrm{ScV}}_{6}{\mathrm{Sn}}_{6}$ might exhibit varied CDW phases in different experimental conditions and provides insights to explore rich charge orders in kagome materials.