Order-by-disorder charge density wave condensation at q = (1/3,1/3,1/3) in kagome metal ScV6Sn6

The recent discovery of a charge density wave order at the wave vector P (1/3, 1/3, 1/3) in the kagome metal ScV6Sn6 has created a mystery because subsequent theoretical and experimental studies show a dominant phonon instability instead at another wave vector H (1/3, 1/3, 1/2). In this paper, I use first-principles total energy calculations to map out the landscape of the structural distortions due to the unstable phonon modes at H, L (1/2, 0, 1/2), and P present in this material. In agreement with previous results, I find that the distortions due to the H instability cause the largest gain in energy relative to the parent structure, followed in order by the L and P instabilities. However, only two distinct structures occur due to this instability, which are separated by 6 meV/f.u. The instability at L results in three distinct structures separated in energy by 5 meV/f.u. In contrast, six different distorted structures are stabilized due to the instability at P, and they all lie within 2 meV/f.u. of each other. Hence, despite a lower-energy gain, the condensation at P could be favorable due to a larger entropy gain associated with the fluctuations within a manifold with larger multiplicity via the order-by-disorder mechanism.