Order-by-disorder charge density wave condensation at $\text{q}=(\frac{1}{3},\frac{1}{3},\frac{1}{3})$ in kagome metal ScV${}_6$Sn${}_6$

Abstract

The recent discovery of a charge density wave order at the wave vector $P$ $(\frac{1}{3},\frac{1}{3},\frac{1}{3})$ in the kagome metal ScV${}_6$Sn${}_6$ has created a mystery because subsequent theoretical and experimental studies show a dominant phonon instability instead at another wave vector $H$ $(\frac{1}{3},\frac{1}{3},\frac{1}{2})$. 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 $H$, $L$ $(\frac{1}{2},0,\frac{1}{2})$, 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 structure 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.

Fix a typo; 6 pages, 2 figures, 2 tables; crystal structure information are given in ancillary files

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• Orbital selective commensurate modulations of the local density of states in ScV6Sn6 probed by nuclear spins
• Pressure suppresses the density wave order in kagome metal LuNb${}_6$Sn${}_6$
• Anomalous Nernst Effect and Its Implications for Time-Reversal Symmetry Breaking in Kagome Metal ScV6Sn6